text:
Mallorca Travel Guide
Spain #4 in Best Beaches in Spain
Courtesy of Westend61/Getty Images
Getting Around Mallorca
The best way to get around Mallorca is by car. Having your own set of wheels gives you the most freedom to explore the island on your time. Buses are an option, too, but service is limited, especially on weekends. In towns like Palma, there are plenty of taxis, but these are more of an option for inter-city trips rather than for island treks. The same goes for walking and biking. Although there are some lovely pedestrian areas in Palma, Alcúdia and other towns, not to mention beaches, the island is too large to explore on foot or bicycle alone.
To get to Mallorca from the United States, you have several options. You can fly to a mainland Spanish city, such as Madrid or Valencia, and then catch a connecting flight from a carrier like Iberia, Vueling or Air Europa to Palma de Mallorca Airport (PMI) – also known as Son Sant Joan Mallorca Airport – located just southeast of Palma. Alternatively, you can take a ferry (which can accommodate cars) to Palma from a variety of neighboring destinations, including Barcelona, Ibiza or Valencia.
A car will allow you the most freedom to explore Mallorca on your own terms. That said, when you're touring various cities and towns – especially Palma – you should leave the car parked and get around on foot since streets in these historic places are often narrow. You'll find car rental companies, such as Avis, Hertz and Europcar, at the Palma airport. If you're looking for a price break, however, you might check out the local companies, such as Sixt Rent a Car or Centauro Rent a Car, as they sometimes offer better deals. Also, buy a current map in a bookshop or petrol station, as the maps given by rental car companies are often out of date. And keep in mind that using your cellphone while driving is illegal here. Also, to rent a car in Mallorca, you'll need to apply for an international driving permit, which you can obtain here.
Centauro Rent a Car
Mallorca's collection of buses connect most of the island, but they run on limited schedules, especially on the weekends. You can purchase bus tickets on the bus or pay 3 euros (less than $3.50) for an Intermodal Card, a rechargeable card convenient for multiple trips, at the Palma Intermodal Station (the main station in Palma). Prices for bus tickets vary depending on the departure point and the destination.
Consorci de Transports de Mallorca (TIB)
Mallorca's metered taxis are most helpful for travel around Palma – or travel to and from the airport. These taxis, usually cream and black in color, frequent many of the tourist attractions, resorts and hotels. To give you an idea on price, a 25-minute trip, during the hours of 6 a.m. to 10 p.m., from Castell de Bellver and the Palma Cathedral will likely run you around 10 or 12 euros (about $11 to $13.50). Rates increase between the hours of 10 p.m. to 6 a.m. and all day on public holidays.
Mallorca Taxi
Taxi PMI
On Foot Mallorca's large and small towns are best explored on foot, as are the trails of Serra de Tramuntana and many of the gorgeous shorelines. But to traverse the island, you'll need to rely on another mode of transport.
Bike Like many cities, Palma too is becoming increasingly more bike-friendly. Visitors who have traveled by the city's public transportation can pick up rental bikes for free at the Intermodal Station information point in the Placa d'Espanya, though they'll have to return them by the end of the day. From November to May, travelers can pick up and drop off bikes Monday through Friday, from 7 a.m. to 8 p.m. and on Saturday, from 9 a.m. to 6 p.m. From June to October, travelers can drop off bikes until 8 p.m. on Saturday and from 9 a.m. to 8 p.m. on Sunday.
Explore More of Mallorca
Previous: When to visit
Next: Neighborhoods
#1 in Best Places to Visit in Spain
#3 in Best Cheap European Vacations
#2 in Best Beaches in Spain


text:
\section{Introduction}
\label{sec_intro}

The physical observables of gauge theories are associated with
gauge-invariant quantities, which are therefore of utmost
interest. However in most of the analytical or semi-analytical
approaches, the determination of the expectation values of these
gauge-invariant quantities rely on understanding also the
gauge-dependent sector of the theory.  This is one of the reasons
why so much effort has been devoted to understand the properties of
correlation functions in Yang Mills theories in the past.

Several techniques are used to study these quantities. From the
analytic side, standard perturbation theory (that make use of the
Faddeev-Popov construction) is the most efficient tool to access the
ultraviolet regime of the theory, but fails at momenta of the order of
1~GeV. Indeed, the effective coupling (which is the expansion
parameter of perturbation theory) is large in this regime. The
standard perturbation theory even predicts that the coupling constant
diverges at the so-called infrared (IR) Landau pole.  For the
low-energy regime, the preferred analytical techniques are
nonperturbative renormalization-group and Schwinger-Dyson equation
methods \cite{vonSmekal97,Alkofer00,Zwanziger01,Fischer03,Bloch03,Pawlowski:2003hq,Fischer:2004uk,Aguilar04,Boucaud06,Aguilar07,Aguilar08,Boucaud08,Fischer08,RodriguezQuintero10,Huber:2012kd}.
These rely on a set of exact equations that are truncated, by
making some ansatz on a sector of the theory.

Another technique that has been used is lattice simulations that have played a central
role in our understanding of the correlation functions, in particular
in the Landau gauge which is rather easy to implement in
simulations. The extensive numerical work that has been performed in
the past decades
\cite{Cucchieri_08b,Cucchieri_08c,Cucchieri09,Bogolubsky09,Dudal10},
in conjunction with various semi-analytical techniques including various SD studies,
  allowed to settle the controversy between two possible solutions of
  Schwinger-Dyson equations.  The
  so-called scaling solution corresponds to a gluon propagator that
  tend to zero at low momentum and a ghost dressing function (the
  propagator multiplied by the momentum squared) that diverges in this
  limit
  \cite{vonSmekal97,Alkofer00,Zwanziger01,Fischer03,Bloch03,Fischer08}. The so-called massive or decoupling
  solution gives a finite gluon propagator and a regular ghost
  dressing function at low momentum
  \cite{Bloch03,Aguilar04,Boucaud06,Aguilar07,Aguilar08,Boucaud08,RodriguezQuintero10,Huber:2012kd}. Lattice
  simulations clearly favored the second option in dimensions higher
  than two and the first one in the two-dimensional case
  \cite{Cucchieri_08c,Maas_07}.

In the past years, two of us have developed a new approach to access
the infrared behavior of the correlation functions. It relies on the
fact that, as is well known since the work of Gribov \cite{Gribov77}, the
Faddeev-Popov construction which is at the heart of most of the
analytical approaches, is not fully justified \footnote{Another approach to
study the impact of Gribov copies in the infrared sector of Yang-Mills
theory has been followed for many years, mainly by Zwanziger \cite{Zwanziger89,Zwanziger92,Zwanziger01,Dudal08}. Different
approximations performed in that scheme gave propagators compatible
with both massive and scaling scenarios.}. This is due to the fact
that this procedure does not completely fix the gauge. This so-called
Gribov ambiguity is however known to be unimportant in the high
momentum regime, and is only susceptible of modifying the infrared
properties. The idea pushed forward
in \cite{Tissier:2010ts,Tissier:2011ey} consists in modeling the
influence of the Gribov copies by adding a mass term for the gluons to
the usual Faddeev-Popov action (this leads to the Curci-Ferrari model
in the Landau gauge \cite{Curci76}). This idea was made more precise
in \cite{Serreau:2012cg} where a new Landau gauge-fixing was proposed,
which takes into account the Gribov ambiguity from first principles
and which leads, as far as perturbation theory is concerned, to the
same results as those obtained with the massive extension considered
in \cite{Tissier:2010ts,Tissier:2011ey}.
A one-loop calculation for the
gluon propagator and the ghost dressing function was performed that compared very well
with lattice simulations in $d=4$, with a
maximum error of $\sim$ 10$\%$, both for $SU(2)$ and $SU(3)$.

It may look surprising that the infrared (often called
nonperturbative) regime of the theory can be reproduced to that level
of precision with a modest one-loop calculation. Our interpretation of
this fact is that the mass regularizes the theory in the infrared. For
example, we found renormalization schemes were the Landau pole
disappears. Moreover we made in \cite{Tissier:2011ey} an estimate  showing that,
in the infrared regime, the loop corrections to the propagators are
suppressed by powers of the external momenta (in particular, the 2-loop
corrections are roughly an order of magnitude smaller than the one-loop
contributions), which indicates that the perturbation theory {\it in presence
of a mass term} may be under control.

These encouraging results naturally lead us to consider other correlation
  functions. In consequence, in this article, we generalize our
  previous work to 3-point correlation functions. These functions are
  extremely interesting for many reasons:
  \begin{itemize}
   \item They
  have been calculated in lattice simulations
  \cite{Parrinello:1994wd,Alles:1996ka,Boucaud:1998bq,Cucchieri:2004sq,Ilgenfritz:2006gp,Cucchieri:2006tf,Cucchieri08} and
  this offers concrete data to compare with.
  \item Once the parameters of the model have been fixed for the 2-point
  functions, the calculation of 3-point functions becomes a {\it pure
    prediction} without any parameter to adjust. This then becomes a
  very challenging test of the scheme proposed in \cite{Tissier:2010ts,Tissier:2011ey}.
  \item These functions
  are much richer than 2-point functions. In particular, instead of
  depending on a single momentum, they depend on three independent
  momenta squared. Moreover, they include various tensorial structures
  that could make their study even richer (even if these structures
  have not yet been studied  by lattice simulations).
  \end{itemize}

  In the past few years, several works aimed at describing these
  3-point correlation functions in the infrared regime, both with
  lattice simulations
  \cite{Parrinello:1994wd,Alles:1996ka,Boucaud:1998bq,Cucchieri:2004sq,Ilgenfritz:2006gp,Cucchieri:2006tf,Cucchieri08}
  and with semi-analytical methods
  \cite{RodriguezQuintero:2011au,Dudal:2012zx,Huber:2012kd,Aguilar:2013xqa}.
  However, the complexity of the standard semi-analytical methods (as
  Schwinger-Dyson equations or Non-Perturbative Renormalization Group
  equations) have delayed their study. In particular very few results
  on the ghost-antighost-gluon vertex are available
  \cite{RodriguezQuintero:2011au,Dudal:2012zx,Huber:2012kd,Aguilar:2013xqa}
  and essentially only models for the 3-gluon vertex have been
  proposed (see, for example, \cite{Huber:2012kd}).  On the contrary,
  the scheme developed in \cite{Tissier:2010ts,Tissier:2011ey} and
  that we follow here relies on a standard and simple 1-loop
  calculation.  Our main aim in this article is to show that we obtain
  3-point vertex functions which reproduce very well the lattice data
  for a relatively small computational effort. Note that Gracey
  \cite{Gracey:2012wf} studied the power corrections to the
  perturbative ultraviolet behaviour both in the model considered here
  and in the refined Gribov-Zwanziger model. These corrections are
  different so that lattice simulations with good precision would
  allow to make a definite difference between both methods.

  The outline of the article is the following. In
  Section~\ref{sec_oneloop}, we describe in more details the model and
  present our one-loop calculation. We then describe in
  Section~\ref{sec_renorm} the renormalization schemes that we
  implemented and finally describe our results and compare them to the
  lattice data available for the 3-point correlation functions in
  Section~\ref{sec_res}. We give our conclusions in
  Section~\ref{sec_conc}.

\section{One-loop calculation}
\label{sec_oneloop}

Our starting point is the Curci-Ferrari action in the Landau gauge,
written in Euclidean space, that reads:
\begin{equation}
  \label{eq_action}
  \begin{split}
      S=\int d^dx&\left[\frac 14 F_{\mu\nu}^aF_{\mu\nu}^a+ih^a\partial_\mu
    A_\mu^a +\partial_\mu\overline c^a(D_\mu c)^a\right.\\
&\qquad\left.+\frac 12 m_0^2 (A_\mu^a)^2\right]
  \end{split}
\end{equation}
where the covariant derivative applied to a field $X$ in the adjoint
representation reads $(D_\mu X)^a=\partial_ \mu X^a+g_0f^{abc}A_\mu^b
X^c$, $g_0$ is the bare coupling constant, $f^{abc}$ are the structure
constants of the gauge group and
$F_{\mu\nu}^a=\partial_\mu A_\nu^a -\partial_\nu A_\mu^a+ g_0
f^{abc}A_\mu^a A_\nu ^b$ is the field strength. Apart for the bare
mass $m_0$ of the gluons, the action is that of the Yang-Mills theory
with the Faddeev-Popov action in the Landau gauge. All our
analytical calculations will be done for a generic $SU(N)$ gauge group.

