text:
\section{\label{sec:intro}Introduction}

Due to the high partonic densities reached, processes with more than two partons from the two colliding protons participating in the actual scattering ---the so called multiple parton interactions--- are likely to happen at the LHC~\cite{Bartalini:2017jkk}.
Double parton scattering (DPS),
the simplest form of  multiple parton interactions,
involves two simultaneous hard collisions. It  has been indeed  observed at the LHC (see, e.g., Ref. \cite{Aad:2013bjm}).
The DPS cross section is expressed in terms of double parton distribution functions (dPDFs)~\cite{Paver:1982yp,Diehl1}.
The latter are related to the number density of two partons located at a given transverse separation in
coordinate space with given longitudinal momentum fractions.
The information encoded in  these distributions therefore complements that accessed through electromagnetic probes in terms of  generalized parton distributions (GPDs)~\cite{Guidal:2013rya,Dupre:2016mai}, one of the flagships of the future Electron Ion Collider (EIC)~\cite{Aidala:2020mzt}.
If measured, dPDFs would therefore represent
a novel tool to study the three-dimensional hadron structure \cite{blok1,blok2,fabbro,ffe,Rinaldi:2018bsf}.
Indeed, they are
sensitive
to  two-parton correlations not accessible via one body
distributions, {\it e.g.}
Parton Distribution Functions (PDFs) and GPDs --see Ref. \cite{Bartalini:2017jkk,
Kasemets:2017vyh}
for a recent report.
Since they are non perturbative objects, dPDFs have
 been evaluated within models of the hadron structure ---estimates exist at low momentum scales
for the proton dPDFs~\cite{bag,noi2,noi1,kase,plb,JHEP2016,Traini:2016jru}.
In order to match theoretical predictions with future experimental
analyses,  the results of these  calculations are then evolved using the proper QCD evolution equations to reach the  high momentum scale  of the data.
Developments on the evolution properties
of dPDFs
can be found in, {\it e.g.},
\cite{Diehl:2017wew}.

Recently, the double PDFs of the pion have also attracted considerable attention.
A first estimate has been performed using light cone wave functions obtained within the AdS/QCD correspondence~\cite{Rinaldi:2018zng,
Rinaldi:2020ybv} ;
then a calculation
within a Nambu--Jona-Lasinio (NJL) framework was presented in Ref.~\cite{jhep19}.
The latter represents the first evaluation of pion dPDFs in a field theoretical approach, which
allowed a systematical study of the different contributions to the pion observables. This exercise has been  effective to examine the validity of commonly used approximations for which dPDFs could be expressed
in terms of GPDs ---and were found to be violated, especially at low momentum scale and in the valence region.
These results have been recently confirmed in a similar
NJL framework by an independent calculation \cite{bar}.

Studies for the pion are especially important
in view of possible lattice calculations. This is  pertinent
in particular
when a corresponding evaluation for  nucleon observables on the lattice  appear much more involved.
However, the communities studying parton distributions from global QCD analyses and lattice QCD calculations are collaborating
towards a synergy to further improve our knowledge of PDFs~\cite{Lin:2017snn}, thanks
 to the access --on the lattice-- to moments of PDFs as well as to the formalism of quasi-PDFs and its matching procedure to lightfront PDFs, {\it e.g.}~\cite{Ji:2013dva}.
This effort is expanding to all collinear PDFs, GPDs and Transverse momentum dependent parton distributions (TMDs) of the nucleons~\cite{Olness:tocome}.
Since similar considerations are premature for multi parton PDFs, it seems opportune to consider the
two-current correlations in the pion ---quantities that could be related to dPDFs through moments--- with current operators
evaluated at different space points but at equal time, from a model point of view. Such correlations
have been calculated on the lattice, {\it e.g.}, in Ref.~\cite{Burkardt:1994pw} and more recently in Refs.~\cite{Zimmermann:2017ctb,Bali:2018nde}.

The novel possibility to compare results
with lattice data reinforces the theoretical relevance of model calculations of
two-current correlations in the pion.

