text:
\section{Introduction}

Potential models
have been applied to explain quarkonium spectroscopy~\cite{appel}
in cave paintings dating from the mesolithic era of
QCD~\cite{potmod1,potmod2,potmod3,potmod4,potmod6}.
In the beginning, they were based on parametrisations of the
potential~\cite{potmod1,potmod2,potmod5}
which were --- at best --- QCD motivated
and subsequently fitted to
the observed spectrum. During the past few years, however,
a two-body Schr\"odinger-Pauli-type Hamiltonian incorporating
the static potential and
relativistic corrections due to spin dependent interactions as well
as perturbations of the heavy quark propagator around the
static Wilson line has been derived
directly from the QCD Lagrangian to order $v^4$ in the heavy quark
velocity~\cite{EF,EFG,BBMP,baliwachter}.
One-loop matching coefficients with renormalisation group running
between terms within the effective
Hamiltonian and QCD have been
obtained~\cite{chen,baliwachter,balzereit,manohar,soto}.
Non-QCD input has still been required until all
non-perturbative potentials have recently been determined
from quenched lattice QCD by one of the
present authors~\cite{baliwachter,baliwachter1}.
Parametrisations have been fitted to these lattice potentials
enabling Schr\"odinger-Pauli-type solutions to be formed
that are genuine predictions of (quenched) QCD.
The spectroscopy for quarkonia shows similar behaviour to that obtained
using quenched NRQCD; however due to the use of a Hamiltonian
formulation of the problem
the potential approach allows the calculation of a wider range of
states than it is possible within NRQCD,
in a manner that is both accurate and more
robust against finite size effects
(FSE).
Moreover, once the Hamiltonian is obtained, the quark mass can easily be
varied.

We would like to mention that so far retardation effects have been
neglected within the potential approach\cite{volleut}.
However, it appears
likely that such effects, which
have their origin in radiation of ultra-soft gluons, can be
incorporated into the potential formulation in a rather elegant
and straightforward
manner~\cite{pNRQCD}
that should automatically account for spin exotic
states and mixing between quark model and hybrid states~\cite{bali}.
This work indicates that --- at least for the lowest lying
bottomonium states in the quenched approximation
--- such effects are tiny, which explains the good
agreement of our results with Lattice NRQCD predictions.

The obvious drawbacks of the potential approach are
(a) that it cannot easily be extended to higher orders in
the velocity where more and more non-potential type contributions will
have to be included and (b) that --- unlike HQET/NRQCD ---
it only applies to heavy-heavy systems.
Bottomonia systems are the ideal application and ---
having access to all excited states --- we are indeed provided
with much more insight than if we were just able to calculate the
lowest few excitations.

In this paper we shall investigate the major sources of error in lattice
calculations of the bottomonium spectrum.
For simplicity, we will only employ Cornell-type parametrisations
of the potentials, neglecting a weakening
of the effective QCD coupling at small quark separation.
We study finite volume and discretisation effects by solving the order $v^2$
Hamiltonian on (three-dimensional) lattices, varying the physical
volume and lattice spacing.
Moreover, we study the size of relativistic and radiative
corrections and estimate possible quenching effects by simulating
the order $v^2$ and order $v^4$ Hamiltonians in the continuum,
using parametrisations of the potentials that are motivated by fits to
quenched lattice data~\cite{baliwachter}.
We shall argue that, in order to reproduce the observed spectrum correctly,
the unquenched potential must
have a significantly stronger effective Coulomb coefficient at
intermediate distances than
determined within the quenched approximation, even when ignoring
the weakening of this coefficient with the distance in the latter case.

The principal effect of this is that observable quantities
which exhibit a large sensitivity to the short distance
potential (e.g. states of small physical extent or fine splittings)
will yield results that are inconsistent with those obtained
from states that are more sensitive to physics at larger distances.
These discrepancies will depend on the mean radius of the state in a
manner that is far less benign than the na\"\i{}ve
perturbative expectation of an enhanced
slope of the logarithmic running of the coupling
in the quenched approximation would suggest.

The paper is organised as follows.
In Sec.~\ref{Expect} we present some simple theoretical expectations
for the spin averaged spectrum and comment on results from Lattice
spectroscopy investigations in view of these general considerations.
In Sec.~\ref{Method} we discuss the methods used for solving
the Schr\"odinger-Pauli equation both in the continuum and
using a discrete lattice formulation with boundary
conditions imposing various cubic group representations to fix the
orbital angular momentum, before we present our results in Sec.~\ref{Result}.
We start with a discussion of systematic uncertainties imposed by
truncating the expansion of the QCD Lagrangian at a given order in $v$ as well
as due to radiative corrections to the matching coefficients of
operators of dimension higher than four. Subsequently,
results on the quarkonium spectrum as a function of the
inverse quark mass with various effective Coulomb coefficients
around those suggested by quenched and partially unquenched Lattice
simulations are presented. The implications
on the expected $n_f = 3$, $m_u \approx m_d \approx 5$~MeV,
$m_s \approx 100$~MeV
Coulomb coefficient are discussed, and we rationalise both, the calculated
mass dependence of the quenched $1P\,1S$ splitting and the analysis methods
common in lattice heavy quark simulations.
Finally, we proceed to a discussion of the dependence of the results
on the lattice volume and spacing and characterise the likely finite
volume errors and rotational symmetry
restoration properties in the continuum limit of the lattice theory.
In Sec.~\ref{Summary}, we summarise our results and present a brief outlook.

\section{General expectations}
\label{Expect}
Na\"\i{}vely one might expect that prior to a lattice simulation the
lattice resolution $a$, at which the real world will be studied,
is selected. In practice, however, the theory is non-dimensionalised and
simulated at a given value of the bare coupling.
Subsequently, the dimensionful lattice
spacing is determined by matching an observable to its experimental value.
If this observable depends on quark masses, the process of fixing
the lattice scale cannot be disentangled from the problem of
adjusting the quark masses, and simultaneous matching of two or more
quantities to experiment has to be performed.
It is therefore common to either choose a non-hadronic quantity,
such as~\cite{sommer} $r_0$ (which is related to the
static QCD potential) or to choose quantities defined at almost vanishing
quark mass, such as $f_\pi$, to alleviate this problem. Despite
the significant difference between the mass of a charm and a bottom
quark, the spin averaged $1P\,1S$ splittings of
the $\Upsilon$ and $J/\psi$ systems are found to be
essentially the same in experiment. Therefore,
it has been suggested that, in the above mentioned sense, this
splitting was a particularly
good quantity to set the lattice scale $a$~\cite{aida}.

We note that in the potential picture the
spin averaged splittings scale as $\Delta m \propto m^{-\frac{1}{3}}$ for
a purely linear potential and as $\Delta m \propto m $ in the pure Coulomb
case. For a logarithmic potential, the splittings are independent of
the quark mass (see e.g.\ Ref.~\cite{potmod4}).
With a string tension $\kappa\approx 450$~MeV transition from one
of these limits to the other sets in at a separation of order 0.5~fm,
the static potential in the region $0.2$~fm$<r<1$~fm being approximately
compatible with a logarithmic parametrisation, which provides an
explanation of the similarity
between the spin averaged
charmonia and bottomonia level splittings.

It has been reported in quenched simulations, however, that the $1P\,1S$
splitting shows a significant slope as a function of~\cite{boyle,aoki}
$m_\Upsilon^{-1}$. Moreover, both
the $2S\,1S$ and $1P\,1S$ splittings are found to be
almost $20\%$ smaller than the experimental values
if one sets the lattice spacing from light hadronic
quantities~\cite{aida,nrqcd2,manke,ctd,trottier}
like $f_\pi$ or $m_\rho$ or the square root of the
string tension 420~MeV$<\sqrt{\kappa}<$~450~MeV,
as determined from Regg\'e trajectories.
Furthermore, calculations over a mass range extending above bottom
have displayed a steep rise in the splittings~\cite{aoki} in
the $m \rightarrow \infty$ limit, starting somewhat above the $b$ quark.
{}From the potential picture, this can be explained as follows:
as one increases the quark mass beyond the bottom mass, the states
under consideration move deeper into the Coulomb region and
splittings will diverge linearly in $m$, while in the limit of
light quark masses splittings should grow like $m^{-1/3}$. This
suggests that the beauty and charm masses lie within a broad
minimum of the $1P\,1S$ and $2S\,1S$ splittings, the extent of
experimental agreement largely being accidental. Of course in the
limiting cases themselves, the potential picture will not be applicable: at
light quark masses the description as a non-relativistic system
breaks down while at extremely heavy quark masses, retardation
effects will eventually dominate the dynamics~\cite{volleut}.

It has been argued that
the relevant physical momentum scales that affect bottomonia masses
differ from those of light hadronic quantities.
Neglecting
sea quark loops in the quenched approximation alters
the running of the QCD coupling, thereby resulting in
large quenching errors
when comparing quantities determined by different momentum
scales~\cite{aida,ctd,trottier,sesam}.
Indeed, in the presence of two light flavours of
dynamical fermions the disagreement between
mass ratios determined on the lattice and in experiment
appears to be reduced~\cite{sesam,ctd}.
Some authors, therefore, suggest
to adapt the lattice scale $a$ to the system
under consideration in order to reduce quenching
uncertainities~\cite{aida}.

The ``different lattice spacings for different systems'' argument
obviously reduces the predictive power of quenched and
partially unquenched simulations while
it does not even work
consistently within the $\Upsilon$ system:
by integrating a Schr\"odinger-Pauli
equation with quenched
lattice potentials, the $\Upsilon$ $2S\,1S$
and $1P\,1S$ have been found~\cite{baliwachter}
to be significantly smaller than one would have expected from
the value of $am_{\rho}$. Deviations between experimental
and quenched lattice ratios between $m_{\rho}$ and
splittings incorporating
larger radial states like $3S\,2S$ or $2P\,1P$,
however, are found to be small~\cite{baliwachter,sesaminprep}.
The first observation is in agreement with Lattice NRQCD
results~\cite{aida,sesam}.
Unfortunately, NRQCD precision results
are only available for the $1S$, $1P$ and, to a lesser extent, $2S$ states,
such that the above mentioned inconsistencies within the quenched
$\Upsilon$ spectrum are largely hidden behind
statistical errors and, possibly, FSE for
$3S$ or $2P$ states.

We remark that the relevant
exchange momentum will in general not only depend on
the system but also on the state under consideration.
One should also keep in mind that
within the non-perturbative regime universality of the QCD
$\beta$-function is lost.
Therefore, interpreting differences between mass ratios determined within
the quenched approximation and in full QCD as effects of
an altered running of {\em the} strong coupling constant with
{\em one} relevant scale is an overly simplistic
picture. We conclude that neglection of sea quarks results
in a scatter between different scale determinations
of up to 20~\%, a systematic uncertainty
of the quenched approximation that cannot be {\em repaired}
or discussed away.