The Feynman rules are the standard ones, except for the free propagator of
the gluon which reads:
\begin{equation}
  \label{eq_propag_AA}
  \langle
  A_\mu^aA_\nu^b\rangle_0(p)=\delta^{ab} P^\perp_{\mu\nu}(p)\frac 1{p^2+m_0^2}
\end{equation}
where we introduced the transverse projector (and, for later use, the
longitudinal one):
\begin{align}
  P^\perp_{\mu\nu}(p)&=\delta_{\mu\nu}-\frac{p_\mu p_\nu}{p^2}\\
  P^\parallel_{\mu\nu}(p)&=\frac{p_\mu p_\nu}{p^2}
\end{align}

Instead of computing the correlation functions, we compute as
usual the vertex functions which are obtained by considering only the
one-particle irreducible (1PI) diagrams. We parametrize the two-point vertex functions in terms of three scalar
functions:
\begin{align}
&
\Gamma^{(2)}_{A_\mu^aA_\nu^b}(p)=\delta^{ab}\big(\Gamma^\perp(p)P^\perp_{\mu\nu}
+\Gamma^\parallel(p)P^\parallel_{\mu\nu}\big)\\
& \Gamma^{(2)}_{c^a \overline c^b}(p)=\delta^{ab} \frac{p^2}{J(p)}
\end{align}
The full propagators for the gluon and ghost then read:
\begin{align}
\langle  A_\mu^aA_\nu^b\rangle(p)=\delta^{ab} \frac{P^\perp_{\mu\nu}(p)}{\Gamma^\perp(p)}  \\
\langle  c^a\overline c^b\rangle(p)=\delta^{ab} \frac{J(p)}{p^2 }
\end{align}
The function $J$ is the so-called dressing functions. The 1-loop
expressions for $\Gamma^\perp$ and $J$ were computed in
\cite{Tissier:2010ts,Tissier:2011ey}. The longitudinal part of the gluon two-point
function is not directly accessible in lattice simulations and was
therefore not considered in the past. It proved however interesting to
compute it because it appears in some Ward identities that we used to
check the consistency of our results. The 1-loop expressions for
these three functions are given in the supplemental material
\cite{supplemental}.

\subsection{Ghost-antighost-gluon vertex}

The one-loop calculation for the
ghost-antighost-gluon vertex function requires computing the two
Feynman diagrams showed in Fig.~\ref{fig_diagccbA}.
\begin{figure}[tbp]
  \centering
  \includegraphics[width=.4\linewidth]{diagcbcA1.pdf}\hfill
  \includegraphics[width=.4\linewidth]{diagcbcA2.pdf}
  \caption{One-loop Feynman diagrams for the ghost-antighost-gluon
    vertex.}
  \label{fig_diagccbA}
\end{figure}
The tensorial structure is rather simple. At one loop, the vertex is
proportional to $f^{abc}$ where $a$, $b$ and $c$ are respectively the
color indices of the ghost, antighost and gluon external legs.
We will consider here and below only this color structure. This is
an exact property for $SU(2)$, and for general $SU(N)$, it remains true at two loops and also in the large $N$
limit. However, this is only an approximation for $SU(3)$
(currently used in the literature \cite{BallChiu}).
The Lorentz index $\mu$ of the gluon external leg can be carried by one of
the external momenta. Because of the momentum conservation, there are
actually only two scalar components. Following Ball and Chiu
\cite{BallChiu}, it is however convenient to express the vertex in
terms of a rank two tensor $\Gamma_{\nu\mu}$ such that:
\begin{equation}
  \label{eq_vertex_cbcA_def}
  \Gamma^{(3)}_{c^a\overline c^b A_\mu^c}(p,k,r)=-i g_0 f^{abc} k_{\nu}\Gamma_{\nu\mu}(p,k,r)
\end{equation}
with
\begin{equation}
\label{eq_vertex_KbcA_def}
  \begin{split}
  \Gamma_{\nu\mu}(p,k,r)&=\delta_{\mu\nu}a(r^2,k^2,p^2)\\
&-r_{\nu}p_{\mu}b(r^2,k^2,p^2)  +k_{\nu}r_{\mu}c(r^2,k^2,p^2)\\
&+r_{\nu}k_{\mu}d(r^2,k^2,p^2)+k_{\nu}k_{\mu}e(r^2,k^2,p^2)
  \end{split}
\end{equation}
Note that lattice simulations access the vertex function only through the
correlation function, {\it i.e.} the vertex function with external legs
contracted with the full propagators. Since the gluon propagator is transverse,
the function $c$ is not accessible to lattice simulations.
In fact, the lattice simulations on the
ghost-antighost-gluon correlation function that have actually been performed \cite{Cucchieri08} are presented in terms of a scalar function
which is obtained by contracting the external gluon leg with the transverse
propagator and with the bare ghost-antighost-gluon vertex, normalized by the
same expression at tree level:
\begin{equation}
\label{GccbA}
 G^{c\overline c A}(p,k,r)=\frac{k_\nu P^\perp_{\mu\nu}(r)k_\rho
\Gamma_{\rho\mu}(p,k,r)} {k_\nu P^\perp_{\mu\nu}(r)k_\mu }
\end{equation}
A simple
calculation shows that this correlation function depends
on a unique linear combination of the scalar functions defined in (\ref{eq_vertex_KbcA_def}):
\begin{equation}
a+k\cdot r (b+d)+k^2 e
\end{equation}
with the functions $a,b,d$ and $e$ evaluated at $(r^2,k^2,p^2)$. Although this is the only available
numerical data, it is interesting to
compute the 5 scalar functions $a,b,c,d$ and $e$ because this gives an
internal check of the validity of the calculation, see below. Moreover, future lattice
studies may lead to a determination of the various tensorial components independently.

In our calculations, we decomposed each diagram on the tensorial
structure of Eq.~(\ref{eq_vertex_KbcA_def}), following the ideas of
\cite{Passarino78}. We can then deduce the contribution of a diagram to each of
the scalar functions $a$ to $e$ in terms of
integrals. To do so, it is convenient to rewrite the product of a
massive propagator and of a massless propagator as:
\begin{equation}
  \label{eq_urko}
\frac 1{p^2(p^2+m^2)}=\frac 1 {m^2}\left(\frac{1}{p^2}-\frac{1}{p^2+m^2}\right)
\end{equation}
We can thus express the scalar functions in terms of a few simple
integrals. By using Feynman parameters, we can perform the momentum
integral and obtain expressions with at most one integral over a
Feynman parameter that cannot be performed analytically for generic
momentum configurations. The expression are lengthy and not
particularly instructive. We give them in the supplemental material
\cite{supplemental}. The calculation simplifies in the case  of one
vanishing external momentum. In particular, when the ghost or antighost momentum
vanishes, the vertex function have no loop corrections \cite{Taylor71}. For vanishing gluon
momentum, the vertex is non-trivial and we find, in $d=4-\epsilon$:
\begin{equation}
  \label{eq_1loopexceptional}
  \begin{split}
  \Gamma_{\mu\nu}(p,-p,&0)=\delta_{\mu\nu}\bigg\{1+\frac{g_0^2
N}{128 \pi ^2}\bigg[9/2+s\\&+5s^{-1}-(7 s^{-1}+5s^{-2}) \log (s+1)\\&-(s-1) s
\log \left(s^{-1}+1\right)\bigg]\bigg\}
  \end{split}
\end{equation}
were we introduced $s=p^2/m^2$. Note that the previous (bare) vertex is finite
due to the non-renormalization theorem to be discussed below. The equivalent expression in $d=3$ reads:
\begin{equation}
  \label{eq_1loopexceptional_3d}
  \begin{split}
  \Gamma_{\mu\nu}(p,-p,&0)=
\delta_{\mu\nu}\bigg\{1+\frac{g_0^2
N}{384 \pi m s}\bigg[2(6s^2\\&-5s-21)-3\pi\sqrt
s(2s^2-s+288)\\&+6s^{-1/2}(2s^3-s^2-68s+7)\arctan(\sqrt{s})\bigg]\bigg\}
  \end{split}
\end{equation}

\subsection{Three gluon vertex}

The one-loop calculation for the three-gluon correlation
function requires computing the three Feynman diagrams showed in
Fig.~\ref{fig_diagAAA}.
\begin{figure}[bp]
  \centering
  \includegraphics[width=.3\linewidth]{diagAAA1.pdf}\hfill
  \includegraphics[width=.4\linewidth]{diagAAA2.pdf}
  \includegraphics[width=.4\linewidth]{diagAAA3.pdf}
  \caption{One-loop Feynman diagrams for the 3-gluon vertex.}
  \label{fig_diagAAA}
\end{figure}
Again, the color structure is rather simple at one loop, being
proportional to $f^{abc}$.  As for the ghost-antighost-gluon vertex, we will
ignore the possibility of more involved color structures (that are absent
at two-loops order, for $SU(2)$ gauge group and also in the large $N$ limit of $SU(N)$ gauge groups)
Accordingly, we define:
$$\Gamma_{A^a_\mu A^b_\nu A^c_\rho}^{(3)}(p,k,r)=-ig_0f^{abc}\Gamma_{\mu\nu\rho}(p,k,r).$$
The Lorentz structure is richer  than in the previous case since there are now three Lorentz
indices. We have used the decomposition of Ball and Chiu
\cite{BallChiu} to extract six scalar functions:
\begin{widetext}
\begin{equation}
  \begin{split}
\Gamma_{\mu\nu\rho}(p,k,r)&=A(p^2,k^2,r^2)\delta_{\mu\nu}(p-k)_\rho+
B(p^2,k^2,r^2)\delta_{\mu\nu}(p+k)_\rho
-C(p^2,k^2,r^2)(\delta_{\mu\nu}p.k-p_{\nu}k_{\mu})(p-k)_\rho\\
&+\frac{1}{3}S(p^2,k^2,r^2)(p_{\rho}k_{\mu}r_{\nu}+p_{\nu}k_{\rho}r_{\mu})+
F(p^2,k^2,r^2)(\delta_{\mu\nu}p.k-p_{\nu}k_{\mu})(p_{\rho}k.r-k_{\rho}p.r)\\
&+H(p^2,k^2,r^2)\left[-\delta_{\mu\nu}(p_{\rho}k.r-k_{\rho}p.r)+\frac{1}{3}(p_{
\rho}k_{\mu}r_{\nu}-p_{\nu}k_{\rho}r_{\mu})\right]+\text{cyclic permutations}
  \end{split}
\end{equation}
The scalar functions have the following symmetry properties: $A$, $C$
and $F$ are symmetric under permutation of the first two arguments;
$B$ is antisymmetric under permutation of the first two arguments; $H$
is completely symmetric and $S$ is completely antisymmetric. As for
the ghost-antighost-gluon vertex, only a subset of these functions are
measurable in lattice
simulations; when the external legs are contracted with the gluon
propagators (which is transverse), the functions $B$ and $S$
disappear. In lattice simulations \cite{Cucchieri08}, the quantity which
  has been considered is a scalar function obtained by contracting
the external legs of the vertex with transverse propagators and the
tree-level momentum structure of the 3-gluon vertex, normalized to the
same expression at the bare level:
\begin{equation}
\label{GAAA}
G^{AAA}(p,k,r)=\frac{[(r-k)_\gamma\delta_{\alpha\beta}+\text{cyclic
permutations}] P^\perp_{\alpha\mu}(p)P^\perp_{ \beta\nu }
(k)P^\perp_ { \gamma\rho }
(r)\Gamma_{\mu\nu\rho}(p,k,r)}{[(r-k)_\gamma\delta_{\alpha\beta}
+\text{cyclic
permutations}]
P^\perp_{\alpha\mu}(p)P^\perp_{ \beta\nu } (k)P^\perp_ { \gamma\rho }
(r)[(r-k)_\rho\delta_{\mu\nu}
+\text{cyclic
permutations}]}
\end{equation}