In this paper we analyze the correlations
of two vector currents
in the NJL model, showing
in particular their time-time component,
and attempting for this quantity a direct  comparison with lattice data.

The paper is structured as follows.
In section \ref{II} we
define two-current correlations in the pion and their isospin decomposition, while
in section  \ref{III} we describe the NJL evaluation scheme and we give
the explicit expressions of the results of the calculation.
In section \ref{IV} we show a comparison
of our numerical results
with lattice data.
Conclusions are collected in section \ref{V}.

\section{\label{II}
Definitions and isospin decomposition}

Experimental measurements of pion dPDFs appear rather challenging at
the moment. Nevertheless, from a complementary viewpoint,
lattice evaluations of matrix elements that can be connected to
the Mellin moments of double parton distributions are possible~\cite{Diehl1}. A relevant step towards this goal has been done in Ref.~\cite{Bali:2018nde}, where lattice data
of correlation functions of two local currents in a pion,
\begin{align}
\left\langle \pi^{k}\left(P\right)\left|\mathcal{O}_{i}^{q_{1}q_{2}}(y)\,\mathcal{O}_{j}^{q_{3}q_{4}}(0)\,\right|\pi^{k^{\prime}}\left(P\right)\right\rangle ,
\label{basic-matel1}
\end{align}
have been presented. In the expression above, the pion charges ---$k,k^{\prime}=+,-,0$---
may be different in the bra and ket state, while the four-momentum
$P$ is the same in both, and the two currents are applied at the
same time but at different spatial positions, {\it i.e.}, one has $y^{\mu}=\left(0,\,\vec{y}\right)$.
It differs from the dPDFs which are defined
from a similar product
of two one body operators  taken at a distance $y'^{\mu}=\left(y'^+=0,y^-\,,\vec{y'}_\perp\right)$.
Hence, the currents of interest here are
\begin{align}
\mathcal{O}_{n}^{qq'}(y) & =\bar{q}(y)\,\Gamma_{n}\,q'(y)\,,\label{op-def}
\end{align}
where $q$ and $q'$ are $u$ or $d$ quark fields and $\Gamma_{n}$ are the Dirac bilinears $1,i\gamma_{5},\gamma^{\mu},\gamma^{\mu}\gamma_{5}$
for $n=S,P,V^{\mu},A^{\mu},$ respectively. In the present work we will
only consider the time component of the vector current, {\it i.e.}
\begin{align}
\mathcal{O}_{V^{0}}^{qq'}(y)=\bar{q}(y)\gamma^{0}q'(y)\,,\label{curr-def}
\end{align}
and we will compare our model results with Lattice
data in the case of two equal currents of this kind.