Present day high precision data on the (partially) unquenched
static QCD potential
is limited to two light quarks with
mass $m_q>25$~MeV.
Apart from one very exploratory study~\cite{mtc},
determinations of relativistic corrections for dynamical fermions
are completely missing.
Within statistical accuracy, data on the static potential
obtained with two flavours of Wilson sea quarks as well as within
the quenched approximation
are compatible with the parametrisation,
$V_0(r) = \kappa r-e/r$,
down to distances as small as $0.2$~fm.
{}From a fit to data with $r\geq r_{\min}=0.2$~fm
one of the authors has obtained $e= 0.292(5)$
in quenched simulations and
$e= 0.352(9)$ in the
two flavour case with $m_u=m_d\approx 50$~MeV~\cite{sesaminprep}.
If we allow for an additional
term, $f/r^2$, to mimic running coupling effects, we end up with
$e\approx 0.32$ and $e\approx 0.37$, respectively.
The latter fits incorporate the running of the Coulomb coefficient to
distances $r\approx 0.1$~fm, significantly less than the mean
radius of $\Upsilon(1S)$, $\langle r^2\rangle^{1/2}\approx 0.25$~fm,
but only affect the parameter $e$ slightly, in
comparison to the
change induced by ``switching on'' two sea quarks.
We conclude that the renormalisation of the effective
intermediate distance Coulomb-coefficient
is the dominant effect of unquenching, rather than the
slightly different running of the coupling with the scale at large
momenta.

For the sake of consistency with Ref.~\cite{baliwachter}
we use the value $e=0.32$  throughout this article
for what we call ``quenched'' while we estimate a value
$e\approx 0.40$ for what we consider to be the real world
with three flavours of light quarks.
It is apparent from both, lattice data on the $1P\,1S$ splitting,
and from the above information on the static potential
that the Coulomb term is indeed underestimated
in the quenched approximation. In what follows, we will investigate
the dominant effect of unquenching by just varying the Coulomb
coefficient in a Cornell potential simulation.

\section{Method}
\label{Method}
Throughout this paper we only use the Cornell-type
parametrisation of QCD potentials, and neglect running coupling effects
which would weaken the interaction at short distance.
This means that we are likely to (slightly) overestimate fine structure
splittings
while the effect on spin averaged splittings is small. Physical states with
small spatial extent like the $1S$ state should be thought of as
being shifted into
the direction of the corresponding prediction at somewhat weaker
Coulomb coupling.
Within this model, we estimate the sizes of various
systematic effects, allowing conclusions on the degree
of accuracy of lattice predictions on the $\Upsilon$ system.

Quenching effects and the importance of relativistic corrections are studied
by solving a continuum Schr\"odinger equation by use of the Numerov method.
Like in Ref.~\cite{baliwachter}, we start from the Hamiltonian,
\begin{equation}
H = 2\left[m + \delta m(m)\right] + H_0 + \delta H_{\mbox{\scriptsize kin}}
+ \delta H_{\mbox{\scriptsize SI}}
+\delta H_{\mbox{\scriptsize SD}},
\end{equation}
with
\begin{equation}
H_0=\frac{{\mathbf p}^2}{m}+\overline{V}(r),
\end{equation}
where
\begin{equation}
\label{potcent}
\overline{V}(r)=V_0(r)-\frac{1}{4m^2}\left\{c_D(m)b-
2\left[c_D(m)-\frac{1}{3}\right]\kappa\right\}\frac{1}{r}.
\end{equation}
The parametrisation,
\begin{equation}
\label{potstat}
V_0(r) = \kappa r-\frac{e}{r},
\end{equation}
corresponds to the static QCD potential, the
additional terms of Eq.~(\ref{potcent})
giving rise to order $v^4$ corrections to the energy levels.
After solving the unperturbed Schr\"odinger equation,
\begin{equation}
\left(H_0-E_{nl}\right)\psi_{nll_z}({\mathbf x})=0,\quad
\psi_{nll_z}({\mathbf x})=\frac{u_{nl}(r)}{r}Y_{ll_z}(\theta,\phi),
\end{equation}
the remaining order $v^4$ relativistic corrections are computed as
perturbations.
The kinetic correction reads as follows,
\begin{equation}
\delta H_{\mbox{\scriptsize kin}}=-\frac{p^4}{4m^3}.
\end{equation}
For the spin independent corrections we obtain,
\begin{equation}\label{potsi}
\delta H_{\mbox{\scriptsize SI}}=\frac{1}{2m^2}
\left\{4\pi e\left[1+\frac{c_D(m)}{2}-d_s(m)\right]\delta^3(r)
-\frac{2e}{r}p^2-\left(\frac{\kappa}{3r}-\frac{e}{r^3}\right)L^2\right\},
\end{equation}
while the spin dependent correction terms read,
\begin{eqnarray}
\delta H_{\mbox{\scriptsize SD}}(r)&=&\frac{1}{2m^2}\left\{
\left[-\frac{\kappa}{r}+ \frac{4c_F(m) (e-h) -e}{r^3}\right]
{\mathbf L\cdot S}\right.\nonumber\\\label{potsd}
&+&6c_F^2(m)\frac{(e-h)}{r^3}T\\\nonumber
&+&\left.8\pi\left[2c_F^2(m)-d_v(m)\right](e-h)
\delta^3(r)\frac{\mathbf
S_1\cdot S_2}{3}\right\},
\end{eqnarray}
with
\begin{eqnarray}
\frac{{\mathbf S_1\cdot S_2}}{3}&=&
\frac{1}{6}\left[s(s+1)-\frac{3}{2}\right],\\
\mathbf L\cdot S
&=&\frac{1}{2}\left[j(j+1)-l(l+1)-s(s+1)\right],\\
 T=
\frac{{\mathbf x\cdot S_1}{\mathbf x\cdot S_2}}{r^2}
-\frac{\mathbf S_1\cdot S_2}{3}&=&
-\frac{6({\mathbf L\cdot S})^2+3{\mathbf L\cdot S}-2s(s+1)l(l+1)}
{6(2l-1)(2l+3)}.
\end{eqnarray}
In the present investigation, we choose to
approximate the matching coefficients by their tree-level
values,
$c_F(m)=c_D(m)=1$ and $d_s(m)=d_v(m)=\delta m(m)=0$,
as it is usually done in
Lattice NRQCD simulations too.
If the quark mass $m$ differs from the gluon momentum cut-off
$\mu$ at which the potentials have been evaluated, radiative
corrections have to be considered\footnote{Results for the one-loop running of $c_F(m)$ can be found in
Ref.~\cite{eichhill}, for $c_D(m)$ in Refs.~\cite{balzereit,manohar}
and for $d_v(m)$ in Ref.~\cite{chen}.
A two-loop renormalisation group improved
result for $c_F(m)$ has been obtained recently~\cite{amoros}.
The binding energy of the $\Upsilon$ ground state is known to order
$m\alpha_s^4$ in perturbation theory~\cite{pineda}.
The Hamiltonian for the unequal quark mass case
can be found in Refs.~\cite{baliwachter,antonio}. $d_s(m)$ can be
obtained from Ref.~\cite{soto}.}.

With relations, such as $\langle nll_z| f(r){\mathbf p}^2|nll_z\rangle
=m\langle nll_z|f(r)[E_{nl}-\overline{V}(r)]|nll_z\rangle$, all perturbations
can be reduced to functions of the expectation values
$\langle r^{\alpha}\rangle$ with $\alpha=-4,\ldots,1$
and $4\pi\langle \delta^3(r)\rangle=|\psi(0)|^2$ and
the unperturbed
energy levels $E_{nl}$.
We use the parameter values of Ref.~\cite{baliwachter},
\begin{equation}
\label{eq:params}
r_0^{-1}=406 \mbox{~MeV},\quad h = 0.065,\quad b =3.81\kappa.
\end{equation}
We can convert $r_0$, defined as the distance $r$ at which~\cite{sommer}
$r^2dV(r)/dr=1.65$, into the string tension,
\begin{equation}
\label{eq:string}
\kappa=\frac{1.65-e}{r_0^2}.
\end{equation}
The above
value of $r_0$ has been obtained by optimising the spectrum with respect to
all experimentally observed bottomonium states. The advantage
of this procedure over a matching of just the two lowest lying
splittings is that this $r_0$ comes out to be in closer
agreement with scales obtained from light hadronic observables, such as
$m_{\rho}$ or $f_{\pi}$. $e$ is varied starting from the
(quenched) value $e=0.32$ in order to estimate sea quark effects while
$m$ is varied between 1 and 15~GeV for investigation of the mass dependence
of splittings. The values of $m$ that optimally reproduce the bottomonium
and charmonium levels (within the quenched set-up) have been found to be
$m_b\approx 4.68$~GeV and $m_c\approx 1.33$~GeV, respectively. An increase
of $e$ by 25~\% results in an increase of these mass estimates
by only 1~\% and 4~\%, respectively.

We expect
electromagnetic interactions to yield an
increase of the parameter
$e$ by $(1/3)^2\alpha_f(m_b)\approx 10^{-3}$ for
$\Upsilon$ states and $(2/3)^2\alpha_f(m_c)\approx 3.5\times 10^{-3}$
for $J/\psi$ states.
thereby having a negligible impact on the spectrum.
$\alpha_f$ denotes the QED fine structure constant. The change
results in an increase of about 2~MeV for a QCD prediction of $m_b$ and
of about 8~MeV for $m_c$.

We estimate FSE
for the $\Upsilon$ system by numerically solving the Schr\"odinger equation
on three-dimensional cubic lattices. For this purpose, we work at
order $v^2$ only and employ the
following definition of the
lattice Laplacian,
\begin{equation}
\nabla^2 \psi({\mathbf x}) = \frac{1}{a^2}
\sum_{j=1}^3\left[\psi({\mathbf x} + a{\mathbf e}_j)+
\psi({\mathbf x} - a{\mathbf e}_j) - 2\psi({\mathbf x})\right],
\end{equation}
which is correct up to order $a^2$ lattice artifacts
(${\mathbf e}_j$ denotes a unit vector in direction
$j$). Note that --- to this order in $v$ --- we use the
standard Schr\"odinger equation,
\begin{equation}
\left[\frac{p^2}{m}+V_0(r)-E_{n}\right]\psi_{n}({\mathbf x})=0,
\end{equation}
with the static potential $V_0(r)$ of Eq.~(\ref{potstat}) only,
instead of $\overline{V}(r)$ of Eq.~(\ref{potcent}). $n$ is to be understood
as a multi-index that completely characterises a given state.
We choose the coordinate system such that the origin is in the
centre of an elementary cube, therefore avoiding problems
with the divergence of $V_0(r)$ at $r=0$.
Throughout the simulations the parameters of Ref.~\cite{baliwachter}
are used:
\begin{equation}
\sqrt{\kappa} = 468 \mbox{~MeV},\quad e = 0.32,\quad m=4.676 \mbox{~GeV}.
\end{equation}

The discretised Hamiltonian is solved by use of
a successive over-relaxation algorithm.
Excitations are accessed via Gram-Schmidt orthogonalisation
with respect to previously obtained solutions. Only one octant
needs to be simulated, and different
orbital states are generated by enforcing combinations of periodic (even)
or anti-periodic (odd) boundary conditions along various lattice
directions.
We use the $z$-axis as our quantisation axis. Thus, we always
apply the same boundary conditions along the $x$- and $y$-directions,
such that four different combinations are realised:
even $x$, even $z$ ($ee$); even $x$, odd $z$ ($eo$); odd $x$, even
$z$ ($oe$); odd $x$, odd $z$ ($oo$). All other solutions can be obtained
as linear superpositions of the solutions obtained in this manner
with eventually permuted
lattice axes.