The scalar functions $A$, $B$, $C$, $S$, $F$ and $H$ are computed in
the same way as described above. Our expression for generic momenta
involve at most one integral over a Feynman parameter and cannot be
expressed in terms of elementary functions. They are given
in the supplemental material \cite{supplemental}. When one momentum
vanishes, the integral over the Feynman parameter can be performed
analytically which simplifies considerably the results. For $d=4-\epsilon$:
\begin{equation}
\label{eq_3gluonexceptional}
\begin{split}
  \Gamma_{\mu\nu\rho}(p,0,-p)=& \bigg\{ 1 -\frac{N g_0^2}{768\pi^2 }\bigg[-\frac
  {136}{\epsilon}(1-\epsilon \log \bar m)+\frac 13(36 s^{-2}-594
  s^{-1}+319+6s)+(3s^2-2)\log  s\\
  &-4 s^{-3}(1+s)^3(s^2-9s+3)\log(1+s)\\
  &+\frac{(4+s)^{3/2}}{s^{3/2}}\left(24-30s+s^2\right) \log\left(\frac{\sqrt{4+s}+\sqrt
      s}{\sqrt{4+s}-\sqrt s}\right)\bigg]\bigg\} (p_\mu\delta_{\nu\rho}+p_\rho\delta_{\mu\nu})\\
  &- \bigg\{ 2 +\frac{N g_0^2}{384\pi^2 }\bigg[-\frac
  {136}{\epsilon}(1-\epsilon \log \bar m)+\frac 13(18 s^{-2}-321
  s^{-1}-97+24s)+(s-1)(s^2-2s-2)\log  s\\
  &-2s^{-3}(1+s)^2(s-1)(s^3-7s^2+7s-3)\log(1+s)\\
  &+\frac{\sqrt{4+s}}{s^{3/2}}\left(48+16
    s+22 s^2-11 s^3+s^4 \right) \log\left(\frac{\sqrt{4+s}+\sqrt
      s}{\sqrt{4+s}-\sqrt s}\right)\bigg]\bigg\} p_\nu\delta_{\mu\rho} \\
  & -\frac{N g_0^2}{384 \pi^2 m^2}\bigg[(-36 s^{-3}+278
  s^{-2}-74 s^{-1}-10)-s^2\log  s\\
  &+ s^{-3}(1+s)^2(36s^{-1}-44-4s-12s^2+2s^3)\log(1+s)\\
  &+\sqrt{s(4+s)}s^{-3}(-144s^{-1}+80+4s+10s^2-s^3) \log\left(\frac{\sqrt{4+s}+\sqrt
      s}{\sqrt{4+s}-\sqrt s}\right)\bigg] p_\mu p_\nu p_\rho
\end{split}
\end{equation}
where $\bar m^2=m^2e^\gamma/(4\pi)$ with $\gamma$ the Euler
constant. The divergent term $\propto 1/\epsilon$ disappears
once the renormalized vertex functions are expressed in
terms of the renormalized parameters, see Sect.~\ref{sec_renorm}.

In $d=3$, the same quantity reads:
\begin{equation}
\label{eq_3gluonexceptional_3d}
\begin{split}
  \Gamma_{\mu\nu\rho}(p,0,-p)=&\bigg\{1 -\frac{N g_0^2}{128\pi m\sqrt s}\bigg[
  \frac\pi 2 (2-3s^2)+\frac{2}{3s^{3/2}}(3s^3+23s^2+56s-15)\\&
  -s^{-1}(4+s)(16-18s+s^2)\arctan(\sqrt s/2)
  +2s^{-2}(s-5)(s+1)^2\arctan(\sqrt s)\bigg]\bigg\} (p_\mu\delta_{\nu\rho}+p_\rho\delta_{\mu\nu}) \\
  & - \bigg\{ 2 +\frac{N g_0^2}{128\pi m\sqrt s}\bigg[
  \pi (-s^3+3s^2-1)+\frac{2}{3s^{3/2}}(15s^3-51s^2+53s-15)\\&+
  2(-s^3+6s^2+2s-16-32 s^{-1})\arctan(\sqrt s/2)
  +2(2 s^3 - 9 s^2 - 5)(1-s^{-2})\arctan(\sqrt s)\bigg]\bigg\} p_\nu\delta_{\mu\rho}\\
& -\frac{N g_0^2}{128\pi m^3 \sqrt s}\bigg[
  \pi  (s^{-1}+s^2)+\frac{2}{3s^{5/2}}(-21s^3+5s^2-139s+75)\\& +2 s^{-2}(s^4-5s^3-16s^2-40s+96)\arctan(\sqrt s/2) \\&
  -2s^{-3}(s+1)(2s^4-7s^3-9s^2-15s+25)\arctan(\sqrt s)\bigg] p_\mu p_\nu p_\rho
\end{split}
\end{equation}
\end{widetext}

\subsection{Checks}
We present in this section the different checks that can be performed
on our one-loop expressions.  First, as explained in the Appendix, the
vertex functions fulfill the following Slavnov-Taylor identity:
\begin{equation}
  \label{eq_BRST_constraint}
  \begin{split}
&[\Gamma^\perp(p)P^\perp_{\mu\rho}(p)+\Gamma^\parallel(p)P^\parallel_{\mu\rho}
(p)]\Gamma_{\mu\nu}(r,p,k)\\
&-[\Gamma^\perp(k)P^\perp_{\mu\nu}(k)+\Gamma^\parallel(k)P^\parallel_{\mu\nu}(k)
]\Gamma_{\mu\rho}(r,k,p)\\
&\qquad=r_\mu J^{-1}(r)\Gamma_{\rho\nu\mu}(p,k,r)
  \end{split}
\end{equation}
We have verified analytically that our one-loop expressions satisfy
this relation. This gives a nontrivial check for most of the scalar
functions, except however $F$ and $H$ which are associated with
transverse momentum structures and that do not appear in
Eq.~(\ref{eq_BRST_constraint}).

Second, we have compared our expressions in the limit of vanishing
mass with those of \cite{Davydychev}. Because we used the relation
(\ref{eq_urko}), there appear in our expressions terms in $1/m$ that
would naively diverge in the limit of small mass. We can check
explicitly that the limit is actually regular but the analytic
comparison is cumbersome. We have made instead a numerical comparison
of our expressions and those of \cite{Davydychev} for 50 momentum
configurations, taking the mass of the gluon much smaller than the
momenta. We have mainly considered the scalar functions appearing in
the ghost-antighost-gluon vertex (\ref{eq_vertex_KbcA_def}) and the
functions $F$ and $H$ that, as discussed above, are not constrained by
Eq.~(\ref{eq_BRST_constraint}). In all cases, our expressions in the
massless limit agree with \cite{Davydychev} at the numerical precision
level.

Finally we have considered the following equality, which is derived in the
Appendix.
\begin{equation}
  \label{eq_non_renorm}
  \begin{split}
  \widetilde\Gamma_\mu(p,k,r)+
\widetilde\Gamma_\mu(k,p,r)-&\frac{r_\mu}{r^2}\bigg[
\frac{p_\nu}{p^2}\widetilde\Gamma_\nu(k,r,p)\\&+\frac{k_\nu}{k^2}
\widetilde\Gamma_\nu(p,r,k)\bigg]=    0
  \end{split}
\end{equation}
where
\begin{equation}
  \label{eq_gammatilde}
  \widetilde \Gamma_\mu(p,k,r)=k_\nu \Gamma_{\nu\mu}(p,k,r) r^2 J^{-1}(r)
\end{equation}
To our knowledge this relation have not been derived before.
We have checked numerically for 50 momentum configurations that the previous identity is indeed satisfied, with no
constraint on the mass.

\subsection{Infrared behavior}

It is instructive to discuss the behavior of the different vertex
functions when all the external momenta are much smaller than the mass
scale. A straightforward analysis shows that, in this limit, the
leading contribution comes from the diagram with as much ghost
propagators as possible. Multiplying all momenta by a common
coefficient $\kappa$, we obtain the following behaviors, valid in
arbitrary dimension:
\begin{equation}
\label{compIR}
 \begin{split}
  \Gamma_{\mu\nu}(\{\kappa p_i\})-\delta_{\mu\nu}&\sim \kappa^{d-2},\\
  \Gamma_{\mu\nu\rho}(\{\kappa p_i\})&\sim \kappa^{d-4}.
 \end{split}
\end{equation}
As a consequence of these behavior, $G^{AAA}$ diverges as
$\log\kappa$ in $d=4$ and diverges as $1/\kappa$ in $d=3$ when $\kappa
\to 0$.

\section{Renormalization and Renormalization Group}
\label{sec_renorm}

In this section, we describe the renormalization schemes that we implemented
and explain how the renormalization-group ideas are implemented.
As we explain below, some care must be taken when comparing the (bare) lattice data with the
renormalized analytical results.

\subsection{Renormalization and schemes}
As usual, the
divergences appearing in the one-loop expressions can be absorbed
into a redefinition of the coupling constant, mass and fields. In $d=3$ no ultraviolet divergences are
present but a (finite) renormalization is done anyway in order to be able to exploit renormalization-group
methods and improve perturbation theory. We
define the renormalized quantities as:
\begin{align}
 A_0^{a\,\mu}= \sqrt{Z_A} A^{a\,\mu},&\hspace{.5cm}
 c_0^{a}= \sqrt{Z_c} c^{a},\hspace{.5cm}
 \bar c_0^{a}= \sqrt{Z_c} \bar c^{a},\hspace{.5cm} \nonumber\\
g_0&= Z_g g \hspace{.5cm} m_0^2= Z_{m^2} m^2
\end{align}
From now on, except when explicitly stated, all quantities are the renormalized ones.
The relations between bare (with subindices ``0'') and renormalized vertices are the following:
\begin{align}
\label{renormvertices}
 \Gamma^{(2)}_{A_\mu^aA_\nu^b}(p)&=Z_A \Gamma^{(2)}_{A_\mu^aA_\nu^b,0}(p) \nonumber\\
 \Gamma^{(2)}_{c^a \overline c^b}(p)&=Z_c  \Gamma^{(2)}_{c^a \overline c^b,0}(p) \nonumber\\
 \Gamma^{(3)}_{c^a \overline c^b A_\mu^c}(p,r)&=Z_c \sqrt{Z_A} \Gamma^{(3)}_{c^a \overline c^b A_\mu^c,0}(p,r)\nonumber\\
 \Gamma^{(3)}_{A_\mu^aA_\nu^bA_\rho^c}(p,r)&=Z_A^{3/2} \Gamma^{(3)}_{A_\mu^aA_\nu^bA_\rho^c,0}(p,r)
 \end{align}

We have used two renormalization schemes to fix the renormalization
factors, that were already presented in \cite{Tissier:2011ey}. The
vanishing-momentum (VM) scheme is characterized by
\begin{align}
\label{eq_def_vanishing}
& \Gamma^\perp(p=\mu)=m^2+\mu^2, \hspace{.4cm}J(p=\mu)=1\nonumber\\
&\Gamma^\perp(p=0)=m^2.
\end{align}
The infrared safe scheme (IS) relies on a non-renormalization theorem
for the mass \cite{Dudal02,Wschebor07,Tissier08} (this
non-renormalization theorem was conjectured is \cite{Gracey:2002yt}),
which is imposed here for the finite part of the renormalization
parameters. It is defined by:
\begin{align}
\label{rencond}
&\Gamma^\perp(p=\mu)=m^2+\mu^2, \hspace{.4cm} J(p=\mu)=1,\nonumber\\
&Z_{m^2} Z_A Z_c=1.
\end{align}
In both cases, we use the Taylor scheme to fix the renormalization
factor of the coupling constant. This leads to:
\begin{equation}
  \label{eq_taylor}
  Z_g\sqrt{Z_A} Z_c=1
\end{equation}
The explicit expressions for the different renormalization factors are given in
\cite{Tissier:2011ey}.

It is important to relate the objects observed on lattice simulations $G_0^{c\overline c A}$ and $G_0^{AAA}$
given by Eqs.~(\ref{GccbA}) and (\ref{GAAA}) to the renormalized vertices. The quantities that are used
on the lattice are bare vertices without renormalization factors. When expressed in terms of the renormalized
vertices as in Eq.~(\ref{renormvertices}), we obtain:
\begin{align}
\label{renorm3point}
  G_0^{c\overline c A}(p,k,r)&= G^{c\overline c A}(p,k,r)\nonumber\\
  G_0^{AAA}(p,k,r)&=\frac{Z_c}{Z_A} G^{AAA}(p,k,r)
 \end{align}
where the renormalized expressions correspond to those written in Eqs.~(\ref{GccbA}) and (\ref{GAAA}) but
with the corresponding renormalized vertices instead of the bare ones. In order to arrive to this result
we exploited the Taylor's non-renormalization theorem (\ref{eq_taylor}). Of course, the lattice results are regularized
and accordingly the factor $Z_c/Z_A$ is finite but it is necessary to include it when comparing our renormalized results
to those coming from lattice simulations.