As shown in Ref. \cite{Bali:2018nde}, the matrix elements \eqref{basic-matel1}
are not all independent due to constraints from isospin symmetry and
discrete symmetries. We follow the treatment of Ref. \cite{Bali:2018nde}
defining the isosinglet current:
\begin{align}
\mathcal{O}_{n}^{\text{s}} & =\mathcal{O}_{n}^{uu}+\mathcal{O}_{n}^{dd}\,,
\end{align}
as well as the isotriplet currents
\begin{align}
\mathcal{O}_{n}^{a} & =\bar{Q}\tau^{a}\Gamma_{n}Q\,, & a & =1,2,3\label{iso-current}
\end{align}
where $\tau^{a}$
are
the Pauli matrices and $Q=(u,d)$ is the
isodoublet
of quark fields. As a consequence, the following isospin decomposition is
obtained
\begin{align}
\left\langle \pi^{j}\left(P\right)\right|\mathcal{O}_{n}^{\text{s}}\left(y\right)\mathcal{O}_{n^{\prime}}^{\text{s}}\left(0\right)\left|\pi^{i}\left(P\right)\right\rangle  & =\delta^{ij}\,F_{0}(y)\,,\nonumber \\
\left\langle \pi^{j}\left(P\right)\right|\mathcal{O}_{n}^{a}\left(y\right)\mathcal{O}_{n^{\prime}}^{b}\left(0\right)\left|\pi^{i}\left(P\right)\right\rangle  & =\delta^{ab}\delta^{ij}\,F_{1}(y)+\bigl(\delta^{ai}\delta^{bj}+\delta^{aj}\delta^{bi}\bigr)\,F_{2}(y)
\nonumber \\ & +
\bigl(\delta^{ai}\delta^{bj}-\delta^{aj}\delta^{bi}\bigr)\,iF_{3}(y)\,,\nonumber \\
\left\langle \pi^{j}\left(P\right)\right|\mathcal{O}_{n}^{b}\left(y\right)\mathcal{O}_{n^{\prime}}^{\text{s}}\left(0\right)\left|\pi^{i}\left(P\right)\right\rangle  & =i\epsilon^{bij}\,G_{1}(y)\,,\nonumber \\
\left\langle \pi^{j}\left(P\right)\right|\mathcal{O}_{n}^{\text{s}}\left(y\right)\mathcal{O}_{n^{\prime}}^{b}\left(0\right)\left|\pi^{i}\left(P\right)\right\rangle  & =i\epsilon^{bij}\,G_{2}(y)\,.\label{Iso_descomp}
\end{align}
Here the real functions $F_{\ell}$ and $G_{\ell}$ ---quantities evaluated in what follows--- depend on the pion momentum $P$
and on the current indices $n,n^{\prime}$~\cite{Bali:2018nde}.

\section{\label{III}Two-current correlations in the NJL model.}

\subsection{Leading order}
We describe now the calculation of the two-current correlations,
and in particular of the functions
$F_i$, with $i=0,1,2$, and $G_l$, with $l=1,2$,
in
the NJL framework. This framework is
the most realistic model for the pseudoscalar
mesons based on a local
quantum field theory built only with quarks~\cite{Klevansky:1992qe}.
It respects the
realization of chiral symmetry and
gives a good description of low energy properties. Mesons are described as bound states, in
a fully covariant fashion, using the Bethe-Salpeter amplitude,
in a field theoretical framework.
In this way, Lorentz covariance is preserved.  The NJL model is a
non-renormalizable field theory and therefore a {regularization procedure has to be implemented.}
 We have performed our calculations in the Pauli--Villars  regularization
scheme ---a well established method.
The NJL model, together with its
regularization procedure, can
be regarded as an effective theory of QCD.
Some basic features of the NJL model and details on the regularization scheme are
reported in Appendix~\ref{App.NJL_Basic_Equations}.
Model calculations of meson partonic structure within
this approach have a long story of successful predictions~\cite{Davidson:2001cc,Theussl:2002xp,
RuizArriola:2002bp,Courtoy:2008nf,
Courtoy:2007vy,
Courtoythesis,
Noguera:2011fv,Weigel:1999pc,
ns,
Broniowski:2017gfp,Ceccopieri:2018nop}.

Collinear parton distributions evaluated within a low energy model can be associated to a RGE scale denoted by $Q_0$. The determination of that {\it hadronic scale} reflects the degrees of freedom of the model ---here the NJL model contains only valence quarks~\cite{Stratmann:1993aw,Traini:1997jz}. The identification of such a low lying scale enables predictions from the model to measured quantities, through perturbative QCD evolution.