For a cubic lattice the relevant discrete symmetry group is $O_h$.
States can be classified in accord to the five irreducible
representations $A_1$, $A_2$, $E$, $T_1$ and $T_2$. $A_1$ and
$A_2$ are one-dimensional, $E$ is two-dimensional and $T_1$ and
$T_2$ both are three-dimensional.
The implemented boundary conditions determine the symmetry of the
wave function under reflections with respect to a lattice plane through
the origin.
While this suffices to unambiguously
single out $T_1$ ($eo$), $T_2$ ($oe$) and
$A_2$ ($oo$) states, both $A_1$ and $E$ states fall into the same $ee$
class.

Each $O_h$ state has overlap to various continuum states with
different angular momenta.
In order to allow for an identification
of the continuum spin content, the expectation value $\langle L^2\rangle =
l(l+1)$
has been traced. Moreover, lattice spacing and volume have been
changed and continuum and infinite volume extrapolations performed.
In Table~\ref{tab:rep}, we have listed which states we expect to find within
each set of boundary conditions. $S$ waves can only be
found with $ee$ boundary conditions and $P$ waves only with
$eo$ boundaries. In the latter case, with antiperiodic boundaries in the
$z$-direction, we will only obtain the $l_z=0$ state.
$D$ waves will be generated with both,
$ee$ boundaries (two states, corresponding
to $l_z=\pm  2$) and with $oe$ boundaries (three states of which only the
$l_z=0$ state is possible with odd boundary conditions in the $z$ direction).
Finally, $F$ waves will be obtained in the
$eo$ and $oe$ (three states in each sector, of which we will only find
one in either case) as well as in the $oo$ (one state) sectors.

Lattices with octants of
up to $72^3$ sites
are being realised and lattice spacings down to
$a=0.025$~fm are simulated, enabling us to study both, finite volume effects
and the restoration of rotational symmetry
between different lattice representations with overlap to the same continuum
angular momentum.

\section{Results}
\label{Result}
\subsection{Relativistic and radiative corrections}
\label{correc}

We intend to estimate the uncertainties on spin averaged
order $v^4$ NRQCD level splitting predictions, due to higher order
corrections.
For this purpose, in Fig.~\ref{fig3}, we have plotted the average velocity
$\langle nl|v^2|nl\rangle$ for various states as a function of
the inverse quarkonium ground state mass, $M_{\Upsilon}^{-1}$.
The vertical lines correspond to bottomonium and charmonium. For
bottomonia states, we typically find $\langle v^2\rangle
\approx 0.1$
while for charmonia we obtain $\langle v^2\rangle\approx 0.4$.
Two sources of uncertainties that are common to both, the
potential approach and Lattice NRQCD, exist:
(a) radiative corrections to the coefficients of the NRQCD
Lagrangian and (b) higher order relativistic corrections.
Note that for the moment being our estimates apply
to an exact prediction from
order $v^4$ NRQCD with tree-level matching coefficients.
We ignore errors that are
due to the lattice discretisation or an inadequate representation
of the potentials at short distance by the parametrisation used.
In particular for $S$ wave
and, to a lesser extent, $P$ wave fine structure splittings
we expect such effects to be another significant source of uncertainty.

If we start from the non-relativistic result for a mass splitting,
$\Delta M_{v^2}$, calculated at order $v^2$, the correct relativistic
splitting can be obtained as an
expansion in powers of the typical heavy quark velocity $v^2$,
\begin{equation}
\Delta M = \Delta M_{v^2}\left(1+c_1v^2+c_2v^4+\cdots\right).
\end{equation}
We find values $c_1v^2=0.034(0.036)$ for the
$\overline{2S}\,\overline{1S}$ and $c_1v^2=0.025(0.029)$ for
the $\overline{1P}-\overline{1S}$ bottomonium splittings.
The first numbers refer to the quenched estimate ($e=0.32$) while the
numbers in brackets refer to $e=0.40$. The {\em overline} symbol denotes
arithmetic
averaging of all masses of states with the given quantum numbers;
apparently, the sizes of the correction
terms only weakly depend on quenching.
For the $J/\psi$ system, we obtain
the values $0.103(0.115)$ and $0.070(0.082)$, respectively.
Thus, in both cases we find, $c_1\approx 1/3$.

We have set all coefficients of the NRQCD Lagrangian
to their tree-level values. However, when matching the effective
theory to QCD, radiative corrections come into play.
As long as we are only concerned with the spin averaged spectrum,
$\delta H_{\mbox{\scriptsize SD}}$ [Eq.~(\ref{potsd})] does not contribute.
Therefore, the only uncertainties enter in the terms
of Eqs.~(\ref{potcent}) and (\ref{potsi})
that contain the coefficient $c_D(m)$.
Discarding these terms
results in a shift of
the $\overline{2S}\,\overline{1S}$ splitting of 5~MeV
and 16~MeV in the $\overline{1P}\,\overline{1S}$ splitting
for bottomonia and 2~MeV and 16~MeV
for charmonia states, respectively.
Based on the
one-loop results of Refs.~\cite{balzereit,manohar}, we estimate the uncertainty
in $c_D$ to be as big as 25~\% for $\Upsilon$ states and 100~\%
for $J/\psi$ states\footnote{In Ref.~\cite{baliwachter},
one of the present authors has quoted somewhat
different numbers that were based on the calculations
of Ref.~\cite{chen}. However, an error in the re-parametrisation
invariance relations used in this reference has recently been
discovered~\cite{georgi}.} for simulations on lattices with
resolutions $a\approx 0.08$~fm.

By assuming $c_2<c_1$, which is motivated by the observation that
$c_1\approx 1/3<c_0=1$, we expect the order $v^6$ correction
to be smaller than 2~MeV and 1.3~MeV for bottomonia
$\overline{2S}\,\overline{1S}$ and
$\overline{1P}\,\overline{1S}$ splittings, respectively. In case of charmonia,
we can only roughly estimate the corresponding values
to be 45~MeV and 20~MeV.
Taking the additional uncertainty in $c_1$ due to radiative corrections
to $c_D$ into account, we expect to be accurate within 5--6~MeV for $\Upsilon$
$\overline{1P}\,\overline{1S}$ and 3--4~MeV for $\overline{2S}\,\overline{1S}$
splittings which corresponds to a
relative precision of about 1~\%, while of the $J/\psi$
system we estimate 50~MeV and 40~MeV, respectively, which amounts to
an expected accuracy of only 10~\%.

Unfortunately, the singlet $S$ states for the $\Upsilon$ system
have not been discovered in experiment yet. The triplet levels are
increased by 10(12)~MeV and 6.5(7.5)~MeV in respect to the corresponding
spin-averaged results, obtained at $e=0.32 (0.40)$,
for $1S$ and $2S$ states, respectively.
By allowing
an uncertainty of 25~\% on the matching coefficient
within Eq.~(\ref{potsd}), we estimate cumulated uncertainties of
about 8--9~MeV and 5--6~MeV for bottomonium $\overline{1P}1^3S_1$
and $2^3S_11^3S_1$ splittings, respectively.
Note that a further uncertainty of up to
10~MeV has to be added to
lattice results on the $1^3S_1$ state obtained
around $a\approx 0.08$~fm to account for discretisation
errors of the wave function at the origin~\cite{inprep2}.

The uncertainty in the $P$ wave
fine structure, which by itself is an order $v^4$
effect, is much bigger of course. One might hope --- again by
assuming $c_3<c_2$ --- that
relativistic corrections are suppressed by a factor of order
$v^2$ in respect to the leading order result. This alone would
imply an uncertainty of 10~\% for the bottomonium and 40~\% for
the charmonium fine structure. The uncertainty in radiative
corrections is dominated by the error of $c_F^2(m)$,
which, based on the two-loop calculation of Ref.~\cite{amoros},
we expect to be about 25~\% for bottom quarks and
70~\% for charm quarks. In linearly adding these
two sources of error, we end up with relative precisions
of 35~\% and 110~\% for order $v^4$ $\Upsilon$ and $J/\psi$
fine structure splitting predictions, respectively, i.e.\ the predictive power
for the charmonium fine structure is {\em zero}.
However, meaningful results can still be obtained for ratios of
fine structure splittings since these turn out to be (almost)
independent of
the matching coefficients.

\subsection{Mass dependence and quenching effects}

As has been argued above, when the quark mass is increased quarkonia
states move deeper into the Coulomb region and, with $m$ being
the only remaining dimensionful parameter, all splittings will
eventually diverge linearly with the quark mass.
This can be seen from Fig.~\ref{fig1} where we compare
the $2S\,1S$ splitting (calculated at order $v^2$)
at a quark mass $m=5$~GeV with that
at $m = 15$~GeV. Of course, this also means that harder and harder
gluons will obtain momenta lower than the (diverging) ultra-soft scale,
$mv^2$, and the potential approach will loose validity, due to
significant retardation effects. If we ignore this problem for the moment
being, for very heavy quark mass we would expect the $2S\,1S$ and
$1P\,1S$ splittings to become degenerate and
diverge like,
\begin{equation}
M(2S)-M(1S)=\frac{3}{16}e^2m.
\end{equation}
The situation is visualised in Fig.~\ref{fig2} for the unquenched case.
The dotted curve is the expectation for a pure Coulomb potential
which will asymptotically be approached by the two other curves as
$m$ is increased.
Around the bottom quark mass this pure Coulomb contribution amounts to about
20~\% of the splittings while for the charm quark mass it contributes only
slightly more than 5~\%.
A similar divergent behaviour is expected to set in for the
$3S\,1S$ and $2P\,1S$ splittings at somewhat bigger quark masses.