\subsection{Renormalization Group}
Once the correlation functions for the renormalized field are expressed in
terms of the renormalized coupling constant and renormalized mass, we get
finite expressions both in $d=3$ and in $d=4$. The direct comparison of these expressions with the lattice
results was not completely satisfactory at energies of a few GeV. This is to
be attributed to large loop corrections (in $d=4$ large logarithms $\propto \log(p/\mu)$)
and we therefore had
to use a renormalization-group improvement of our one-loop expressions. To do
so, we introduce the $\beta$ function and anomalous dimensions of the fields as:
\begin{align}
\beta_g(g,m^2)&=\mu\frac{dg}{d\mu}\Big|_{g_0, m^2_0},\\
\beta_{m^2}(g,m^2)&=\mu\frac{dm^2}{d\mu}\Big|_{g_0, m^2_0},\\
\gamma_A(g,m^2)&=\mu\frac{d\log Z_A}{d\mu}\Big|_{g_0, m^2_0},\\
\gamma_c(g,m^2)&=\mu\frac{d\log Z_c}{d\mu}\Big|_{g_0, m^2_0}.
\end{align}
We can then use the RG equation for the vertex function with $n_A$ gluon
legs and $n_c$ ghost legs:
\begin{equation}
\begin{split}
\Big( \mu \partial_\mu -\frac 1 2 &(n_A \gamma_A+n_c \gamma_c)\\&+\beta_g
\partial_{g}+
\beta_{m^2}\partial_{m^2}\Big)\Gamma^{(n_A,n_c)}=0,
\end{split}
\end{equation}
to relate these functions at different scales:
\begin{equation}
\label{eq_int_RG}
\begin{split}
\Gamma^{(n_A,n_c)}(&\{p_i\},\mu,g(\mu),m^2(\mu))=z_A(\mu)^{
n_A/2}z_c(\mu)^{
n_c/2}\\
&\times\Gamma^{(n_A,n_c)}(\{p_i\},\mu_0,g(\mu_0),m^2(\mu_0)).
\end{split}
\end{equation}
where $g(\mu)$ and $m^2(\mu)$ are obtained by integration of the
beta functions with initial conditions given at some scale $\mu_0$ and:
\begin{equation}
\label{eq_def_z_phi}
\begin{split}
\log z_A(\mu)&=\int_{\mu_0}^\mu\frac
     {d\mu'}{\mu'}\gamma_A\left(g(\mu'),m^2(\mu')\right),\\ \log
     z_c(\mu)&=\int_{\mu_0}^\mu\frac
     {d\mu'}{\mu'}\gamma_c\left(g(\mu'),m^2(\mu')\right).
\end{split}
\end{equation}

There remains to choose the RG scale $\mu$ at which Eq.~(\ref{eq_int_RG}) is
evaluated. For a correlation function with typical momentum $p$, in the
UV regime $p\gg m$, it is important to take $\mu\simeq p$. However, in the IR
regime, the theory is effectively massive and no large logarithm are present.
It is therefore not necessary to integrate the flow down to RG
scales smaller than $m$. We therefore used a running scale: \footnote{A
conceptually more satisfying criterion would be to use the mass at the running
scale $\mu$ instead of $\mu_0$. However, the variation of the mass is small in
the range of energy of interest for us so that the difference between these two
schemes is tiny.}
\begin{equation}
 \label{eq_rg_scale}
 \mu=\sqrt{p^2+\alpha\, m^2(\mu_0)}
\end{equation}
where $\alpha$ is a parameter that, in principle, can vary between zero and values of order one.
In practice we used various values of
$\alpha$ between 0 and 3. We discuss for the two schemes and for $d=4$ and $d=3$ the dependence on $\alpha$ in the following section.

\section{Results}
\label{sec_res}

In this section, we present the results for the 2 and 3-point
functions both in $d=4$ and in $d=3$. As explained in
\cite{Tissier:2010ts,Tissier:2011ey} the perturbative scheme considered here
does not work in $d=2$. In that case, the loop corrections contains
infrared divergences that a IR Landau-pole remains present, even if a
mass for the gluons have been introduced. For this reason, we only
present results for higher dimensions.

\subsection{Fixing parameters}

Following \cite{Tissier:2010ts,Tissier:2011ey}, we consider here the values of the
mass and coupling constants at some renormalization
scale $\mu_0$ as fitting parameters. Since the lattice results
are much more precise for the propagators than for the
3-point correlation functions, we look for the set of parameters
that lead to the best fit of the 2-point correlation functions.
[Note that
the global normalization of the ghost and gluon two-point correlation functions
are not accessible so we have to
introduce a multiplicative factor in front of our analytic expression
of the propagators, which must be fixed by comparison with the lattice data.]
The values of the mass and coupling constant
thus determined are then used for computing the 3-point
correlation function. When comparing the latter with lattice results,
we are thus left with only one free parameter associated with the
global normalization of $G^{AAA}$.
For each lattice parameter beta, we fixed this multiplicative factor
by considering a particular momentum configuration
(with one vanishing momentum) and used the same value for the other
momentum configurations \footnote{In principle, this normalization of $G^{AAA}$ could be fixed by
normalizing the lattice results with the gluon and ghost propagators
in such a way that the continuum limit is well defined. We would then
have one less parameter to fix when comparing with lattice data. This would
give a more stringent test of theoretical results.}. In previous work
we compared both the $SU(2)$ and the $SU(3)$ cases with lattice results \cite{Tissier:2010ts,Tissier:2011ey}. In the present
article, given that the available lattice simulations for the infrared behaviour of
3-point functions are for the $SU(2)$ group, we only present numerical results for that case.

When comparing lattice data with analytical results,
it is important to have simultaneously a small relative and absolute error
since the propagators tend to zero in the ultraviolet.
Therefore, we use the following indicators to quantify the precision of our results:
\begin{align}
\label{eq_chi}
\chi^2_{AA}&=\frac{1}{4N}\sum_i(\Gamma_{\rm lt.}^\perp(\mu_0)^2+\Gamma_{\rm lt.}^\perp(p_i)^2)\left(\frac{1}{\Gamma_{\rm
lt.}^\perp(p_i)}-\frac 1{\Gamma_{\rm th.}^\perp(p_i)}\right)^2\nonumber\\
\chi^2_{c\overline c}&=\frac{1}{4N}\sum_i( J^{-2}_{\rm lt.}(\mu_0)+ J^{-2}_{\rm lt.}(p_i))
\left(J_{\rm lt.}(p_i)-J_{\rm th.}(p_i)\right)^2\nonumber\\
\end{align}
It corresponds to a sort of average between the (normalized) absolute error and the relative error.
In order to chose the parameters we took a value that gives a compromise between optimal values for both propagators.
We analyzed the errors for various values of $\alpha$ in both schemes both in $d=4$ and in $d=3$. For moderate values
of $\alpha$ (between 1 and 3) we do not observe an important dependence on $\alpha$. In the VM scheme, if the parameter
$\alpha$ is too small, the system shows a IR Landau pole and the results do not fit well the lattice data. For that
scheme we chose $\alpha=1$ and all results presented in that scheme corresponds to that value.
 In the IS scheme, there is no Landau pole. For the $d=4$ case, the curves are almost insensitive to $\alpha$, even when it tends to 0.
 In the $d=3$ case, the best fits are obtained for $\alpha=0$. In the following, all our results in the IS  scheme are given for $\alpha=0$.
The corresponding values are presented in Tables~\ref{tab_best_fit} and \ref{tab_best_fit_3d}.

As our 1-loop expressions are certainly not exact
and given a certain tolerance of the estimate of the propagators, there are many possible values of the associated parameters.
In Fig.~\ref{errorcontourlevels} we present the contour levels associated to errors 4, 7 and 10\% for the quantities $\chi_{AA}$ and $\chi_{c\overline c}$
both in $d=4$ and $d=3$ in schemes IS and VM. We can see that there is a region of acceptable parameters (with errors in both
2-point functions lower than 10\%) in almost all cases. The only exception is the VM scheme in $d=3$. In that dimension, the IS scheme
is much more precise than the other (and in fact gives an excellent fit for both 2-point functions simultaneously).
The same observation is also true for the 3-point functions discussed below.
\begin{figure}[htbp]
 \includegraphics[width=4.2cm]{ErrorE1d4alpha0.jpg}
 \includegraphics[width=4.2cm]{ErrorE2d4alpha1.jpg}\\
 \includegraphics[width=4.2cm]{ErrorE1d3alpha0.jpg}
 \includegraphics[width=4.2cm]{ErrorE2d3alpha1.jpg}\\
 \caption{Contour levels for the quantities $\chi_{AA}$ and $\chi_{c\bar c}$ for the IS scheme (left) and VM scheme (right), both for $d=4$ (above) and $d=3$ (below).
 The large diagonal region corresponds to chi cc and the small elliptic one to chi AA.
 From dark to light: 4\%, 7\% and 10\%.}
\label{errorcontourlevels}
 \end{figure}
We observe that there is a large degeneracy of possible acceptable values for the parameters compatible with lattice data for
the ghost propagator. On the contrary, fitting the gluon propagator is much more demanding and the region of acceptable
parameters is much smaller.
\begin{table}[htbp]
 \begin{tabular}{|l|r|r|r|}
 \hline
  Scheme&$\alpha$&$g_0$&$m_0$ (GeV)\\
 \hline
 \hline
  IS&0.0& 5.2&0.44\\
 \hline
  IS&1.0& 5.2&0.43\\
 \hline
  IS&2.0& 5.8&0.48\\
 \hline
  IS&3.0& 6.3&0.53\\
 \hline
  VM&1.0& 7.5&0.77\\
 \hline
  VM&2.0& 9.0&0.78\\
 \hline
  VM&3.0& 9.1&0.75\\
 \hline
 \end{tabular}
\caption{Fitting parameters retained for computing correlation functions in $d=4$ for different schemes.}
\label{tab_best_fit}
\end{table}

\subsection{$d=4$}
We first present the results for the gluon propagator and the ghost dressing
function. The $\beta$ functions were integrated with initial condition at
$\mu_0=1$~GeV and we used the values of the mass and coupling constants given in Table I.

For all these schemes, we find a good agreement with the lattice data, with an
error in-between 5 and 10$\%$ for $\chi_{AA}$ and $\chi_{\overline c c}$. However, the
ghost-antighost-gluon vertex functions are best reproduced with the VM scheme.
We also present curves with the IS scheme.
The difference between the two sets of curves gives an indication of the error
of our calculation.

The gluon propagator and ghost dressing functions are depicted in
Fig.~\ref{fig_propags_4d}.
\begin{figure}[htbp]
 \includegraphics[width=\linewidth]{AAd4.pdf}
 \includegraphics[width=\linewidth]{CCd4.pdf}
\caption{Gluon propagator (top) and ghost dressing function
(bottom) as a function of momentum in $d=4$. The points are lattice
data of \cite{Cucchieri_08b}. The plain line (color online
blue) corresponds to the infrared safe scheme with $\alpha=0$;
the dashed line (color online red) corresponds to
the vanishing momentum scheme with $\alpha=1$.}
\label{fig_propags_4d}
 \end{figure}
We show in Fig.~\ref{fig_cbcA_4d} our results for $G^{c\overline c A}$ and in
 Fig.~\ref{fig_AAA_4d} for $G^{AAA}$ for different momentum
 configurations.