Let us describe the main steps of our calculation.
We define, following Eq.
\eqref{Iso_descomp},
\begin{equation}
G_{\alpha\beta}^{ij}\left(\vec{y}\right)=\left\langle \pi^{j}\left(P\right)\right|\mathcal{O}_{n}^{\beta}\left(y\right)\mathcal{O}_{n^{\prime}}^{\alpha}\left(0\right)\left|\pi^{i}\left(P\right)\right\rangle \, ,
\end{equation}
with $\alpha, \beta=\text{s},1,2,3.$ In order to proceed to the calculation
in the NJL model, we perform the Fourier transform to momentum space
\begin{align}
G_{\alpha\beta}^{ij}\left(\vec{q}\right) & =\int d^{3}y\,e^{-i\vec{q}\cdot\vec{y}}G_{\alpha\beta}^{ij}\left(\vec{y}\right)\nonumber \\
 & =\int d^{3}y\,e^{-i\vec{q}\cdot\vec{y}}\left\langle \pi^{j}\left(P\right)\right|\left.\mathcal{O}_{n}^{\beta}\left(y\right)\mathcal{O}_{n^{\prime}}^{\alpha}\left(0\right)\right|_{y^{0}=0}\left|\pi^{i}\left(P\right)\right\rangle \, .
\label{ms}
\end{align}
We use in this expression the following definition of the state for the pion
$i$
\begin{equation}
\left|\pi^{i}\left(P\right)\right\rangle =\int d^{4}y_{1}\,d^{4}y_{2}\,\frac{d^{4}k}{\left(2\pi\right)^{4}}e^{-i\frac{1}{2}P\cdot\left(y_{1}+y_{2}\right)}\,e^{-ik\cdot\left(y_{1}-y_{2}\right)}\bar{q}\left(y_{1}\right)\phi_{\pi^{i}}\left(k,P\right)q\left(y_{2}\right)\left|0\right\rangle \, ,
\label{A.5}
\end{equation}
with $\phi_{\pi^{i}}$ the quark-pion vertex function for a $\pi^i$.
In the NJL model
the amplitude
$\phi_{\pi^i}\left(k,P\right)$ is independent on the relative
and total quark-antiquark momenta, $k$
and $P,$ respectively, and we have
\begin{equation}
\phi_{\pi^{i}}\left(k,P\right)=ig_{\pi qq}i\gamma_{5}\tau^{i}\,,
\label{ampli}
\end{equation}
where $g_{\pi qq}$ is the quark-pion coupling constant and $\tau^{i}$
is the isospin matrix associated to the corresponding pion $\pi^i$.

Inserting Eq.~(\ref{A.5}) in the definition~(\ref{ms}),
we obtain contributions
associated to different Feynman diagrams. The fact that $G_{\alpha\beta}^{ij}\left(\vec{y}\right)$
is defined at $y^{0}=0$ implies that
\begin{equation}
G_{\alpha\beta}^{ij}\left(\vec{q}\right)=\int\frac{dq^{0}}{2\pi}\,\mathcal{T}\label{A.9-1} \, ,
\end{equation}
where $\mathcal{T}$ is the Feynman amplitude corresponding to the diagram.

\begin{figure}
\begin{centering}
\includegraphics[scale=0.3]{Diagrama_rombo_local.pdf}
\includegraphics[scale=0.4]{Diagrama_trapecio_local.pdf}
\par\end{centering}
\caption{Examples of the two types of diagrams contributing to the leading
order of the time component of the two local vector current correlations: {\it rhombus} (a) and {\it trapezoid} (b).}
\label{Fig Leading local diagrams}
\end{figure}

The two contributions to be considered at leading order are shown in Fig.
\ref{Fig Leading local diagrams}. In the following, we will call them
{\it rhombus} and {\it trapezoid} diagrams,
respectively. Therefore one has
\begin{eqnarray}
G_{\alpha\beta}^{\left(0\right)ij}(\vec{q})=G_{\alpha\beta}^{\left(r\right)ij}(\vec{q})+G_{\alpha\beta}^{\left(t\right)ij}(\vec{q}) \, ,
\end{eqnarray}
where $G_{\alpha\beta}^{\left(r\right)ij}(\vec{q})$ and $G_{\alpha\beta}^{\left(t\right)ij}(\vec{q})$
stand for contributions from the rhombus and trapezoid diagrams, respectively,
which read