In Fig.~\ref{mass1}, we display the dependence of the ratio,
\begin{equation}
R=\frac{M(2^3S_1)-M(1^3S_1)}{M(\overline{1^3P})-M(1^3S_1)},
\end{equation}
on the inverse quarkonium ground state
mass for various values of the Coulomb strength.
For this purpose, we operate at fixed $r_0=406$~MeV [Eq.~(\ref{eq:params})]
and adjust the string tension in accord with Eq.~(\ref{eq:string}).
The upper curves correspond to the order $v^2$ results, the lower curves
to the order $v^4$ predictions.
The Figure suggests a value $e\approx 0.40$ for real world QCD,
which is somewhat larger than the $n_f=2$, $m_u=m_d\approx 50$~MeV upper
limit $e=0.37(1)$ from a fit to a parametrisation that incorporates
an $f/r^2$ term.
Given the observed quark mass and flavour
dependence~\cite{sesaminprep,cppacs},
the value $e\approx 0.40$ appears to be very reasonable.
Within the systematic uncertainties discussed above, the
experimental value of $R$ for the $J/\psi$ system
is compatible with this choice of $e$ too.
We obtain a quenched ($e=0.32$)  bottomonium estimate,
$R\approx 1.38$ which, while agreeing
with Lattice NRQCD results~\cite{nrqcd2}, disagrees
with experiment. The failure of
the quenched potential to reproduce the observed
$\Upsilon$ spectrum
has also been noticed in Ref.~\cite{mich}.

In Fig.~\ref{mass2}, we display the splittings between
the $1^3S_1$ $\Upsilon$ ground state and $2^3S_1$ and $3^3S_1$ states
(solid curves) as well as
$\overline{1^3P}$ and $\overline{2^3P}$ states (dashed curves)
for three values of the Coulomb coefficient, calculated to order $v^4$.
All splittings decrease
slightly with increasing quarkonium mass until they reach a
turning point, after which they start to diverge. The position of
this point critically depends on the level;
for physically larger states it is shifted towards
higher masses. It also depends
on the strength of the Coulomb coefficient which explains why
$R$ reacts in a very sensitive way towards quenching.
While most level differences can be reasonably well reproduced with
values $0.40\leq e\leq 0.45$, all splittings with respect to
$1^3S_1$ are considerably underestimated, an effect that
cannot be absorbed into redefinitions of the quark mass
$m_b$ and the scale $r_0$ alone. We also note that differences between
excitations and the $2^3S_1$ or $\overline{1P}$ levels exhibit
a reduced dependence on $e$, compared to the
splittings with respect to the physically smaller $1^3S_1$ state that are
displayed in the figure.

By incorporating a weakening of the QCD coupling at shorter
distance into the parametrisation of the interaction
potential~\cite{eichq},
the prediction can be brought in line
with experiment within the estimated uncertainties of
Sec.~\ref{correc}. The $1S$ state turns out to be
most sensitive towards the running of the coupling.
In quenched Lattice NRQCD simulations~\cite{nrqcd2},
after adjusting the scale
from the $2^3S_11^3S_1$ and $\overline{1P}\,1^3S_1$ splittings,
all other level spacings have been found to be overestimated,
and this despite the fact that
our study of FSE suggests that the NRQCD $3^3S_1$ mass is underestimated
by up to 50~MeV on the finite simulation volume.
The potential results suggest that the
disagreement within the $\Upsilon$ spectrum
as well as between determinations of the lattice spacing
from light hadronic quantities and quarkonia level splittings will
indeed be reduced in unquenched simulations.
A determination of the minimal lattice resolution required to
resolve the running
of the QCD coupling sufficiently well for a precision determination of
$\Upsilon$ levels is the subject of an ongoing study~\cite{inprep2}.

In Fig.~\ref{mass3}, we investigate the $1^3P_2\,1^3P_0$ (solid
curves) and $1^3P_1\,1^3P_0$ (dashed curves) fine splittings
as a function of the inverse $\Upsilon$ mass for three values of
the Coulomb coefficient. For $e=0.40$, we underestimate
experiment by a factor of almost {\em two}.
If we had included a running coupling
into our parametrisation, the predicted splittings might have been
even somewhat smaller.
For lattice spacings 0.067~fm$ <a<0.092$~fm, by assuming (somewhat
arbitrarily) an ${\overline{MS}}$-scheme gluon
momentum cut-off $\mu=\pi/a$,
we obtain a one-loop estimate $1.06<c_F^2(m)<1.13$~\cite{baliwachter},
a range far away from the required 80--90~\% correction. This result
indicates, if we accept the conjecture that the spectrum
should be described by QCD, that higher order contributions to
the matching coefficients are important.
As expected, predictive power
of the potential approach (and Lattice NRQCD) on the fine structure
is indeed limited by a huge systematic
uncertainty. Note that the
difference has nothing to do with uncertainties in ``tadpole'' factors
since a non-perturbative renormalisation of
lattice results with respect to the continuum is included into the
parametrisations published in Ref.~\cite{baliwachter}.
We expect to be accurate within 10~\%
for ratios of fine structure splittings, though.
Indeed, the ratio
of the two splittings at $e=0.40$ comes out to be
$\rho\approx 1.56$, compared to the experimental value $\rho=1.66$.

\subsection{Finite size effects}

In this Section, we will investigate FSE on
the spin averaged spectrum for the quenched case. For this
purpose, we restrict ourselves to the order $v^2$ Hamiltonian.
In Fig.~\ref{rad}, we display the root mean squared
radii of various wave functions for $e=0.32$ and $e=0.40$. Since the spatial
extents of the states
are apparently only weakly affected by the change in $e$,
FSE in unquenched simulations are likely to behave in a very similar way,
up to string breaking effects.
FSE on the fine structure are expected to be negligible due to the short range
nature of spin interactions\footnote{Only the ${\mathbf L\cdot S}$
term of Eq.~(\ref{potsd}) contains a long range $1/r$
interaction. This contribution, however,
is numerically tiny.}. Note that all effects that we will discuss
are entirely due to squeezing of the wave
function and the presence of mirror charges on a torus.
In lattice simulations additional sources of
FSE in general exist and the behaviour of the
quark propagator itself might be affected by the volume.
Our prejudice, however, is that for heavy quarks such an effect
can be neglected, as long as one remains comfortably separated from the
deconfinement transition. This is definitely the case
on volumes of $(1.5$~fm$)^3$.

In Fig.~\ref{fse1}, we investigate the effect of a finite volume onto
various splittings. The results have been obtained
with lattice spacings $a=0.025, 0.05,0.1$ and 0.2~fm and are extrapolated
to the continuum limit.
Note that on the cubic lattice, the $1D$ state exists in
two representations, $1T_2$ and $1E$, that will only become degenerate
in the infinite volume continuum limit.
Obviously,
the spectrum is very much affected by the box size for a
lattice extent $L<1.5$~fm
while for $L>2$~fm most levels have effectively approached their
infinite volume limits.
However, for the $3S$ level an extent as
big as $2.5$~fm is required.
Another representation of the data is displayed in Fig.~\ref{fse2}
where we show $\delta M(L)=M(L)-M(\infty)$ as
a function of $L$.
In Table~\ref{tab:fse} we display the minimal lattice extents
$L_{\mbox{\scriptsize 3 MeV}}$ at which FSE were found to be
smaller than 3~MeV for various states. For this purpose, the box size has been
increased in steps of 0.05~fm.
We have also included the root mean squared radii of Fig.~\ref{rad}.
We find a linear behaviour,
$L_{\mbox{\scriptsize 3 MeV}}=a\langle r^2\rangle^{1/2}+b$
with $a\approx 2.25$ and $b\approx 0.65$~fm.

The finite size behaviour of the $1S$ level
is well parameterised for $L>1$~fm by a polynomial in $L^{-3}$,
\begin{equation}
\delta M(L) = \sum_{i=1}^4\left(\frac{a_i}{L}\right)^{3i},
\end{equation}
with
\begin{equation}
a_1=-0.088 \mbox{~fm},\quad
a_2= 0.477 \mbox{~fm},\quad
a_3=-0.712 \mbox{~fm},\quad
a_4= 0.717 \mbox{~fm}.
\end{equation}
The leading order coefficient is found to be rather small,
compared to those of higher order correction, which is consistent
with the fact that FSE set in rather suddenly.
Parametrisations for other states are consistent with small
coefficients of $L^{-3}$ terms
too. While the finite size behaviour for $n=1$ states
is monotonous, this is not the case for radial excitations anymore.
In particular, the result for $3S$ (triangles) suggests
that for some states infinite volume extrapolations
of finite volume data might become dangerously non-trivial.

In Fig.~\ref{fse3} we display the $2P$ wave function, obtained
on an $a=0.05$~fm lattice for various lattice extents, varying from
0.8 up to 2~fm. We show a cross section through the $x-z$ plane at
$y=0$. Of course, the wave function vanishes within the plane $z=0$ and
exhibits approximate rotational symmetry around the $z$-axis.
{}From Fig.~\ref{fse2}
one sees that the energy decreases up to 1.3~fm and increases
again thereafter, until a second turning point is approached
around 1.7~fm. From Fig.~\ref{fse3} we conclude that the second node
of the wave function only fits onto the lattice for an extent slightly
bigger than 1.2 fm, which explains the first turning point, while
the second maximum of the wave function only starts to fit onto the lattice
for $L>1.6$~fm,
giving rise to the second turning point.

In Figs.~\ref{fse4} and \ref{fse5} we display cross sections through
the $1D$ wave function in the $E$ representation within the
$x-z$ and $x-y$ planes, respectively.
In Figs.~\ref{fse6} and \ref{fse7}, we show another $1D$ wave
function in the $E$
representation.
The energies of these two states are identically degenerate
on all volumes. Finally, in Fig.~\ref{fse8}, we display
a $1D$ wave function in the $T_2$ representation. The wave function
vanishes at $x=0$ and $y=0$. Interestingly, Fig.~\ref{fse8}
looks very much like a
rotated version of Fig.~\ref{fse4}.
On any finite lattice, we find the $1T_2$ energy
level to differ from that of $1E$, even after the continuum extrapolation.

\subsection{Finite lattice spacing effects}
We investigate the restoration of the continuum symmetry as
the lattice spacing is reduced. We pay particular interest to
states within different representations of the cubic symmetry group $O_h$
that are expected to contain the same $O(3)$ spin content. For instance, at
a lattice spacing $a=0.1$~fm and infinite volume we
find the $1T_2$ state to be by 4~MeV heavier than the $1E$ state.
Unlike FSE, finite $a$ effects
critically depend on the form of the action employed. With our
discretisation of the Laplacian, we would expect order $a^2$ effects
to leading order. Note that in our simulation, we have used a
continuum parametrisation of the static QCD potential. In a lattice
simulation, we would only obtain such a potential with a perfect
gauge action. In general, one would expect the static potential to
suffer under discretisation errors too. Insofar, the
results stated here should be understood as mere lower limits on
the discretisation errors of ``real'' lattice simulations
of the $\Upsilon$ spectrum.