 In all cases, the results are compared with the
 corresponding results obtained in lattice simulations
 \cite{Cucchieri08}. The agreement is excellent.
 It is a
   striking result that the set of parameters adapted for describing
   the 2-point correlation function gives simultaneously a good
   agreement for the 3-point functions. When comparing the
   results with lattice data, it is important to note that the data
 for the 3-point functions (particularly for the $G^{AAA}$ functions)
 have large statistical errors and a full analysis of systematic
 errors has not been done yet. In consequence we can not completely neglect
 the errors coming from the lattice data with respect to those coming
 from the present calculation.
\begin{figure}[htbp]
 \includegraphics[width=\linewidth]{CCAg0d4.pdf}
 \includegraphics[width=\linewidth]{CCAsimd4.pdf}
 \includegraphics[width=\linewidth]{CCAoted4.pdf}
\caption{Ghost-antighost-gluon correlation function $G^{c\overline c A}$ for one vanishing momentum (top figure),
all momenta equal (middle figure), two momenta orthogonal, of equal norm (bottom) as a function of momentum, in $d=4$.
The lattice data of [\onlinecite{Cucchieri08}] are compared with our calculations.
See caption of Fig.~\ref{fig_propags_4d} for the
legend.}
\label{fig_cbcA_4d}
 \end{figure}
\begin{figure}[htbp]
 \includegraphics[width=\linewidth]{AAAg0d4.pdf}
 \includegraphics[width=\linewidth]{AAAsimd4.pdf}
 \includegraphics[width=\linewidth]{AAAoted4.pdf}
\caption{Three gluon correlation function $G^{AAA}$ for one vanishing momentum (top figure),
all momenta equal (middle figure), two momenta orthogonal, of equal norm (bottom) as a function of momentum, in $d=4$.
The
lattice data of [\onlinecite{Cucchieri08}] are compared with our calculations.
See caption of Fig.~\ref{fig_propags_4d} for the
legend.}
\label{fig_AAA_4d}
 \end{figure}

 \subsection{$d=3$}
A similar analysis can be performed in $d=3$.
We summarize in Table~\ref{tab_best_fit_3d} the parameters retained for the different renormalization schemes.
\begin{table}[htbp]
 \begin{tabular}{|l|r|r|r|}
 \hline
  Scheme&$\alpha$&$g_0$ (GeV$^{1/2}$)&$m_0$ (GeV)\\
 \hline
 \hline
  IS&0.0& 2.4&0.55\\
 \hline
  IS&1.0& 2.5&0.55\\
\hline
  IS&2.0& 2.5&0.55\\
 \hline
  IS&3.0& 3.0&0.65\\
 \hline
  VM&1.0& 4.0&1.00\\
 \hline
  VM&2.0& 4.5&0.95\\
 \hline
  VM&3.0& 6.1&1.11\\
 \hline
 \end{tabular}
\caption{Fitting parameters retained for computing correlation functions in $d=3$ for different schemes.}
\label{tab_best_fit_3d}
\end{table}
As explained before, the VM scheme does not give
results with good simultaneous agreement with lattice data for both propagators.
However, there is an excellent agreement in the IS scheme (with
errors in-between 5 and 10$\%$ for $\chi_{AA}$ and $\chi_{\overline c c}$). In particular
the IS scheme correctly reproduces the increase of the gluon propagator
at low momentum. The best choice for $\alpha$ is zero.
We do not have a solid argument explaining why the
preferred renormalization scheme is different in $d=4$ and in
$d=3$. The gluon propagator and ghost dressing functions are depicted
in Fig.~\ref{fig_propags_3d}. The agreement remains very
good and, moreover, all qualitative aspects of the curves are
correctly reproduced. In particular, we find
  that the $G^{AAA}$ becomes negative at small momenta
  and diverges for vanishing momenta, in agreement with lattice
  results \footnote{$G^{AAA}$ also becomes negative in $d=4$ but at scales much smaller, probably difficult to observe in the lattice.
  More precisely, we obtain a divergence as $1/p$ in $d=3$ but only as  $\log(p)$ in $d=4$.}.

\begin{figure}[htbp]
 \includegraphics[width=\linewidth]{AAd3.pdf}
 \includegraphics[width=\linewidth]{CCd3.pdf}
\caption{Gluon propagator (top) and ghost dressing function
(bottom) as a function of momentum in $d=3$. The points are lattice
data of \cite{Cucchieri_08b}. The plain line (color online
blue) corresponds to the infrared safe scheme with $\alpha=0$;
the dashed line (color online red) corresponds to
the vanishing momentum scheme with $\alpha=1$.}
\label{fig_propags_3d}
 \end{figure}

 We show in Fig.~\ref{fig_cbcA_3d} our results for $G^{c\overline c A}$ and in
 Fig.~\ref{fig_AAA_3d} for $G^{AAA}$ for different momentum
 configurations. As for the four dimensional case, we used the parameters
 that lead to the best fits for the 2-point functions as inputs in our calculation of the 3-point functions.
 Consequently
 those functions are calculated without any free
 parameter (with the exception of the renormalization factor for the $G^{AAA}$ function mentioned previously).
 We obtain a very good agreement as in $d=4$.
\begin{figure}[htbp]
 \includegraphics[width=\linewidth]{CCAg0d3.pdf}
 \includegraphics[width=\linewidth]{CCAsimd3.pdf}
 \includegraphics[width=\linewidth]{CCAoted3.pdf}
\caption{Ghost-antighost-gluon correlation function $G^{c\overline c A}$ for one vanishing momentum (top figure),
all momenta equal (middle figure), two momenta orthogonal, of equal norm (bottom) as a function of momentum, in $d=3$.
The lattice data of [\onlinecite{Cucchieri08}] are compared with our calculations.
See caption of Fig.~\ref{fig_propags_3d} for the
legend.}
\label{fig_cbcA_3d}
 \end{figure}
\begin{figure}[htbp]
 \includegraphics[width=\linewidth]{AAAg0d3.pdf}
 \includegraphics[width=\linewidth]{AAAsimd3.pdf}
 \includegraphics[width=\linewidth]{AAAoted3.pdf}
\caption{Three gluon correlation function $G^{AAA}$ for one vanishing momentum (top figure),
all momenta equal (middle figure), two momenta orthogonal, of equal norm (bottom) as a function of momentum, in $d=3$. The
lattice data of [\onlinecite{Cucchieri08}] are compared with our calculations.
See caption of Fig.~\ref{fig_propags_3d} for the legend.}
\label{fig_AAA_3d}
 \end{figure}

\section{Conclusions}
\label{sec_conc}
In the present article we have presented a perturbative calculation of
3-point correlation functions in Landau-gauge, Yang-Mills theories in
$d=4$ and $d=3$ in all momentum regimes including the infrared.  Very
few analytical results were known up to now for infrared behavior of
the ghost-antighost-gluon vertex
\cite{RodriguezQuintero:2011au,Dudal:2012zx,Huber:2012kd,Aguilar:2013xqa}. For
the 3-gluon functions only educated ansatzes have been proposed
previously (see \cite{Huber:2012kd} and references therein).
Following \cite{Tissier:2010ts,Tissier:2011ey}, we introduced a bare
gluon mass so as to obtain controlled perturbative expressions both in
the ultraviolet and in the infrared regime and gives an infrared-safe
perturbative expansion for non-exceptional momentum configurations for
all $d>2$. Note that, in the gauge-fixing procedure of
\cite{Serreau:2012cg}, the mass-term naturally appears in the process
of lifting of the Gribov ambiguity.

We fixed the parameters of
the model by fitting the 2-point function to lattice simulations and by using two families
of renormalization group schemes. The resulting parameters are
  then used to calculate the 3-point functions. The comparison of the
  resulting functions with lattice simulations is therefore performed
 without any extra free-parameter (with the only exception of a renormalization factor in the $G^{AAA}$ function)
 and is very good. First, all qualitative
properties observed in lattice correlators are correctly
explained in a simple way. For example, it is observed in
lattice simulations that the 3-gluon correlator becomes negative in
$d=3$ at low momenta and even seems to diverge when all momenta go to
zero. This is a consequence of the IR divergence of the diagrams with ghost loops when all momenta go to zero.
Second, not only the qualitative
agreement is very good, but also the comparison with lattice simulations gives an excellent quantitative agreement.
Note that the available lattice data still have large statistical errors and more precise results
(possibly with other tensor structures) would be welcome to give sharper test of our findings.

All these results strongly support the idea that at least an important
part of the infrared effects present in Quantum Chromodynamics can
take its origin in the Gribov-copies as has been suggested in last
years \cite{Gribov77,Zwanziger89,Zwanziger92,Dudal08}.  Contrarily to
previous analysis of these effects, the present approach does not
require the introduction of extra fields and the Feynman rules remain
almost identical to those of the standard perturbative analysis. Only
the gluon mass parameter is new and the calculation of many
correlators become treatable in practice, as shown in the present
article. Consequently, these studies can be extended in many aspects.
We are currently considering also the introduction of quarks that can
be done very easily. We also started studying the influence of higher
loop contributions to the 2-point correlation functions.

Of course, there are many open questions to be analyzed in the future. First of all, the inclusion of a mass term violates the nilpotency of standard BRST
transformations. Even if this difficulty is present in all approaches that take into account in various ways Gribov-copies effects, it has major consequences.
In particular, standard definition of the physical space of non-abelian gauge theories, based in the cohomology of the BRST charge is no longer applicable.
A new definition of the physical space is then required in order to be able to control the unitarity of the S matrix on it. This is a major problem that clearly goes
beyond the present article and that we would like to consider in the future.

\begin{acknowledgments}
The authors want to acknowledge A.~Maas for kindly making available the lattice data and for useful exchanges. They want also
acknowledge M.~Q.~Huber and J.~A.~Gracey for useful suggestions.
 The authors want acknowledge partial support from PEDECIBA and ECOS programs. N.~W. wants to thanks the LPTMC (UPMC), where
 most of the present work has been done, for its hospitality.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Turner County is the name of two counties in the United States:

 Turner County, Georgia
 Turner County, South Dakota

redpajama_set_name: RedPajamaWikipedia


text:
was a town located in Yuri District, Akita Prefecture, Japan.

In 2003, the town had an estimated population of 6,359 and a density of 19.72 persons per km². The total area is 322.53 km². The town is named for the nearby Mount Chōkai which is on the boundary of Akita Prefecture and Yamagata Prefecture, southwest of town.

On March 22, 2005, Chōkai, along with the city of Honjō; and the towns of Higashiyuri, Iwaki, Nishime, Ōuchi, Yashima and Yuri (all from Yuri District), merged to create the city of Yurihonjō.

Chōkai contains several villages, including Jinego (上笹子; Kami-Jinego), Fushimi (伏見), Kawauchi (上川内; Kami-Kawauchi), and Hitane (上直根; Kami-Hitane).  Highway 108 is the town's largest highway, connecting to Yuri and Honjō in the NW and Highway 13 in the SE.

There are two rivers in Chōkai -- Koyoshi River and Jinego River.

History
 On March 31 1955, the villages of Kawauchi, Hitane, and Jinego merged to form the village Chōkai.
 On November 1 1980, Chōkai became a town.
 On March 22 2005, the city of Honjō merged with the towns of Iwaki, Ouchi, Yuri, Nishime, Higashi-Yuri, Yashima, and Chōkai to form the city Yurihonjō.

Schools
 Chōkai Junior High School.
 Chōkai Elementary School (consoldiated from Hitane, Jinego, and Kawauchi Elementary Schools in 2014).

External links
Yurihonjō official website

Dissolved municipalities of Akita Prefecture
Yurihonjō


text:
Biografia
Attilio Rossi, nato nel 1909 ad Albairate e scomparso nel 1994 a Milano, ha attraversato il secolo XX con un'esperienza pittorica che ha spaziato dall'arte astratta all'iperrealismo, fino a collocarsi sulla frontiere della figurazione più avanzata, tenendo conto delle più importanti sperimentazioni dell'arte contemporanea. A lui è stato dedicato il giardino pubblico fra Via Arena e Via Conca del Naviglio a Milano.

Nell'ultimo periodo del suo lavoro artistico, le sue darsene, le sue nature morte e i suoi autoritratti hanno lasciato spazio al grande ciclo della pittura metafisica.

La sua opera più impegnativa rimane la grande Via Crucis Oggi, costituita da 14 tele che ripercorrono la storia contemporanea con una ricerca formale estremamente audace.
Sue opere si trovano in molti Musei, tra cui il Museum of Modern Art of New York. e in numerose e prestigiose collezioni private.

Il vivace impegno culturale di Attilio Rossi è confermato anche dagli amici che lo frequentarono: Soldati, Reggiani, Licini, Fontana, Bogliardi, Veronesi, Ghiringhelli, Gatto, Sinisgalli, Quasimodo, Giolli, Bardi, Modiano, Carra', Belli e Persico.

Attilio Rossi ha esposto i propri quadri in numerose esposizioni personali in Italia e all'estero e in numerose grandi esposizioni collettive. Ha anche partecipato alla Biennale di Venezia (1948 e 1962) e alla Quadriennale di Roma.
Il Comune di Milano gli ha dedicato nel 1975 un'importante mostra a Palazzo Reale. Tra le sue antologiche va ricordata l'ampia rassegna del 1987 alla Civica Galleria d'Arte Moderna di Gallarate.
Nel 1996, due anni dopo la sua scomparsa, la Società per le Belle Arti ed Esposizione Permanente di Milano gli ha dedicato un'ampia mostra antologica corredata da un importante catalogo curato da Luciano Caramel.

Nel corso della sua attività artistica Attilio Rossi ha vinto numerosi premi e ha ricevuto nel 1974 dal Comune di Milano la medaglia d'oro per la cultura e l'arte. Nel 2003 il suo nome è stato iscritto tra i cittadini illustri nel Famedio di Milano.