\begin{eqnarray}
G_{\alpha\beta}^{\left(r\right)ij}(\vec{q}) & = & \int\frac{d^{4}k}{(2\pi)^{4}}\frac{dq^{0}}{2\pi}(-)\left\{ \text{Tr}\left[\bar{\phi}_{\pi^{j}}iS_{F}\left(\frac{P}{2}+k+q\right)\tau^{\alpha}\Gamma_{n^{\prime}}iS_{F}\left(k+\frac{P}{2}\right)\right.\right.\nonumber \\
& \times & \left.\left.\phi_{\pi^{i}}iS_{F}\left(k-\frac{P}{2}\right)\tau^{\beta}\Gamma_{n}iS_{F}\left(k+q-\frac{P}{2}\right)\right] \right .
\nonumber \\
& + & \left . (q^{\mu}\leftrightarrow-q^{\mu},\left(\alpha,n^{\prime}\right)\leftrightarrow\left(\beta,n\right))\right\} \label{romboG} \, ,
\end{eqnarray}

\begin{eqnarray}
G_{\alpha\beta}^{\left(t\right)ij}(\vec{q}) & = & \int\frac{d^{4}k}{(2\pi)^{4}}\frac{dq^{0}}{2\pi}(-)\left\{ \text{Tr}\left[\bar{\phi}_{\pi^{j}}iS_{F}\left(\frac{P}{2}+k\right)\tau^{\beta}\Gamma_{n}iS_{F}\left(k+\frac{P}{2}+q\right)\right.\right.\nonumber \\
 & \times & \left.\left.\tau^{\alpha}\Gamma_{n^{\prime}}iS_{F}\left(k+\frac{P}{2}\right)\phi_{\pi^{i}}iS_{F}\left(k-\frac{P}{2}\right)\right]\right.\nonumber \\
 & + & \left.\text{Tr}\left[\bar{\phi}_{\pi^{j}}iS_{F}\left(\frac{P}{2}+k\right)\phi_{\pi^{i}}\,iS_{F}\left(k-\frac{P}{2}\right)\tau^{\beta}\Gamma_{n}\right.\right.\nonumber \\
 & \times & \left.\left.iS_{F}\left(k-\frac{P}{2}+q\right)\tau^{\alpha}\Gamma_{n^{\prime}}iS_{F}\left(k-\frac{P}{2}\right)\right] \right.\nonumber \\
& + & \left. (q^{\mu}\leftrightarrow-q^{\mu},\left(\alpha,m^{\prime}\right)\leftrightarrow\left(\beta,m\right)) \right\}.
 \label{trapecioG}
\end{eqnarray}
Here $\tau^{\alpha}=\left(\tau^{\text{s}}=1,\,\vec{\tau}\right),$
with $\vec{\tau}$ the standard Pauli matrices.

According to their isospin structure, which is determined by $\phi_{i}$ and
$\tau^{\alpha}$ terms, the two expressions above yield four types
of contributions once the isospin traces are evaluated ---a straightforward lengthy procedure. For the {\it rhombus} contribution, they read

\begin{eqnarray}
G_{ss}^{\left(r\right)ij}(\vec{q}) & = & \delta_{ij}2N_{c}(ig_{\pi qq})^{2}[I_{\Gamma}^{r}(m,\vec{q})+I_{\Gamma}^{r}(m,-\vec{q})\,,\nonumber \\
G_{sa}^{\left(r\right)ij}(\vec{q}) & = & 2i\epsilon_{jia}N_{c}(ig_{\pi qq})^{2}[I_{\Gamma}^{r}(m,\vec{q})-I_{\Gamma}^{r}(m,-\vec{q})]\,,\nonumber \\
G_{as}^{\left(r\right)ij}(\vec{q}) & = & 2i\epsilon_{ija}N_{c}(ig_{\pi qq})^{2}[I_{\Gamma}^{r}(m,\vec{q})-I_{\Gamma}^{r}(m,-\vec{q})]\,,\nonumber \\
G_{ab}^{\left(r\right)ij}(\vec{q}) & = & (\delta_{ja}\delta_{ib}-\delta_{ji}\delta_{ab}+\delta_{jb}\delta_{ia})2N_{c}(ig_{\pi qq})^{2}[I_{\Gamma}^{r}(m,\vec{q})+I_{\Gamma}^{r}(m,-\vec{q})]\,,\label{rombo4}
\end{eqnarray}
with