As an illustrative example, in Fig.~\ref{finite3s}, we display the spatial
structure of the $3S$ state for various lattice spacings. While the
general structure of the wave function is still quite well reproduced,
even at $a=0.2$~fm, the peaks themselves are not very well sampled anymore.
In Fig.~\ref{finitea1} we extrapolate $S$ and $P$ states to the continuum
limit. We observe that at finite lattice spacings all levels are
somewhat underestimated --- except for the $1S$ level which turns
out to be
slightly overestimated. Moreover, with increasing radial excitation
$n$, the slope
of the extrapolation in $a^2$ decreases. The lines have been obtained from
fits to the $a=0.025$, 0.05 and 0.1~fm data points. This region is
enlarged in Fig.~\ref{finitea2}.

We interpret the overestimation
of the $1S$ level to be connected to the fact that we placed the origin
--- and therefore the singularity of the Coulomb potential --- at
the centre of an elementary lattice cube. As we increase the lattice spacing,
the $S$ waves sample less and less of the potential around the singular
region and, therefore, we underestimate this negative contribution to the
total energy. The same argument holds had we taken a potential measured
on the lattice, instead of the continuum parametrisation, since in this case
the singularity would have been naturally
cut off by the lattice spacing too. The
decrease of the slope of the extrapolation with increasing number of nodes
of the wave function can be explained by an underestimation of the kinetic
energy due to the reduced curvature on a coarse lattice.

In Fig.~\ref{finitea3}, we investigate how degeneracies of
different representations of $O_h$ that correspond to the same
$O(3)$ spin content become restored in the continuum limit
for $1D$ and $1F$ states.
The $D$ state in the $T_2$ representation suffers less under both, finite
$a$ effects and FSE than that in the $E$ representation. This is possibly
due to the less complex structure of the wave function (Fig.~\ref{fse8}).
We observe the same for $F$ wave functions in the $A_2$ representation.
While all states are in nice agreement with the leading order $a^2$
expectation up to a resolution $a=0.1$~fm, higher order terms have a
considerable effect at $a=0.2$~fm. This is in particular so for the
$1A_2$ state.

\section{Conclusions}
\label{Summary}
We confirm that ratios of spin averaged bottomonium level splittings
react in a sensitive way towards quenching.
The main origin of this sensitivity is a renormalised
overall-value of the intermediate energy
effective QCD coupling, rather than an
altered running of the coupling between different short distance
scales.
We find that the extent of agreement of spin averaged
$2S\,1S$ and $1P\,1S$ splittings between the
$\Upsilon$ and $J/\psi$ systems is somewhat accidental. Around the
mass of the charm quark the slope of these splittings as a function
of the inverse quark mass is quite significant but compensated for by
a divergent term that gains influence within the region of the
bottom quark mass.

We have estimated systematic uncertainties of calculations
of quarkonia level splittings based on order $v^4$ NRQCD
due to ${\mathcal O}(\alpha_s v^4,v^6)$ correction
terms. We end up with estimated accuracies of 1--2~\% and 10~\% on
spin averaged $\Upsilon$ and $J/\psi$ level splittings, respectively.
For the fine structure, our estimates are 35~\% and a factor {\em two},
respectively. The main sources of uncertainty in all cases are radiative
corrections to the matching coefficients of dimension five and six
operators within the effective Lagrangian, rather than
higher order relativistic
effects. Unless non-perturbative matching methods become available,
we have little control over the bottomonium fine structure.
By incorporating existing one- and two-loop
results the uncertainty can be somewhat
reduced. However, a comparison of the predicted fine structure
with experiment indicates that even higher order contributions are
significant and likely to exceed our estimated effect of
25~\%. A slow
convergence of perturbation theory
is indicated by a recent two-loop calculation of $c_F(m)$ too~\cite{amoros}.

We investigated finite volume effects, which we expect to be smaller
for quarkonia than for light mesons. Nonetheless, even for
bottomonia, a linear lattice extent bigger than 2~fm is advisable, at least
if one is interested in radial excitations, such as the $2P$ or $3S$
levels.
Except for the $1S$ state, we failed to find simple parametrisations
of the finite size behaviour of energy levels, based on superpositions
of a power series in the inverse spatial volume, and contributions that are
exponentially suppressed. A general result, however, is
that the coefficients of terms proportional to $L^{-3}$ come out
to be smaller than those that accompany
higher order corrections, which results
in a rapid reduction of FSE, once a critical volume has been by-passed.
We regard this result as relevant for all mesonic physics on the lattice.

Finally, we investigated finite lattice spacing effects. A non-vanishing
spacing $a$ is required in lattice simulations of
effective field theories to provide an ultra violet
cut-off for gluon momenta, which means that the continuum limit cannot be
taken. An unwanted by-product of the lattice regularisation is
the violation of the continuum rotational symmetry and dispersion
relation. By parameterising the potential, obtained at finite lattice spacing,
with a continuous rotationally symmetric curve and subsequently solving
the Hamiltonian in the continuum as well as on discrete lattices, we have
qualitatively investigated the finite $a$ behaviour.
We find it worthwhile to simulate Lattice NRQCD --- where one is confined
to lattice spacings in the region of the inverse quark mass ---
with different gluonic
and fermionic actions and in particular
to realise $D$ waves in both possible
representations of the cubic symmetry group to gain control over
discretisation errors.

Solving the Schr\"odinger-Pauli equation
with lattice potentials on finite volumes provides us with
a powerful tool to predict finite size effects
in lattice simulations and to optimise smearing functions.
The next step will be to extend the method to heavy-light systems
within a Bethe-Salpeter framework which is theoretically not
as rigorously founded as the potential approach for quarkonia
but should
still yield very valuable information on finite size
effects and wave functions, which can then be used in
lattice spectroscopy or determination of decay matrix elements.
Another extension is the inclusion of
retardation effects and incorporation of a running coupling into
the parametrisation.
Work along these lines is in progress.

\acknowledgements
GSB has been funded by the Deutsche Forschungsgemeinschaft
(grants Ba1564/3-1 and Ba1564/3-2) and thanks
the Department of Physics and Astronomy at the University of Glasgow
for providing an inspiring atmosphere when this project was started.
GSB acknowledges helpful discussions with Nora Brambilla, Joan Soto and
Antonio Vairo. PB has been funded by PPARC (grant PP/CBA/62), and wishes
to thank the hospitality of the University of California, Santa Barbara,
where some of this work was carried out.
All computations have been performed on a 64~MB, 133~MHz Pentium PC.
We would like to express our gratitude to everyone who has contributed
to the development of Linux, the GNU compilers and gnuplot.

redpajama_set_name: RedPajamaArXiv


My friend Kira Corser, an artist, teacher, painter, speaker and lover of the ocean, planned an event today at the museum near the Monterey Wharf.
It was all about her passion: saving the oceans by way of using the arts.
My super supervisor, Paulette Lynch, articulated how the Arts Council for Monterey County uses Arts as the answer to societies problems: all of them. She brought home the fact that saving the oceans and other societal woes are now our children's problems and the Arts Council holds art classes in various parts of the Monterey County, to answer some of those issues. What the children learn, is taken home to educate parents and younger siblings. There are classes in drama, dance, music and writing, that engages children from improvised neighborhoods and affluent ones, as well.
And Ellen Martin, the executive director of First Night spoke passionately about how the organization First Night involves children in arts that teach the importance of saving the ocean. Her many projects uses plastic bottles and plastic bags and tops of bottles and lots of other trash items to create beautiful objects that reflect marine life. Children learn about saving the oceans as they construct the objects, she said.
There were two other speakers, who were on the side of science and they expressed their agreement that arts and science needs to support one another, and there are many ways that is accomplished.
One example one scientist used was to use humor to teach folks how not to get close to marine animals. Instead of the usual legal and unfriendly signage that is more often used to keep people away from marine life, the picture was an artistic showing of a mans legs coming out from under a marine animal with the sign: don't let this happen to you. It teaches the danger in a humorous way, and encourages folks to respect animal life. The real lesson here, however, was to demonstrate how artists and scientists work together for a common goal.


text:
GizmoLead
SanDisk unveils Ultra Dual USB Drive with micro-USB and USB 2.0 connector
SanDisk has launched SanDisk Ultra Dual USB Drive, a USB flash drive featuring both a micro-USB and a USB 2.0 connector.
The SanDisk Ultra Dual USB Drive is available worldwide in 16GB to 64GB capacities for a price of $19.99 to $49.99.
The SanDisk Ultra Dual USB Drive is designed for Android smartphone and tablet users who need an easy way to move content such as photos and videos from their mobile devices. The drive allows users to safely store and backup files, free-up space, or simply transfer multimedia between their smartphones, tablets and computers.
The SanDisk Ultra Dual USB Drive provides a convenient way to transfer content via an Android-powered smartphone or tablet's micro-USB port and a computer's USB connection.
While other methods of transferring files from a mobile device to a computer require wires, applications or a wireless set-up, the SanDisk Ultra Dual USB Drive simply needs to be connected to a mobile device supporting USB on-the-go (OTG)1 to access up to 64GB2 of 'plug and play' storage capacity.
SanDisk is making content management even easier with the SanDisk Memory Zone app, available for download on Google Play. With the SanDisk Memory Zone app, users are able to better organize files stored on internal and external phone memory for management, viewing, copying and backup – further easing the hassle of freeing up the memory on their mobile device.
editor@gizmolead.com
Ultra Dual USB Drive
The race to achieve quantum supremacy, explained
Anand - October 29, 2019
In a recently published paper, Google claimed it had achieved quantum supremacy – a milestone in quantum computing – which is the ability of...
What we know — and what we still don't — about...
The next big thing in space? Internet-beaming satellite constellations
OpenAI's GPT-2 seems to understand the world, except it doesn't
Will ISRO's Gaganyaan lift India's stature in space?
Apple may launch iPad Mini and cheaper iPad by July
gizmolead - January 21, 2019
Apple is planning to launch an iPad Mini and cheaper entry-level iPad by July, DigiTimes, a Taiwanese website, reported. Apple has shipped 9.7 million tablets...
Spending in app stores to cross $120 bn in 2019
Consumer spending in app stores is expected to cross more than $120 billion in 2019 against $101 billion in 2018, according App Annie. Consumers downloaded 194 billion apps...
YouTube clarifies rules against posting videos of dangerous pranks
YouTube has clarified rules against posting videos of dangerous pranks, as risky challenges prompt people to video themselves doing things like biting into laundry soap or...
CTA reveals consumers buying $398 billion tech products
gizmolead - January 7, 2019
U.S. consumer technology industry, which includes streaming services, will grow 3.9 percent to $398 billion in retail revenues, according to the Consumer Technology Association...
Huawei punishes employees for iPhone tweet blunder
Huawei has punished two employees for New Year greetings sent on the China smartphone maker's official Twitter account using an iPhone from rival Apple, Reuters...
Instagram bug triggers change to feed, fans didn't like
gizmolead - December 28, 2018
Facebook Inc's photo-sharing social network Instagram said on Thursday it has fixed a bug that led to a temporary change in the appearance of...
© 2020 Kizhakedath Media Services. All rights reserved.