Nel campo dell'arte Attilio Rossi ha realizzato libri tra i quali vanno ricordati Buenos Aires en tinta china, 130 disegni con prefazione di Jorge Luis Borges e poemi di Rafael Alberti, e Milano in inchiostro di china, 130 disegni con testo e poesie di Salvatore Quasimodo. Ha anche illustrato numerosi libri.

Ai suoi quadri, ma anche ai suoi acquerelli e ai suoi disegni sono stati dedicati scritti, saggi e articoli da parte di importanti studiosi e critici d'arte come Luciano Caramel, Dino Formaggio, Sebastiano Grasso, Jorge Luis Borges, Franco Russoli (autore di una monografia), Raffaele De Grada, Gian Alberto Dell'Acqua, Dante Isella, Marisa Dalai-Emiliani, Francesco Flora (autore di una monografia), Fernanda Wittgens, Rossana Bossaglia, Leonardo Sinisgalli, Camilla Cederna, Alberico Sala, Raffaele Carrieri. Roberto Tassi, Vittorio Sgarbi, Leonardo Borgese, Eduardo Mallea, Guillermo De Torre, Arturo Serrano Plaja e molti altri.

Attilio Rossi è considerato anche un grande innovatore nel campo dell'arte grafica. Nel 1933, infatti, ha fondato e diretto per due anni la rivista Campo Grafico, rivoluzionaria non solo per la sua originale ed esemplare formula esecutiva, ma perché ha rinnovato completamente la grafica in Italia, aprendola alle influenze del Bauhaus e dell'arte contemporanea (Picasso, Mondrian, Kandinsky e così via). D'altronde i Campisti, collaboratori della rivista, scrissero davvero "regole nuove" della grafica italiana, basti pensare anche a La Rassegna del Brutto, rubrica critica della rivista che metteva sotto i riflettori le realizzazioni grafiche criticabili rispetto ai canoni grafici di leggibilità ed innovazione.
Attilio Rossi ha proseguito questa attività anche negli anni cinquanta, dirigendo la rivista Linea grafica, curando libri e realizzando manifesti.
Anche in questo campo ha scritto libri sui manifesti e sugli alfabeti antichi.

Attilio Rossi è stato anche un importante organizzatore culturale, che ha realizzato e curato numerose mostre d'arte di grande rilievo nel Palazzo Reale di Milano e alla Permanente.
Tra le sue iniziative vi è stata quella di riuscire a ottenere nel 1953 da Pablo Picasso il prestito di Guernica per la grande mostra dedicata allo stesso Picasso a Milano.

Attilio Rossi è stato tra l'altro consigliere di amministrazione dell'Ente Manifestazioni Milanesi, della Triennale e della Permanente.
Attilio Rossi è stato anche presidente del "Centro di Studi Grafici di Milano". Sulle origini del 'Centro' Rossi scriveva nella presentazione della monografia di Campo Grafico (Electa 1983) "Dalle ceneri mai spente di Campo Grafico nasce il Centro di Studi Grafici di Milano".

Va poi ricordato il profondo rapporto che Attilio Rossi ha avuto con la cultura ispanica e latino-americana durante il suo lungo soggiorno in Argentina (1935-1950).
In quel paese, Attilio Rossi è stato dapprima direttore artistico della Casa Editrice Espasa Calpe argentina, dove tra l'altro ha creato e lanciato la prima collana economica del continente, l'Austral (di cui ha realizzato anche il logo).

Poi nel 1938 ha fondato insieme a Guillermo De Torre, Francisco Romero e Gonzalo Losada la Casa Editrice Losada, di cui ha realizzato il logo.

Ha illustrato anche numerosi libri, tra i quali Platero y yo di Juan Ramòn Jiménez, e ha realizzato con Rafael Alberti il libro A la pintura. Alberti gli dedicherà una poesia del suo libro Pleamar. Attilio Rossi ha disegnato numerose copertine dei volumi di cui ha curato la pubblicazione.

Nel corso di questo intenso lavoro editoriale, Attilio Rossi stringerà rapporti di collaborazione e di amicizia con numerosi intellettuali spagnoli. Tra i suoi amici vi sono Rafael Alberti, Josè Bergamin, Ramòn Gòmez de la Serna (sette sue lettere a Rossi sono state pubblicate da Sebastiano Grasso sul Corriere della Sera e su El Pais), Juan Ramòn Jiménez, Amado Alonso, Luis Felipe Jiménez de Asua e molti altri.
Di Rafael Alberti e di Juan Ramòn Jiménez Attilio Rossi dipinge il ritratto.

Altrettanto solidi sono i suoi rapporti con la cultura sudamericana. Tra i suoi amici vi sono Pablo Neruda, di cui illustra i 20 poemas de amor, Jorge Luis Borges, Eduardo Mallea, Ernesto Sabato, Victoria Ocampo, della cui rivista Sur è per diverso tempo critico d'arte.
In Messico conosce e diviene amico di Diego Rivera, di Octavio Paz e di Leon Felipe e di altri intellettuali.

Di Attilio Rossi, oltre ai 10 libri di cui è autore e ai numerosi saggi presenti in volumi collettivi, va infine ricordata l'attività pubblicistica, che ha visto la sua collaborazione su temi artistici e culturali a numerose testate italiane, tra le quali il Corriere della Sera e il Giorno, ed argentine.

Bibliografia
 P. Neruda, 20 Poemas de amor y una cancion desesperada; con 21 dibujos de Attilio Rossi, Buenos Aires, Pleamar, 1948
 S. Quasimodo, Milano in inchiostro di china, Milano, A.Pizzi, 1963
 R. De Grada, Attilio Rossi pittore, Galleria Gianferrari, Milano, 1965
 L. Caramel, Attilio Rossi: le opere 1933-1994, Firenze, Giunti, 1996
 P. Rossi, Buenos Aires 1937: Attilio Rossi e una polemica culturale, Milano, 1998
 L. Caramel, P.Rossi, Attilio Rossi dieci anni dopo : da La Permanente (1996) a Palazzo Leone da Perego, Milano, 2006
 T. Gipponi, Attilio Rossi (1909-1994), Milano, Skira, 2009
 A. Rossi, Buenos Aires en tinta china, poema de Rafael Alberti, prologo di Jorge Luis Borges, Buenos Aires, Losada, 2010
 P. Rossi, Nell'arte di Attilio Rossi : il racconto di due mondi, Milano, 2015

Voci correlate
 La Permanente, Milano

Altri progetti

Collegamenti esterni


Photographers who capture an iconic image are often confronted with a paradox: the celebration of a single photograph overshadows the entirety of an artistic oeuvre. Yet what happens in those rare situations when a single photographer is responsible for scores of iconic images?
This question is explored by the Halsman: Facets and Faces exhibition. Philippe Halsman (b. Riga, 1906; d. New York, 1979) remains one of history's most esteemed photographers, yet there is no consensus as to what constitutes his most important work. The groundbreaking jumpology series that created a bold vision of identity through movement? His famed pictures of Alfred Hitchcock that set a new standard for interpretive portrait photography? His collaborations with Salvador Dalì that are a monument of the Surrealist movement? By juxtaposing these disparate facets of Halsman's artistic expression, this exhibition seeks to assemble a harmonious portrait of a photographer whose genius transcends any single image.
°CLAIR Gallery presents Halsman: Facets and Faces from December 15, 2016 to January 31, 2017 at Franz-Joseph-Strasse 10 in Munich. Vernissage the evening of December 15, 19h30. For more information, contact Anna-Patricia Kahn at anna@clair.me.
Photographer Philippe Halsman had an exemplary career. Over a forty-year period, in Paris during the 1930s and in New York from 1940 on, he developed a broad range of activities (portraits, fashion, reportage, advertisements, personal projects, commissions from individuals and institutions).Born in 1906 in Riga, Latvia, Halsman studied engineering in Dresden before moving to Paris, where he opened a photographic studio in 1932. His years in Paris already heralded the approach he was to develop throughout his long career. A studio and reportage photographer, Halsman took inspiration from the contemporary art scene and participated in promoting it. Though he specialised in portraiture, he also branched out into advertising and publishing, which were thriving at the time. In 1940, the German invasion brought Halsman's prosperous career to a halt, leading him to flee with his family to New York. Though initially unknown, he succeeded in establishing himself on the American market in under a year, and his studio soon became successful. Halsman stood out for his "psychological" approach to portraiture.
The featured images are vintage prints, stamped and certified by the Halsman Archive. Purchase inquiries are welcome via email at anna@clair.me.


James is such a sweetheart. This collectible bear is made of warm mink-coloured plush graduating into darker flecked tips. He has a heart shaped face, muzzle and pads in a complementary warm brown, and subtly defined fingers and toes. His close set black button eyes match his cute embroidered nose. As with all the Silver Tag bears, James is fully jointed, substantially weighted, and has a classic hump. James comes with an individually numbered Certificate of Authenticity. He is 46 cm standing. James is one of 1500. He can be spot cleaned.


text:
If you are accused of a criminal offense, you need an attorney who can navigate California's complex network of statutes and regulations. You want someone who is willing to hear your story and not only vigorously defend the charges you are facing but also present to the court and the prosecutor mitigating evidence surrounding the allegations. An experienced attorney like Adam Richards may obtain decisive results for you even in circumstances where you believe you have no defense. With over a decade defending people accused of crimes in California state courts, Mr. Richards has the expertise, knowledge, and skill to give you best chance at a favorable outcome to your case including in the complex area of DUI prosecutions.
Mr. Richards has represented people accused of crimes in all counties in the Greater Sacramento Area including Sacramento, Yolo, Placer, El Dorado, Solano, San Joaquin, Plumas, Lake, Yuba, Butte, Amador, Napa, Nevada, and Sutter Counties.
If you are under investigation or charged with a crime, call or email today for a consultation.
© 2017 Law Office of Adam J. Richards. Attorney Advertising Notice: Information contained in this Web site may be considered attorney advertising. The material and information contained on these pages is intended to provide general information only and not legal advice. You should consult with an attorney licensed to practice in you jurisdiction before relying upon any of the information presented here. You are advised that the acts of sending e-mail to or view or downloading information from this website does not create an attorney-client relationship.
Disclaimer| Sitemap
Law Office of Adam J. Richards
2530 J Street, Suite 320
adam@ajrlaw.net
© 2017 Law Office of Adam J. Richards. All rights reserved.
Law Firm Website by Law Promo

redpajama_set_name: RedPajamaCommonCrawl


"Easy installation and calibration. Good and clear display, logical functions.
With the depth gauge it is easy to see when the anchor hits the bottom. Or when lifting the anchor, when it breaks out of the bottom. It helps especially in windy and narrow harbors."
The QUICK Marine Lightning division, founded in 2007, offers decorative lights, spots, spotlights and various lamp inserts for the interior, since 2012 these are also available through the QUICKlightning division in resource-saving and environmentally friendly LED technology.
Good to know: QUICK is certified according to ISO 9001.00 (in 2010 ISO 9001: 2008).


So, things were pretty packed last night between a lively discussion with Nick which kept us late a the office, dinner, and updating my presentation to add content that everyone was asking for. So I didn't get to posting a day three post (I know, you were probably hitting refresh all day only to be left disappointed).
I'll recount the tale of the Kala Jamun, an Indian dessert which has become quite the object of focus this week. When out for dinner on Monday night with the product management team, they were kind enough to give me a tour of the local cuisine. For dessert, there were three options and it was hotly debated which one I should try. After an interrogation of the kitchen staff, it was determined that I should not try the Kala Jamun from the Waterfront restaurant as it was made from a store-bought mix. However that kicked off a week-long quest for the perfect Kala Jamun, which Avneesh was kind enough to have located and brought in for me on Wednesday afternoon. Nick quite accurately described them as "wet timbits" (file photo below).
As promised, I took some photos of the office and was able to acquire some photos from the architects as well. I'll introduce the photos in groups, the first of which is the hallway outside the office. I assume that the railing meets an architecural code that reads something like "all railings shall be designed to place the center of mass for large North Americans above the railing, to facilitate a quick and sure descent should they stumble too closely to said railing".
The entranceway to the office is decked out in Vignette branding, a transgression that first needs to be corrected at the legal entity level and the facilities team is ready with new "Open Text" designs to be introduced.
Inside the office, it's a great example of what can be done if you attack the design of a new space with the knowledge that the space will be used primarily for Agile development. I truly hope we'll have the opportunity to design some space in Waterloo with the same goal in mind. Lots of open team spaces, supplemented by ample availability of small meeting rooms.
And while I clearly did a bad job of explaining the Product Management area to someone at the Christmas Party the other day (somehow my explanation of a raised area for collaboration was interpreted as a prison-like setup), I really like how the PM team is available to everyone in a centralized area with lots of space for whiteboarding.
On Thursday, we took the entire office offsite for a big corporate hug (hereby defined as powerpoint, conversation, and lunch) and had a day full of questions, answers, and long term vision. At the end of the day, we took the team photo below.
Evening activities were decidedly less exciting on the last two days as several people had to juggle calls with North America. We ended up doing dinner in the hotel both nights, and in the case of Thursday night trying to get to sleep early to prepare for the 26-hour journey home beginning at 1:00am.
The Hyderabad airport was interesting, and while the hotel staff accompanied us through all of the details they did leave us at the security line. Security was excruciatingly slow, and took without a work of a lie about 30 minutes to process one passenger who was in front of us. We flew from Hyderabad to Dubai at 4:00am, and had a short layover in Dubai. The Dubai skyline teased us, and we vowed that next time we'd schedule a longer layover to take advantage of the massive buildings and take in some indoor skiing. The Dubai to Toronto flight was an excruciating fourteen hours, but the excitement of flying on an Airbus A380 super-jumbo took the edge off. The entertainment system was amazing, with hundreds of movies and even three inflight cameras so you can see what's going on outside of the airplane. The service, the headrests that actually are tall enough to rest my head on, and the entertainment left me wishing that Emirates would do more business in Canada (or take over operation of Air Canada).
I was incredibly excited to get home on Friday afternoon and see my family, and to sleep (which I did until 11am the next morning).