\begin{eqnarray}
I_{\Gamma}^{r}(m,\vec{q}) & = & \int\frac{d^{4}k}{(2\pi)^{4}}
\frac{dq_{0}}{2\pi}\text{tr}\left[
\gamma_{5}
S_{F}\left(k+q+\frac{P}{2}\right)\Gamma S_{F}\left(k+\frac{P}{2}\right)
\right .
\nonumber \\
& \times &
\left .
\gamma_{5}
S_{F}\left(k-\frac{P}{2}\right)\Gamma S_{F}\left(k+q-\frac{P}{2}\right)\right]\,.
\end{eqnarray}
In the equations above, $m$ is the quark mass and we have assumed that $\Gamma_{n}=\Gamma_{n^{\prime}}=\Gamma.$
For the {\it trapezoid} contribution, they read
\begin{eqnarray}
G_{ss}^{\left(t\right)ij}(\vec{q}) & = & \delta_{ij}2N_{c}(ig_{\pi qq})^{2}[I_{\Gamma}^{t_{1}}(m,\vec{q})+I_{\Gamma}^{t_{1}}(m,-\vec{q})+I_{\Gamma}^{t_{2}}(m,\vec{q})+I_{\Gamma}^{t_{2}}(m,-\vec{q})]\,,\nonumber \\
G_{sa}^{\left(t\right)ij}(\vec{q}) & = & 2i\epsilon_{jia}N_{c}(ig_{\pi qq})^{2}[-I_{\Gamma}^{t_{1}}(m,\vec{q})+I_{\Gamma}^{t_{1}}(m,-\vec{q})+I_{\Gamma}^{t_{2}}(m,\vec{q})-I_{\Gamma}^{t_{2}}(m,-\vec{q})]\,,\nonumber \\
G_{as}^{\left(t\right)ij}(\vec{q}) & = & 2i\epsilon_{jia}N_{c}(ig_{\pi qq})^{2}[-I_{\Gamma}^{t_{1}}(m,\vec{q})+I_{\Gamma}^{t_{1}}(m,-\vec{q})+I_{\Gamma}^{t_{2}}(m,\vec{q})-I_{\Gamma}^{t_{2}}(m,-\vec{q})]\,,\nonumber \\
G_{ab}^{\left(t\right)ij}(\vec{q}) & = & 2N_{c}(ig_{\pi qq})^{2}\{\delta_{ji}\delta_{ab}[I_{\Gamma}^{t_{1}}(m,\vec{q})+I_{\Gamma}^{t_{1}}(m,-\vec{q})+I_{\Gamma}^{t_{2}}(m,\vec{q})+I_{\Gamma}^{t_{2}}(m,-\vec{q})]\label{trapecio4}\\
 & + & (\delta_{jb}\delta_{ai}-\delta_{ja}\delta_{bi})[I_{\Gamma}^{t_{1}}(m,\vec{q})-I_{\Gamma}^{t_{1}}(m,-\vec{q})-I_{\Gamma}^{t_{2}}(m,\vec{q})+I_{\Gamma}^{t_{2}}(m,-\vec{q})]\}\,,\nonumber
\end{eqnarray}
with

\begin{eqnarray}
I_{\Gamma}^{t_{1}}(m,\vec{q})& = & \int\frac{d^{4}k}{(2\pi)^{4}}\frac{dq^{0}}{2\pi}
\, \text{tr}\left[\gamma_{5}S_{F}\left(k+\frac{P}{2}\right)
\Gamma S_{F}\left(k+\frac{P}{2}+q\right)
\right .
\nonumber \\
& \times & \left .
\Gamma S_{F}\left(k+\frac{P}{2}\right)\gamma_{5}S_{F}\left(k-\frac{P}{2}\right)\right]\,,
\end{eqnarray}

and

\begin{eqnarray}
I_{\Gamma}^{t_{2}}(m,\vec{q}) & = & \int\frac{d^{4}k}{(2\pi)^{4}}\frac{dq^{0}}{2\pi}\text{tr}\left[\gamma_{5}S_{F}\left(k+\frac{P}{2}\right)\gamma_{5}S_{F}\left(k-\frac{P}{2}\right)
\right .
\nonumber \\
& \times & \left .
\Gamma S_{F}\left(k-\frac{P}{2}+q\right)\Gamma S_{F}\left(k-\frac{P}{2}\right)\right]\,.
\end{eqnarray}