redpajama_set_name: RedPajamaCommonCrawl


text:
Internal Memos #2 – Silver Lining & Lessons of Mic's Implosion
(note: These are internal memos I send out to my team of ~ 70 FTEs, you may find them interesting).
Last week, digital media company Mic shut down abruptly, in essence. Technically it sold for $5M to Bustle, which was founded by former co-founder of Bleacher Report Bryan Goldberg. But after raising $60M in funding and being valued on paper at over $100M, for all intents and purposes, Mic shut down.
I met the founders of PolicyMic way back in 2012, when they presented at the Next Big Thing in the Paley Center when I more or less lived in NYC.
Why this is pertinent to us:
I haven't commented much on the news as it was hard to find any silver lining… but I think a week after, the less obvious takeaways and lessons are more evident.
Mic's challenges speak more to a few specific things:
1) journalism/news,
2) chasing scale, trying to do too much (too many verticals),
3) venture/private equity-funded media companies
4) platform reliance.
How are we different: Well, aside from the fact that we didn't rent two floors in World Trade Center & didn't raise $60M (we never raised anything).
1) This article from Washington Post talks a lot about Mic's impact on journalism… but the best observation is (not surprisingly) in the comments:
"If a kid wants to study journalism and cut their teeth in that industry then more power to them. But the economics and supply-demand in this industry, while never fantastic, just isn't there anymore. For every one person who makes a solid living, there are myriads who make little to nothing and end up walking away from the career to make ends meet. Art, drama, acting, singing, dance, all in the same category. Frankly, it's hard to imagine parents paying or kids taking out loans for this sort of degree but some do, which is fine, their money. This said, it's no mystery or secret that like art, acting, etc, journalism is a tough business to get into and make a solid living."
It's true that if the web democratized publishing & production, it blew the lid off of "journalism" where anyone and everyone could be a journalist, in the loosest sense of the world. Ironically, Bustle's CEO Bryan Goldberg's first company Bleacher Report capitalized on that very trend. So the fact that he is now scooping in & buying the remnants of Mic – which wanted to "re-invent" journalism, is ironic, to put it mildly.
2) Like every other venture-backed media company, Mic embraced other verticals, chasing "scale."
"Since late 2013, Mic has launched World, Identities, Music and Sports sections, in addition to their existing Policy, Arts, and Live News sections. Mic will debut a new data visualization department in the coming weeks and they are in the midst of hiring editors and writers for new sections, including Science, Health, Technology, and more."
That's when according to Rafat Ali (founder of PaidContent, the original blog covering digital media news), they signed their contract of irrelevance. Rafat goes on to comment about the general state of media:
"Everyone I am talking to has consensus on this: bottom is falling out of consumer digital media, and it is really really bad out there for venture backed (or even indie) online media cos. It seems to be coming apart faster than I've ever seen in my two decades of covering this."
I don't disagree with what Rafat is saying, but I think the key thing to note is that applies to unprofitable, venture/PE-backed media companies. That doesn't mix, because you can't really scale content easily, nor should you. I've joked about this with Rafat, but it's worth noting that when I started WatchMojo and would ask Rafat to write about us, he'd tell me to follow-up when we'd raise capital. He graciously admitted feeling a bit bad about that, but the point I want to make is: We in the media and industry falsely fetishize companies that raise capital and congratulate them when doing so, even though oftentimes, THAT's when the march to obsolescence begins for a content creator: when you have to prioritize investors over users (readers/viewers/listeners), clients and your employees who are creating the content.
Indeed, today this article by Vanity Fair does a wonderful job recapping all of the malaise
"But everyone else seems to operate on a relentless pivot schedule. "It's a moment of real pressure," one digital media executive told me. "My sense is, it's tougher times for everybody." Summing up the latest portents, a veteran digital-media strategist warned, "I think this is the tip of the iceberg. I think it's gonna get worse, not better." Tony Haile, founding C.E.O. of the Web-analytics provider Chartbeat, echoed that sentiment. "No one's looking forward to this Q1," said Haile, whose latest project is a publisher-friendly subscription ad-blocking service called Scroll. "You've got that kind of thing going on where everyone's for sale." (…)
And yes, those are the higher-profile ones that industry publications cheerlead, talk up, only to trash and bash down… but the main gem is the following:
"The stakes are arguably the highest, it appears, for the much ballyhooed cabal of independent, venture-funded, super-scale companies, such as Vice, BuzzFeed, and Vox. Reacting to Peretti's confederacy-merger proposal, one prominent founder and C.E.O. wondered whether there was "a problem for the whole space," or "a problem for a handful of companies that really over-raised and over-expected and are now trying to re-adjust." Consumer spending is up, and billions of dollars are being sunk into content, this executive noted, and yet "you have this little pocket of the universe looking desperate. So the reality is: is there a problem in the digital-media space overall, or a strategy problem for a certain set of companies?" In a somber parting memo on the day of Mic's mass layoffs, outgoing publisher Cory Haik lamented the current state of the media universe: "Our business models are unsettled, and the macro forces at play are all going through their own states of unrest. If anyone tells you they have it figured out, a special plan to save us all, or that it's all due to a singular fault, know that is categorically false."
How are we like them/how are we similar:
4) to quote Animal Farm, not all platforms are created equally. YouTube is part of Google, the most powerful advertising system ever created. Google is a fairly mature ecosystem relative to YouTube, but even YouTube has basically had ten years to develop and master its platform. Facebook is still trying to determine what role – if any – video will play at scale, over time. Yes right now video is central to its PR war drum… but over time, it may not be. Each month it seems to change its execution and tactics in video… but because Facebook provides massive audience reach, companies dive in… and venture/PE-backed firms go all in, head first. It's important to note that Facebook remains a child/teen in video, and one should only dip their toes. When you see Jellysmack and First Media boast of high reach on Facebook, it's wonderful… but it's awfully suspect of what Buzzfeed and Mic were saying not too long ago.
[Added later, but mentioned in previous posts] There's also the more fundamental difference in philosophy: Google's DNA is all about sending out traffic, knowing it will get more over time. Ditto revenue share with publishers via AdWords/AdSense. Facebook's Mark Zuckerberg built a system that sucks in all traffic, watch time, and revenues by conditioning brands, publishers and yes, video producers to pay it for reach. Why on earth would he ever reverse that structure and pay material revenue out? This is why Watch was created, to retain as much Feed revenue.
So yes, we at WatchMojo want to diversify in terms of verticals, genres, formats and platforms… but let's be realistic that there may not be a pot of gold at the end of every rainbow.
Do you need to read these articles?
The WaPo article is really interesting if you care about journalism… the Vanity Fair article gives a great digest of what's happened to the digital media industry but adds a good amount of cynicism about the recent panic mode journalism (ironically).
Ultimately, the silver lining is "beware the institutional imperative" to blindly follow others to get written up in industry publications… it's almost better to avoid it all!


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Members of St. John the Evangelist parish are ready to minister to varied needs of their own parish family as well as the needs of the wider community and Church. Just as members of a family come together to help one of their own, we serve those who are hurting or in need, doubting or seeking salvation. Our parish family also comes together to celebrate, thank and to return God's gifts - all are needs of parishioners.
"...Amen I say to you, whatever you did for the least of my brothers, you did for me." Matthew 15:40
St. John the Evangelist parishioners stand ready and eager to collectively wrap our arms around our brothers and sisters when they suffer in trial and / or celebrate special events in their lives. Parishioners seek the parish family as a primary community to serve and to be served - to give and to receive. St. John the Evangelist is a place where service is appreciated and utilized for the good of the Church. But members of our parish family recognize that they also have a need to give beyond their own members only. They have a need to give in the diocese, the community and the Universal Church. The pillar of service is an opportunity for the parish to put into concrete practice the other three pillars of hospitality, prayer, and formation.
In this ministry parishioners help with ongoing projects in the front office such as bulk mailings, data entry, copying and collating, placing phone calls, and preparing bulletins and newsletters.
The parish library is located right off of the gathering space in the church. There are many great Catholic resources from Papal Encyclicals to works from the most recent Catholic aughots. They are all available to peruse and borrow. Those that help with this ministry keep the library items shelved and organized.
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This ministry helps to keep the information and photos on the parish website and social media accounts current and attractive. The ability to write code is not required for this ministry but would be beneficial.
Offertory Collection
Our parishioners generously contribute their financial resources to the operations and mission of our parish family. Detail-oriented people are needed to count the offering collected during weekend Masses and prepare the deposit for the bank.
Church Flower
The church is decorated to enhance each liturgical season. Members of the flower committee plan the decorations for the season, order flowers and come together to put everything in place.
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This ministry includes the upkeep of the gardens and trees that surround the parish buildings, cemetery and property boundaries. If you have a love for gardening this ministry could use you to help spread joy through stewarding creation.
It takes many hands to keep our church looking clean! The parishioners who clean the church are on a weekly rotation, approximately twice a year. There is an established routine to follow that includes cleaning, dusting, mopping, and straightening the church to an acceptable condition.
During the winter months it can become dangerous in our parking lot and on our sidewalks for our parishioners. This ministry is one of service and hospitality as they work diligently to clear the snow and ice to help make it safe for parishioners to attend Mass.
Parishioners with a particular set of skills may be called upon to help complete various projects at the parish. These skills might include experience in carpentry, electrical, plumbing, or painting.
Parish Work Day
The parish work day is a day devoted to enhancement, repair and maintenance tasks throughout the church grounds, identified and performed through the stewardship of parishioners.
In this ministry parishioners who are trained professional nurses assist with checking blood pressures following the Masses on the first weekend of the month.
The Lord's Diner
The Lord's Diner exists to combat hunger in the Wichita community. The Diner's mission is to serve a nutritious meal with dignity and respect to anyone who is hungry. Parishioners of St. John the Evangelist volunteer on the 2nd Monday of every month.
Emergency Meals
Parishioners who participate in this ministry help to prepare meals or provide goods for families or individuals in crisis situations or severe illnesses. This may be for a one time event or an ongoing situation.
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Those who are unable to get out into the community miss the relationship and conversation of spending time with others. This ministry connects parishioners who wish to provide support and companionship through visits to those who are homebound.
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This ministry exists to proclaim the dignity of human life - created in the Image of God - as the basis for the fundamental human right to life. The focus is four parts; education on the sanctity of human life, pastoral care for vulnerable persons, public policy advocacy, and prayer & worship.
Providing Rides to
There are parishioners here at St. John the Evangelist who are unable to drive to church but would very much like to be present at Mass. The ministry seeks to provide transportation to and from weekend Mass for those unable to drive.
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So you are getting ready to purchase a swimming pool heater and want to know which is best for you. This is a common problem for many people because there are so many types of heaters available. We briefly explain each type of swimming pool heater in this article to help you choose the best one for you and your needs, and to therefore allow you to make the best purchase.