Hey figure fans! Here's two more Joes for my assault team. I think these two nicely round out the group. Stay tuned for an upcoming helicopter crew, and hopefully a Navy SEAL strike team in the near future.


text:
Design Inspired By Aero Gt Concept Bell & Ross Launches New Br 03 Aero Gt Watch
Bell & Ross at the 2016 BaselWorld Baselworld Jewellery Show announced two new models BR 03 Aero GT inspired by the Aero GT concept car.
Road and time … AERO GT
'In order to create new models, I need a new source of inspiration every year,' acknowledges Bruno Belamich, creative director. 'Following the great success of our B-Rocket motorcycles in 2014, I want to further design Bell & Ross cars to produce cars that are' convincing 'even in the eyes of automotive professionals. Most The important thing is that this real challenge brought me great fun, 'the designer recalled.
In 2016, Bell & Ross will firmly focus on one of its designers' favorite areas in the racing world. The brand has designed the Aero GT, an avant-garde concept car and GT (high-performance sports car) luxury sports car, with the same streamlined design as the fighter. This one-of-a-kind car was carefully created by the watchmaker's design studio, rather than a whim. 'The Aero GT concept car is an extension of our expertise and demonstrates the brand's creativity and technical strength. I think if we can combine the iconic features of Bell & Ross with cars directly inspired by aviation, That would be very interesting, 'explained Bruno Ramic. 'This concept car is actually a combination of aeronautical technology and GT cars.' This shocking car uses the main principles of Bell & Ross watches: a functional shape, a love of mechanics, and a distinctive In addition to these two unique prototypes, we also introduced two unique watches with distinctive automotive features BR 03 Aero GT. The design of the new watch BR 03 Aero GT is inspired by the automotive world, and the Aero GT concept car is exactly the starting point for the creation of this pair of watches.
AERO GT-Bell & Ross Aviation
Bell & Ross has a relationship with cars
From the beginning Bell & Ross has incorporated iconic features of aeronautics into the design of its watches. As a result, creative director Bruno Ramieci spends a lot of time working on jets, fighters and bombers, but the creator who pursues mechanics, fashion and high performance also loves motorsport. This year, Bell & Ross will showcase computer-generated images (CGT) of the ultra-luxury sports car project Aero GT. 'It took us just over a year to design this concept car. For best results, we collaborated with professionals when designing the car,' said Bruno Ramic. 'Creating a high-performance car with practical characteristics is very important to us.' In the end, this stunning supercar shows Bell & Ross's understanding of cars in a streamlined design like a jet.
Half is a GT concept car
Bell & Ross Aero GT draws inspiration from luxury sports cars ('gran turismo' in Italian). This type of car was first produced in the Pasolini region of Italy in the 1950s. Including a series of well-known cars in the history of cars, especially the famous Ferrari 250 GTO, this model produced only 36 in the 1960s. At that time, these highly versatile cars could be used as excellent family cars, Can also be hired on the track. There are even some 'gentleman owners' who drive directly from the road to the track. Today Bell & Ross Aero GT commemorates this field legend with an advanced avant-garde approach.
Half is an aviation concept car
Aero GT is a supercar inspired by aviation. Bell & Ross continues to demonstrate its deep love for aviation through this creation. This ultra-low, 4.7-meter-long car incorporates aerodynamic principles, like an off-arrow arrow that divides air into two. The sharp-edged, star-shaped arrow-shaped body is like a stealth fighter, as if as long as a pair of wings are installed, it can reach the sky. Viewed from above, the drop-shaped glass roof resembles the glass canopy of a jet cockpit. At the same time, the blade-like rearview mirror was inspired by the small wing of the fighter's head known as the 'front wing'. The two oversized exhaust pipes are like the exhaust pipes of a turbojet engine, and the turbine rims mimic the blades of a supersonic aircraft engine. But the most memorable detail is the longitudinal aileron at the rear, which is exactly the same as the tail of the aircraft. The role of this element is to keep the car stable during sharp turns. Bell & Ross Aero GT sensation car fundamentally integrates racing technology and aviation technology to the extreme.
Modern high-tech configuration
Like the aircraft, the Aero GT uses cutting-edge technology and top performance. This rigorous mid-engine two-seater sports car has an avant-garde look. In the 1950s and 1960s, the most common classic configurations in GT racing were front-engine and rear-wheel drive. Later, the entire engine was moved to the center of the car, just behind the passenger seat. Aero GT uses this scheme to ensure the balance of weight distribution between front and rear, and to drive between lanes, showing first-class steering performance and road control. In order to achieve a light and sturdy effect, the unibody chassis and body are made of carbon fiber. Therefore, this car weighs only 1,320 kilograms, which is very light in the automotive industry!
Power and flexibility
When it comes to the design of the Aero GT, Bruno Ramíci and Pan asked. He envisioned powering the car with a 4.21 V8 twin-turbo engine and the latest 8-speed automatic transmission. The Bell & Ross supercar is proud to have an output power of 610hp. Such a huge amount of power is more than enough to handle any road condition. Pressing the accelerator pedal, the horsepower is full and it is on the brink. It takes less than 3 seconds for the car to accelerate to 100 km / h. Regardless of whether it is in the low speed range or the high speed range, the two turbocharged engines can provide the car with maximum torque and achieve amazing acceleration. Overtaking has only become a form. In terms of maximum speed, the Aero GT is designed to reach a peak speed of 315 km / h. To this end, the Bell & Ross concept car intentionally installed a pitot tube on the top of the right fender. This detector is often used in aeronautics to measure extremely fast speeds. At the same time, heat-resistant ceramic brakes are responsible for slowing down this 'road missile.' In the end, the designer chose rear-wheel drive, which kept the driving pleasure and ensured the responsiveness of the car. Driving the Aero GT is bound to be fun!
BR 03 AERO GT showcases the mechanical beauty of the watch
The design inspiration of the BR 03 Aero GT watch is directly derived from the Aero GT concept car. It is undeniable that there are many similarities between the automobile and the watchmaking industry. Both areas involve power, performance, time and precision; they both require gears, escapements, screws and cams. Making watches for drivers is also a time-honored tradition, most of which are chronographs for professional racing drivers. Therefore, combining both the Aero GT concept car and the BR 03 Aero GT watch is also natural.
Bell & Ross's Pursuit of Perfection
'The BR 03 Aero GT watch and the Aero GT concept car are the result of high technology and high performance,' the creative director affirmed. The design studio has created two watches: a chronograph that embodies the essence of the 'car watch'. The other is the more classic three-hand watch. Both watches have a stainless steel case, echoing the aero-style bodywork of the Aero GT project. To deepen the distinctive style. The designers focused on the specifics and shapes of the watches, making them appear more sporty and streamlined. The Qi crown is made of red aluminum alloy, which is an ultralight aluminum alloy commonly used in sports cars. The skeletonized dial has a multi-layered structure, creating an intriguing depth. At the same time, the hollow-out mechanism of these two BR 03 Aero GT watches not only gives a glimpse into the mystery of the movement, but also makes the watch lighter. These streamlined improvements can also be seen in racing cars. The design of the two watches is intended to highlight the precision and beauty of the watch's powertrain: through the smoke-gray glass windows of the Aero GT concept car, the mechanics of the car are also appreciated.
The BR 03-94 Aero GT
Like the first impression of the Aero GT concept car, this avant-garde and stylish chronograph is a typical driver's watch. Its mechanical device is designed to measure short time intervals. Skeleton dial with metal hour markers. There are two counters on the grey crystal glass: an hour counter and a 30-minute counter with the date function at 3 o'clock. At the same time, the large central hand in the dial shows seconds, and the scale of the speedometer completes the whole. In order to ensure that the time can be read clearly at night or in heavy rain, the time markers and hands are coated with luminous paint. The chronograph hand is red, and its purpose is also to improve recognition. The aluminum start button is also designed in red for easy operation. All the design shows that the function of this watch is enough for professional speed measurement.
Following the model of the AeroGT, the three-hand watch is also powered by a skeleton mechanism. The hour, minute and second hands of the watch are all in the center, just like the fixed small triangular time scale indicating 12 o'clock. The second hand is also red. This small triangular time scale is reminiscent of the dashboard in a GT car.
A loyal partner for watches
Both models feature a black quilted leather strap, reminiscent of a luxury car's interior. The micro-holes and red lines on the strap are like the seats of a top sports car.
In 2014, Bell Ross set off a mechanical wave with two BR 03 B-Rocket watches. Today, Bell Ross has launched two BR 03 Aero GT watches following the creation of a concept car, which has demonstrated the brand's creative strength with utmost popularity. This watch brand that loves aviation technology will expand its territory next? let us wait and see…
Movement: Movement number: BR-CAL.319. Mechanical self-winding movement.
Mirror: Sapphire crystal with anti-glare coating.
Functions: hour and minute hands, small seconds at 12 o'clock. Big date window. Timing function: 12-hour timer at 6 o'clock, speed scale on the flange.
Water resistance: 100 meters.
Case: 42 mm in diameter. Satin-finished stainless steel.
Strap: black calfskin with red piping and super-abrasive black synthetic fabric
Dial: skeleton, metal applied hour-markers. Metal skeleton Superluminova® hour and minute hands.
Buckle: pin buckle. PVD * black-plated steel.
Function: Hour Hand, Minute Hand, Second Hand
Buckle: pin buckle. Satin-finished stainless steel.
Panerai Opens Its First Pop-up Store In Hong Kong
Hong Kong, September 4, 2019-The first pop-up store in Hong Kong, the high-end sports watch brand of Florence, Panerai, was officially unveiled. The store was located in Hong Kong's well-known shopping destination-Harbour City Ocean Centre.
The pop-up store covers an area of 75 square meters and adopts the new special design concept of Panerai creative director AlvaroMaggini. Guests are immersed in the new world of Panerai and enjoy the epic underwater world; its layout fully mobilizes various senses Under the background of rocks, sea sand and shells, it displays a variety of shocking and dangerous creatures, including hungry sharks and poisonous octopuses. With Panerai's virtual reality glasses, customers can explore the unknown underwater world. During the unveiling, guests can also enjoy Italian liqueurs and cocktails, accompanied by marine-style appetizers.
During the media preview of the unveiling ceremony, the brand showcased its latest work for the first time in Hong Kong: for example, the LuminorDue watch with an expanded blue dial lineup, which further highlights the brand's genes and its special connection with the marine world. LuminorDue's 38mm (PAM00926) and 42mm (PAM00927) models feature a titanium case, a high-tech dynamic material that makes the watch lighter. LuminorDue 45mm (PAM00964) is also made of titanium, equipped with a P.4002 watch factory-made movement, with a 3-day power reserve automatic winding mechanism and an eccentric rotor. The entire watch is located in Noosa The Panerai watch factory of Thiel independently designs and creates.
Panerai Harbour City Pop-up Store
Shop 216, Level 2, Ocean Centre, Harbour City, Tsim Sha Tsui, Kowloon