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Liverpool, Mo Salah, dreams of winning the title in the Champions League final
Mohamed Salah wants to score the winner of Liverpool in the final of the Champions League to end the misery of the defeat of Real Madrid against last season.
The striker said that Saturday's final against Tottenham was the perfect opportunity to repair the wrongs of Kiev, where Sergio Ramos forced him to quit the fight and drove to the hospital with a shoulder injury that touched his World Cup. Salah believes he and Liverpool deserve a change of fortune on the biggest stage of European football.
"I'm so happy to have the chance to play another final. I hope I can play the full game this time, "he said. "I am very excited about that. I hope we can fix what happened last season, get a good result and win the competition. "
When asked if he dreamed of scoring Liverpool's sixth European crown goal, he replied, "Not that dream. I hope this will become a reality and I will score in the final and then I will win the African Cup of Nations [contested in Egypt next month]. The excitement of the tournament will be on 1 of June, and fans have got their tickets for the Champions League final.
Salah believes the experience of the final of last season could be decisive for Liverpool against the Spurs team at the first appearance of their club on the occasion of the event in Europe.
He told BeIN Sports: "This is our second consecutive final. We lost the first but everything seems to be better this time and we have more experience than last time. We are all looking to the future and we had a good preparation period in Spain. We are back in Liverpool and we feel very motivated as players and coaches. I hope we can win this time.
"We made some excellent preparations in Spain and it was a good time to prepare for it. The team is now at the best level physically. So I hope this stage has been an advantage for us in the final. "
Author adminPosted on May 29, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on Liverpool, Mo Salah, dreams of winning the title in the Champions League final
The current absence of Arsenal in the Champions League has not been so expensive
For Arsenal, the victory in the final of the Europa League in Baku – the choice of the destination condemned by UEFA – carries the mark of qualification for the Champions League next season compared to Chelsea, who finished third in the Premier League and is therefore qualified. Even if the margin was enough for Unai Emery in his first season as manager, finishing fifth with a point behind the Spurs, a defeat in the final would mean a third consecutive failure to qualify for Arsenal, a blow to the football status and financial difficulties. Final has arrived, fans are excited and they have got their Champions League final tickets as well.
The financial consequences of missing the Champions League can be exaggerated, illuminated by a vague perception that Uefa's euros mark the gap between the richest clubs in the Premier League and the others. Arsenal itself declared in its 2017-2018 annual accounts that it had recorded a £ 35 million decline in 'football revenues' last season – of all its revenues, with the exception of one profit of £ 15 million realized thanks to the real estate development of Islington, which is still ongoing 12 years after the Emirates Stadium opened in 2006.
"The decline [was] mainly due to the club's participation in the UEFA Europa League rather than the most lucrative Uefa Champions League," their report said.
This 35 million pounds would, of course, be huge for most clubs in Europe, but it shows that the fact of not qualifying for the Champions League has a smaller proportional impact on the earnings of a big club than we often do not think so. The absence of Arsenal in Arsene Wenger's last season had cost the club only 8% of his total football revenue of £ 423 million the previous year, 2016-17, the last one he had played in the Champions League.
For a club like Leicester without Arsenal's rich revenue from sponsorships and matches played at the Emirates, their unique participation in the Champions League after the miraculous title victory of the 2016 Premier League provided a relatively larger sum: 70 M £ – 30% of earnings. all 2016-17 revenues from Leicester.
Author adminPosted on May 28, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on The current absence of Arsenal in the Champions League has not been so expensive
Harry Kane would be ready 'tomorrow' to play in the Champions League final
Harry Kane said he would be ready for the Champions League final against Liverpool on Saturday, saying that if he were to play tomorrow, he would be available.
The fitness of the Tottenham striker has been an important topic of discussion since the ankle ligament injury he suffered in the first leg of the quarter-final against Manchester City on April 9. It was the fifth time in three seasons that Kane had damaged ankle ligaments. Previously, the English captain had been absent for three to seven weeks because of problems. Final has arrived and Kane is ready but on the other hand, fans are also ready to watch the incredible match ahead and they have got their tickets for Champions League final match.
Kane has resumed full training last Friday and, if all goes well, he hopes to be in the starting eleventh of Mauricio Pochettino for Madrid. The manager has not yet revealed anything about his intention to start with Kane. The player's optimistic fitness report is also good news for England, which is competing in the first Nations League finals, which begin June 6th.
Kane said, "If the final has to be played tomorrow, I would be able to play. I feel good. I'm back with the team and there has been no problem so far. I am in full training, I do everything. I am now in a place where I am ready to play any game. The manager will evaluate and decide. But so far I feel good and ready.
"Having the gap of three weeks after the end of the [Premier League] season really helped me. From that point on, I could put a plan in place to get ready for this game. We had more time than the other ankle injuries and it worked well. I am in a good place.
"Kane said he had discussed with England manager Gareth Southgate this weekend. "He wanted to wish me good luck for this week," said Kane. "He knows it's a huge game for our players and the Liverpool team. I think he will have some happy players and some unhappy players when we meet, but we have always said that when we meet England, we are in England mode.
"If I'm good enough to play a match [against Liverpool], then I'm good enough to play as many games as possible [with England]." After my last injury, I came back and played six or seven games in a spin. There are no worries from my point of view.
Author adminPosted on May 28, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on Harry Kane would be ready 'tomorrow' to play in the Champions League final
The outsiders of the Champions League final show that football is not dead
In a campaign dominated by big spenders while bookies favourites have won all titles, the final of the Champions League Liverpool against Tottenham is an exception.
Developed through the ages, codified in Victorian England, deceased in 2019.
The most popular sport in the world may be irrevocably altered, but a feeling that it has been damaged, fractured and removed from its roots has recently been reflected.
The successes continued to succeed, keeping the top five European championship titles. Man City has achieved an unprecedented treble by recording the biggest FA Cup victory.
It is a procession to the glory of the favourites else the argument went late.
Except that the final of the Champions League represents an embarrassing refutation of this theory. Liverpool and Tottenham may play in the richest league in the world, but their journey to Madrid – the Spurs' in particular, was marked by drama to recall the initial and innate appeal of the game.
These campaigns are not intended to spend more than everyone else. Tottenham, as they say, has not bought anyone since January 2018.
Liverpool may have spent huge sums of money on Virgil van Dijk and Alisson, but they can claim that the sale of Philippe Coutinho has financed both the £ 142m it has made, a record profit of £ 125m last year and that, generated by the Champions League, they generate their own income.
In the midst of modern fares, Liverpool's progress and staff are out of date. Final is not far away and champions league fanatics have got their Champions League final tickets.
The camp may be more cosmopolitan, larger amounts, idiosyncratic tactics, but there are threads that cross their successes.
It is a challenge that traditionalists can rejoice.
Their players often have modest origins. For Andy Robertson, a defenseman with a resume at Queen's Park, read Alan Hansen, this former Partick Thistle.
See Alan Kennedy for Xherdan Shaqiri, Gini Wijnaldum and Robertson, all relegated from the Premier League to their former employers.
Mark Lawrenson, a member of a South Coast club in Brighton, looks at the Old Boys Battalion in Southampton.
For Trent Alexander-Arnold, the local who played in a Champions League final in his first football season think of Sammy Lee.
Author adminPosted on May 27, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on The outsiders of the Champions League final show that football is not dead
For the first time Atalanta win to claim Champions League Place
Atalanta qualified for the Champions League for the first time in its history on Sunday. He makes sure of his place with a 3-1 victory over Sassuolo in a match wasted by a fight.
Domenico Berardi gave Sassuolo a staggering lead in the 19th minute but Duvan Zapata scored the ball home to equalize in the 35th minute. Berardi was then expelled after the fight at the end of the first half.
Atalanta captain Alejandro Gomez gave his team the lead eight minutes after the restart, and Mario Pasalic led a Gomez centre in the 65th minute. Atalanta finished third in Serie A with 69 points, ahead of Internazionale for their one-on-one record and one point ahead of Milan, who was absent.
Sassuolo ended the match with nine men when Francesco Magnanelli was sent off for a second offence to be booked in the 83rd minute.
Roma beat Parma 2-1 at Stadio Olimpico on Sunday to finish the season in sixth place, while captain Daniele de Rossi made his last appearance for the club.
Lorenzo Pellegrini gave Roma the lead in the first half, but Gervinho appeared to have equalized one point with a tying goal in the last five minutes until Diego Perotti grabbed the winner.
However, the meagre chances of the selection for the Champions League to qualify for the Champions League ended against Inter, Atalanta and Milan. Above all the final is coming soon and fans have got their tickets for the Champions League final.
Roma's decision not to propose a new contract to De Rossi sparked a furious protest from the fans, but a large crowd bade farewell to his second-highest-scoring player while wearing the red jersey and yellow for the 616th and last time.
Claudio Ranieri, who ruled Roma for the last time as interim manager, knew his team needed everything to get into the top four, but they had to settle for sixth place, allowing them to qualify for second place in the Europa League.
Inter slipped into the Champions League next season when a late goal from Radja Nainggolan allowed them to win 2-1 against a gallant Empoli, who were relegated after an amazing match in Serie A on Sunday.
Author adminPosted on May 27, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on For the first time Atalanta win to claim Champions League Place
Liverpool suffered a setback in its plans for the Champions League final against Spurs
Liverpool was frustrated in their efforts to host a friendly this weekend before the Champions League final next Saturday, failing to find a strong opponent.
Jurgen Klopp and his team flew to Marbella on Monday to train in warm weather before the Spurs showdown in Madrid and the Liverpool boss had hoped to end the week with an exhibition match. There will be a 20-day gap between the Liverpool Premier League final – a 2-0 win over the Wolves – and the June 1st final. Klopp was keen to put his players to the test of reasonable opponents in a friendly match. This prospect seems unlikely, however, as most European clubs are on vacation after the close of their national championship. Serie A and Ligue 1 have a match to play this weekend.
According to reports, Liverpool has approached a number of Dutch clubs, including AZ Alkmaar, with a friendly invitation, but their efforts have been postponed. This means that Liverpool may have to play against the under-23s. Roberto Firmino is one of the players Klopp wants to find in the match. He missed Liverpool's last three Premier League games and only 12 minutes of the Champions League semi-final against Barcelona. Klopp is optimistic that the Brazilian will be ready, saying: "He took part in about 70% of the session, tomorrow he will probably be completely in place, we will see, so I hope everything will be fine."
Midfielder Naby Keita is expected to be absent, but Klopp said he was making good progress after an injury to an abductor. preparations for the final contrast with those of their opponents, the Spurs having no intention of playing a friendly match before the match, according to the Evening Standard. Part of the reason is that Mauricio Pochettino has more injury problems to deal with than Klopp, although Harry Kane, Jan Vertonghen and Davinson Sanchez have all resumed training yesterday and can all claim to play.
Get latest updates of Champions League Final Tickets from our trusted online ticketing platform. Football fanatics can book tickets on reliable rates from our online ticketing market place.
Author adminPosted on May 24, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on Liverpool suffered a setback in its plans for the Champions League final against Spurs
Vertonghen would win his battle to get in shape for the Champions League final
TOTTENHAM HOTSPUR Vertonghen would have won his battle to qualify for the Champions League final.
Jan Vertonghen is apparently more likely than not to play in the Champions League final next month.
Jan Vertonghen is winning his battle to be fit for the Champions League final against Liverpool on June 1, according to the Daily Mail.
They report that the Belgian international has accelerated his rehabilitation by taking part in a training session with the rest of the team on Wednesday – which other stars blocked Davinson Sanchez and Harry Kane have also done.
And the defender is ranked 60/40 in the report to play in Madrid, having not played since his injury in the spectacular victory in the semifinals on the return leg against his former club Ajax. Fans are excited for the final and they have got their tickets for the Champions League final.
The Spurs will likely need Sanchez or Vertonghen to team up with Toby Alderweireld as they try to fight the power of Liverpool's top three.
And Vertonghen, who earns £ 100,000 a week in North London (Spotrac) – is by far the most experienced option and the man Mauricio Pochettino would probably choose if he could only have one.
The fact that Vertonghen was appointed to Belgium by coach Roberto Martinez's team for the matches against Kazakhstan and Scotland on 8 and 11 June respectively is also cited as a positive sign.
The extended break between the end of the national season and the final does not make much sense – but it certainly helped Tottenham
fight the impact of the injury and fatigue that dragged him through his season.
Author adminPosted on May 24, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on Vertonghen would win his battle to get in shape for the Champions League final
Alisson reveals his influence on Guardiola before the Champions League final
Alisson revealed how Pep Guardiola's vintage club in Barcelona has brought him to where he is now, heading for the Champions League final in Madrid with the Reds.
After winning the Golden Glove Award for maintaining 21 league titles in the league and claiming to be No. 1 in Brazil, the arrival of Romano Alisson in Rome for 65 million pounds was a resounding success.
But the 25-year-old began his career at Internacional, in his native Brazil, where his style of play was also born.
"I like what I'm doing, so I'll always have the ball in my hands," said the Reds goalkeeper at UEFA. "When I started going to school, I played as a midfielder and then I went to the goal, which made me feel more comfortable.
"Barcelona has always played fast and short balls from the goalkeeper. At that time, it was Victor Valdes. He loved playing with his feet and me too because I always want to play a real role in the game. "
After moving to Europe and signing for Roma, it was obviously the Reds who ended their dream in the Champions League when we beat the Serie A team in a sensational confrontation in the semi-final last year.
"Of course, we wanted more, we wanted to qualify for the final, but we were facing a strong Liverpool team," he admitted.
"Now I'm on the other side and I reached the final after another big comeback against Barcelona.
Since his childish inspiration in the driving force of Barca de Pep, until eliminating the club of the competition, Alisson must have an additional advantage.
Like most Liverpool fans, Alisson is clearly in love with the Champions League and feels most at home against the best of Europe's best.
"I am already very grateful to be able to participate in the final. Every time I go out on the pitch and hear the Champions League anthem, it gives me goosebumps every time I hear it.
"So when I'm in the final, I'll do what I love and I'm very grateful."
Alisson's first season at Anfield could end with a sixth Champions League trophy for the club. Maybe he could become the young goalkeeper Victor Valdes and inspire future generations. It could be the Klopp team in Liverpool that future kids will love.
Author adminPosted on May 23, 2019 May 23, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on Alisson reveals his influence on Guardiola before the Champions League final
Real Madrid gets closer to shocking signing of Champions League finalist
Real Madrid will announce the much-anticipated arrival of Christian Eriksen earlier than expected and after the Champions League final.
Real Madrid gets closer to the shocking signing of Champions League finalist
For the first time in five years, neither Barcelona nor Real Madrid will play in the UEFA Champions League final. However, whites will closely watch Tottenham Hotspur's clash with Liverpool to see if they can get out of both teams in the next summer transfer period. Cricket fanatics are rushing to get their tickets for the Champions League final which is going to be a great match.
According to Fox Sports, Los Blancos will announce the signing of Christian Eriksen immediately after the end of the match and the dedusting. The Danish international has signed a contract with Lilywhites until next June and will leave this year for 120 million euros, instead of leaving for free a year later.
It is believed that Christian Eriksen is the successor of Luka Modric and it is no coincidence that Real Madrid is addressing Tottenham Hotspur to replace the Croatian international. Both teams play a fast and aggressive football style in which midfielders are very important. Therefore, Eriksen excelled in North London, but not from the point of view of silverware.
The 27-year-old has been on the Los Merengues radar for a few months and Zinedine Zidane may finally have a midfielder frequently involved in the scoring action. In addition, Eriksen's claims would not be exorbitant compared to Paul Pogba, who may have to end up at Manchester United for another season.
Although Christian Eriksen is about to become a Real Madrid, he may not be the last player Madrid signs in the Premier League this summer. They have their eyes on the duo Chelsea, Eden Hazard and N'Golo Kante, as well as the leaders of Liverpool, Mohamed Salah and Sadio Mane, in recent months.
Author adminPosted on May 23, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on Real Madrid gets closer to shocking signing of Champions League finalist
Football chiefs hit out at UEFA's Champions League reform plan
Leaders of the biggest European football leagues have attacked the restructuring plans of the Champions League, opposing them to UEFA, which organizes the lucrative competition, and increasing the stakes in a long battle for power.
The leaders of the English Premier League, the Spanish Liga and the German Bundesliga have appeared before UEFA, the governing body of European football, criticizing the proposals that they believe would benefit the richest clubs.
Speaking Tuesday at the FT's "Business of Football" summit in London, Liga President Javier Tebas denounced a "basement culture" in European football and said that UEFA's projects would generate more money for bigger clubs but less for national leagues.
Richard Masters, the acting executive director of the Premier League, said the proposed changes could create opposition between the national leagues and the Champions League.
Christian Seifert, director of the Bundesliga, said the proposals "were not good for football".
The Champions League recast projects are the result of months of discussions between UEFA and the European Club Association, representing the interests of more than 200 teams on the continent. Final is also near and people have bought their tickets for the Champions League final.
ECA is chaired by Andrea Agnelli, who also chairs the Juventus football club.
By restricting access, the amendments would ensure that participation payments for participation in the Champions League – which represent more than € 2 billion this season – remain in the hands of around 20 elite clubs.
"If the race for the Champions League [in the national leagues] is open, it hurts the value of every European Championship," said Seifert.
The proposal was the most elaborate of the ideas presented by UEFA to the leaders of the European football leagues earlier this month.
"I love the Champions League. Before changing it, I would think twice or 100 times, "said Zvonimir Boban, Deputy Secretary General of Fifa, at the same event.
England, Spain and Germany have the three largest leagues of recipes. The Premier League, La Liga and Bundesliga have combined revenues of nearly 11 billion euros for the 2016/17 season, according to Deloitte. The Premier League alone accounts for almost half that amount.
UEFA's proposal to increase the number of European games threatens the broadcasting revenues of the three leagues, which amounted to 5.7 billion euros for the 2016/17 season.
Author adminPosted on May 22, 2019 Categories Football, SportsTags Champions League, Champions League Final Tickets, Champions League Tickets, Football, Football league, Sports, UEFA, UEFA Champions League, UEFA footballLeave a comment on Football chiefs hit out at UEFA's Champions League reform plan
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Q: Why MongoDB C++ Driver not working on SLES11? I've been working on installing the MongoDB drivers on Zlinux, and so far, I've got it all to work on most Linux systems apart from SLES11.
Now in order to get the code on, I had to do a number of updates to the GCC and Boost. This means the system is running the following:
test@ff6d8405cc0c:~/work> g++ --version
g++ (GCC) 5.2.0
Copyright (C) 2015 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

test@ff6d8405cc0c:~/work> cat /usr/local/include/boost/version.hpp | grep "BOOST_LIB_VERSION"
//  BOOST_LIB_VERSION must be defined to be the same as BOOST_VERSION
#define BOOST_LIB_VERSION "1_58"
test@ff6d8405cc0c:~/work> cat /usr/include/boost/version.hpp | grep "BOOST_LIB_VERSION"
//  BOOST_LIB_VERSION must be defined to be the same as BOOST_VERSION
#define BOOST_LIB_VERSION "1_36"

So as I have 2 version of boost I've set my path as follows:
test@ff6d8405cc0c:~/work> echo $PATH
/home/test/bin:/usr/local/bin:/usr/bin:/bin:/usr/X11R6/bin:/usr/games:/usr/lib/mit/bin:/usr/lib/mit/sbin:.:/usr/local/include/:/usr/local/lib/

But my g++ script to test connection to the DB is still failing, this is the script:
#include <cstdlib>
#include <iostream>
#include "mongo/client/dbclient.h" // for the driver

void run() {
 mongo::DBClientConnection c;
  c.connect("localhost");
}

int main() {
    mongo::client::initialize();
    try {
        run();
        std::cout << "connected ok" << std::endl;
   } catch( const mongo::DBException &e ) {
        std::cout << "caught " << e.what() << std::endl;
    }
    return EXIT_SUCCESS;
}

My install of the MongoDB C++ driver works as expected using the following scons flags:
sudo scons --prefix=/usr/local --disable-warnings-as-errors install

But part of me suspects from the error that it's calling the wrong libraries for boost. As when I try to compile the C++, I just get a load of errors:

test@ff6d8405cc0c:~/work> g++ example-connect.cpp -pthread -lmongoclient -lboost_thread -lboost_system -lboost_program_options -lboost_system -lboost_regex -o example-connect
      /usr/local/lib/gcc/s390x-ibm-linux-gnu/5.2.0/../../../libmongoclient.a(dbclient.o): In function boost::thread_exception::thread_exception(int, char const*)':
      /usr/local/include/boost/thread/exceptions.hpp:51: undefined reference toboost::system::system_category()'
      /usr/local/lib/gcc/s390x-ibm-linux-gnu/5.2.0/../../../libmongoclient.a(dbclient.o): In function __static_initialization_and_destruction_0':
      /usr/local/include/boost/system/error_code.hpp:221: undefined reference toboost::system::generic_category()'
      /usr/local/include/boost/system/error_code.hpp:222: undefined reference to boost::system::generic_category()'
      /usr/local/include/boost/system/error_code.hpp:223: undefined reference toboost::system::system_category()'
      /usr/local/lib/gcc/s390x-ibm-linux-gnu/5.2.0/../../../libmongoclient.a(dbclient.o): In function `boost::re_detail::perl_matcher<__gnu_cxx::__normal_iterator, std::allocator > >, std::allocator, std::allocator > > > >, boost::regex_traits > >::match_prefix()':

I've done a bit of research myself, but I'm not 100% sure what to do next to be sure that I'm calling all the right components.

redpajama_set_name: RedPajamaStackExchange