Arkadia's Australian made Premium Syrups deliver a perfect balance of flavour and sweetness. They are available in high-quality 750-millilitre PET bottles with 24 months' shelf life. Why not add an extra special twist to your coffee, frappe or smoothie for an indulging experience?
Contact Arkadia or your preferred coffee roaster to request a sample pack of its most popular flavours: Vanilla, Hazelnut, and Caramel.
For more information, visit www. arkadiabeverages.com.au or call (03) 9543 3113.


text:
In Celebration of Pride and 340B
In Sponsored Content June 3, 2021 358 Views Sponsored Content
Register Now for June 4th Webinar
The month of June is the start of a magical time across much of the United States. This year's Pride Month brings in a little extra celebratory oomph as we begin to come out on the other side of a lockdown, and pandemic, that has had a profound impact on us all. While it does not appear like there is ever going to be that obvious "all clear" signal that we all desire, slowly but surely, we are starting to move towards the first indications of a truly post-COVID world.
With this past year as perspective, we can't help but think about the many LGBTQ individuals who share a unique perspective, unwavering resilience, and a traumatic collective experience following a disease that directly targeted their community – HIV/AIDS. We each know members of our communities who lived through, suffered and died during the acute phase of the AIDS epidemic. These same individuals, and communities, continue to be disproportionately impacted by the ravages of this terrible illness. While it may no longer be the death sentence that ended the lives of so many vibrant individuals, it remains a serious illness, resulting in a great deal of suffering for many. Combating the health repercussions and social impact of the AIDS virus requires tremendous resources to allow individuals to lead normal, active lives.
So, while June is rightfully a time to celebrate and share pride in the ability of historically marginalized Americans to be truly who they are, to love who they want to love, and to live lives on their own terms – it is also a time for us to remember that this is a group that continues to remain vulnerable to discrimination and to a disease that does not discriminate. And so, the month of June is not just a month of pride and celebration but should also be a month of gratitude and awareness. We should take this opportunity to voice our support for the LGBTQ community and show our gratitude to the people who have dedicated their lives towards serving people who remain vulnerable, disproportionately impacted by AIDS and related illnesses. The Tango team would like to celebrate and give thanks to the Ryan White and STD Clinics across the United States who treat, support, and serve.
Please join Tango on June 4th at 1 p.m. EST for a panel discussion webinar. Our exceptional and dedicated panelists will share personal stories, unique perspectives, and sage wisdom gained through years in the trenches as prominent leaders in the RWC and 340B space.
As we all know, the 340B program remains at risk. It is important for us all to celebrate the positive impact the program has had and to advocate on behalf of its continued viability to ensure that it can continue to benefit so many people across our country. Please join us in support, in celebration, and in gratitude!
https://340breport.com/author/threefortyb/
Visante's Top 10 Issues Facing Hospital & Health System Pharmacy in 2022
A Personal Look at Some of the Nation's Top 340B Lawyers
A Q&A with Two 340B Industry Experts About the Importance of Innovation and a Competitive Edge


text:
The Secret Garden review - blooming charming
With Netflix releasing Rebecca on Wednesday, who'd have thought that a kid's film would be this week's best adaptation about an estate haunted by the memory of the deceased lady of the manor? Written and directed by the team behind Channel 4's...
Theatre Lockdown Special 12: An American rarity, a British savoury, and fresh Apples
Can this weekly lineup really now be three months old? As we move towards at least some degree of relaxation on the social restrictions that have long been in place, the offerings of theatre online continue to afford many a reason not to leave...
Artemis Fowl review - flash bang nothing
It's taken over 18 years for Artemis Fowl to reach the big screen, with Miramax originally buying the rights in 2001. Finally, Disney have brought the world's youngest criminal mastermind to life, but was it worth the wait? Well, the fact it's...
Treasure Island, National Theatre at Home review - all aboard this thrilling adventure story
Swaggering pirates, X marks the spot, a chattering parrot, "Yo-ho-ho and a bottle of rum"? All present and correct. But Bryony Lavery's winning 2014 adaptation of Robert Louis Stevenson for the National, directed by Polly Findlay, also features...
Jane Eyre, National Theatre at Home review - a fiery feminist adaptation
The National Theatre's online broadcasts got off to a storming start with One Man, Two Guvnors – watched by over 2.5 million people, either on the night or in the week since its live streaming, and raising around £66,000 in donations. Let's hope...
Rumpelstiltskin, Sadler's Wells Digital Stage review - spins an engaging yarn for young audiences
The latest in Sadler's Wells' Digital Stage programme – an impressively assembled online offering to keep audiences entertained during the shutdown – is balletLORENT's family-friendly dance-theatre production Rumpelstiltskin. It was...
Four Kids and It review – a family friendly yarn that needs more magic
With over one hundred books to her name and several hugely popular TV spin-offs, including the Tracy Beaker adventures, Jacqueline Wilson takes a no-nonsense approach to children's fiction that reflects the realities of jigsaw families, mental and...
System Crasher review – a compelling portrait of childhood violence and pain
Benni, the central character in German writer-director Nora Fingscheidt's haunting new film, has a life of tragedy and violence. She's the product of a dysfunctional family and an abusive childhood that has left her rage-ridden and incapable of...
I and You, Hampstead Theatre review - now streaming online, this YA play is oddly pertinent
The way that theatres and other arts institutions have leapt into action over the past week, providing a wealth of material online and new ways to connect with audiences, has been truly inspirational. Yesterday, the Hampstead Theatre re-released on...
Onward review - do you believe in magic?
Welcome to New Mushroomton: a fantasy land that's forgotten itself. This is how we're introduced to Pixar's Onward, which is set in a Dungeons & Dragons daydream of suburbia. Director Dan Scanlon's film is a tribute to his late father, but it...
Sex Education, Series 2, Netflix review - the teen sex show we deserved
Netflix's Sex Education has returned to our screens and streams. The show made waves last year for its refreshing take on the teen comedy-drama. It took on abortion, consent and female pleasure — subjects strikingly absent from our actual high...
Brighton Festival 2020 launches with Guest Director Lemn Sissay
This morning the largest annual, curated multi-arts festival in England launched and announced its programme of events. With Guest Director, British and Ethiopian poet-playwright-broadcaster Lemn Sissay, MBE, at the helm, Brighton Festival 2020 is...


text:
My Policy Hub
Improving health is our policy
WHG Insights
ACA Now
1201 - PHSA Section 2704: Prohibition of Preexisting Condition Exclusions or Other Discrimination Based on Health Status
Implementation Status
Statutory Text
Amended by section 10103 of the Manager's Amendment. Prohibits a group health plans and issuers offering group or individual coverage from imposing any preexisting condition exclusions. Effective for plan years beginning on or after January 1, 2014. Additionally, applies prohibition on pre-existing conditions exclusion for those under age 19 – including to grandfathered group plans – for plan years beginning on or after 6 months after enactment.
#Insurance Reform, #Preexisting Conditions
A June 28, 2010 interim final rule published by DOL, Treasury and HHS implements the preexisting condition exclusion provisions generally applicable – per the statute – for plan years beginning on or after January 1, 2014 but with early applicability for those under age 19 (September 23, 2010).
An October 13, 2010 Q&A on the CCIIO website addresses the preexisting condition exclusion applicable to children under age 19. A page on www.healthcare.gov provides general information and links to more details about these provisions as they relate to covering children with pre-existing conditions.
On Nov. 14, coinciding with the President's remarks on the Administration's pursuit of an administrative fix for those receiving policy cancellations and following his apology for those facing such cancellations, CCIIO released a letter to state Insurance Commissioners (White House fact sheet) laying out a transitional policy under which insurers "may choose to continue coverage that would otherwise be terminated or cancelled, and affected individuals and small businesses may choose to re-enroll in such coverage" – without complying with 2014 market reforms detailed on p. 2 of the letter – under a set of specified parameters (see p. 2 of the letter). Prior to the announcement, on Nov. 9, CMS also had released a fact sheet on policy cancellation letters and Marketplace options.
On Nov. 21, the Center for Consumer Information and Insurance Oversight released guidance and standard notices for health plans to use in the individual and small group markets under the Administration's transitional policy for – with state insurance commissioner approval – extending into 2014 non-ACA compliant plans that otherwise would or already have been canceled. Also see a White House blog post and CCIIO Q&A on notices. On Nov. 20, President Obama met with Insurance Commissioners regarding the policy.
On Dec. 2, Rep. Darrell Issa (R-CA), chairman of the House Oversight and Government Reform Committee, wrote to 15 insurers asking about, among other issues, ACA-related plan cancellations and providers no longer in networks. On Dec. 4, the House Ways and Means Health Subcommittee held a hearing that addressed, in part, plan cancellations; among those testifying was the Washington state insurance commissioner. On Dec. 6, the House Oversight and Government Reform Committee held an Arizona-based field hearing, "ObamaCare Implementation, The Broken Promise: If You Like Your Current Plan You Can Keep It" (details).
On Jan. 3, CCIIO released Q&As clarifying eligibility for hardship exemption from the individual mandate for policyholders whose plans have been canceled, noting that "in order to receive [the exemption] and be able to purchase catastrophic coverage, you must submit the hardship exemption form and should submit supporting documentation showing your health insurance policy was cancelled to an issuer offering catastrophic coverage in your area." CCIIO indicates that the agency may contact those not including such documentation; the exemption can be revoked if this substantiation is not provided.
On March 5, CCIIO issued guidance extending, for two additional years (to October 1, 2016), the transitional policy enabling non-ACA-compliant small group and individual plans to continue if state Insurance Commissioners elect. It extended the hardship exemption from the individual mandate for canceled policyholders, through which they also can gain access to catastrophic plans, to the same date.
On Mar. 16, HHS, DOL and Treasury issued a final rule amending the definition of excepted benefits and establishing two pilot programs through which employers may provide certain limited wraparound coverage to individual plans, including those purchased in Marketplaces. One pilot enables limited wraparound coverage only for ACA Multi-State Plans, while the other permits it for "part-time workers who enroll in an individual health insurance policy or in Basic Health Plan coverage for low-income individuals established under the Affordable Care Act.
On Jan. 5, 2017, HHS issued a report finding that between 2010 and 2014, the share of Americans with pre-existing conditions who went without health insurance all year fell by 22 percent, meaning 3.6 million fewer people with pre-existing conditions went uninsured.
On Feb. 15, 2017, CMS released a market stability proposed rule on which comments were due by March 7. Key proposals address special enrollment period verification, guaranteed availability, a shorter annual open enrollment period, network adequacy, revised de minimus variations for QHPs, and revisions to the QHP certification calendar.
''SEC. 2704 [42 U.S.C. 300gg–3]. PROHIBITION OF PREEXISTING CONDITION EXCLUSIONS OR OTHER DISCRIMINATION BASED ON HEALTH STATUS. ''(a) IN GENERAL.—A group health plan and a health insurance issuer offering group or individual health insurance coverage may not impose any preexisting condition exclusion with respect to such plan or coverage.''; and (B) by transferring such section (as amended by subparagraph (A)) so as to appear after the section 2703 added by paragraph (4); (3)(A) in section 2702 (42 U.S.C. 300gg–1)— (i) by striking the section heading and all that follows through subsection (a); (ii) in subsection (b)— (I) by striking ''health insurance issuer offering health insurance coverage in connection with a group health plan'' each place that such appears and inserting ''health insurance issuer offering group or individual health insurance coverage''; and (II) in paragraph (2)(A)— (aa) by inserting ''or individual'' after ''employer''; and (bb) by inserting ''or individual health coverage, as the case may be'' before the semicolon; and (iii) in subsection (e)— (I) by striking ''(a)(1)(F)'' and inserting ''(a)(6)''; (II) by striking ''2701'' and inserting ''2704''; and (III) by striking ''2721(a)'' and inserting ''2735(a)''; and (B) by transferring such section (as amended by subparagraph (A)) to appear after section 2705(a) as added by paragraph (4); and (4) by inserting after the subpart heading (as added by paragraph (1)) the following:
Browse ACA Titles
I-Quality, Affordable Health Care for all Americans
II-Role of Public Programs
III-Improving the Quality and Efficiency of Health Care
IV-Prevention of Chronic Disease and Improving Public Health
V-Health Care Workforce
VI-Transparency and Program Integrity
VII-Improving Access to Innovative Medical Therapies
VIII-Community Living Assistance Services and Supports (CLASS ACT)
IX-Revenue Provisions
About Policy Hub
Wynne Health Group
718 7th Street NW
Copyright © 2021 ‐ Wynne Health Group ‐ All Rights Reserved ‐ Privacy Policy ‐ Terms and Conditions ‐ Log in
Copyright © 2021 · MyPolicyHub Theme on Genesis Framework · WordPress · Log in