By comparing Eq. (\ref{rombo4}) and (\ref{trapecio4}) with Eq. (\ref{Iso_descomp})
we obtain the relations,

\begin{eqnarray}
F_{0}(\vec{q}) & = & X_{\Gamma}^{r}(\vec{q})+X_{\Gamma}^{t}(\vec{q})\,,\nonumber \\
F_{1}(\vec{q}) & = & -X_{\Gamma}^{r}(\vec{q})+X_{\Gamma}^{t}(\vec{q})\,,\nonumber \\
F_{2}(\vec{q}) & = & X_{\Gamma}^{r}(\vec{q})\,,\nonumber \\
iF_{3}(\vec{q}) & = & -Z_{\Gamma}^{t}(\vec{q})\,,\nonumber \\
G_{1}(\vec{q}) & = & -Y_{\Gamma}^{r}(\vec{q})-Y_{\Gamma}^{t}(\vec{q})\,,\nonumber \\
G_{2}(\vec{q}) & = & Y_{\Gamma}^{r}(\vec{q})-Y_{\Gamma}^{t}(\vec{q})\,,\label{ottorel}
\end{eqnarray}
with
\begin{eqnarray}
X_{\Gamma}^{r}(\vec{q}) & = & 2N_{c}(ig_{\pi qq})^{2}[I_{\Gamma}^{r}(m,\vec{q})+I_{\Gamma}^{r}(m,-\vec{q})]\,,\nonumber \\
Y_{\Gamma}^{r}(\vec{q}) & = & 2N_{c}(ig_{\pi qq})^{2}[I_{\Gamma}^{r}(m,\vec{q})-I_{\Gamma}^{r}(m,-\vec{q})]\,,\nonumber \\
X_{\Gamma}^{t}(\vec{q}) & = & 2N_{c}(ig_{\pi qq})^{2}[I_{\Gamma}^{t_{1}}(m,\vec{q})+I_{\Gamma}^{t_{2}}(m,\vec{q})+I_{\Gamma}^{t_{1}}(m,-\vec{q})+I_{\Gamma}^{t_{2}}(m,-\vec{q})]\,,\nonumber \\
Y_{\Gamma}^{t}(\vec{q}) & = & 2N_{c}(ig_{\pi qq})^{2}[-I_{\Gamma}^{t_{1}}(m,\vec{q})+I_{\Gamma}^{t_{2}}(m,\vec{q})+I_{\Gamma}^{t_{1}}(m,-\vec{q})-I_{\Gamma}^{t_{2}}(m,-\vec{q})]\,,\nonumber \\
Z_{\Gamma}^{t}(\vec{q}) & = & 2N_{c}(ig_{\pi qq})^{2}[I_{\Gamma}^{t_{1}}(m,\vec{q})-I_{\Gamma}^{t_{2}}(m,\vec{q})-I_{\Gamma}^{t_{1}}(m,-\vec{q})+I_{\Gamma}^{t_{2}}(m,-\vec{q})]\,.\label{xyz}
\end{eqnarray}
In Ref. \cite{Bali:2018nde} it is shown that $iF_{3}\left(\vec{q}\right)$
is different from zero only if $\Gamma_{n}\neq\Gamma_{n^{\prime}},$
and charge conjugation constraints imply that $G_{\ell}\left(\vec{q}\right)=0$
for the cases $\Gamma_{n}=\Gamma_{n^{\prime}}.$ We observe that these
results are automatically reproduced if $I_{\Gamma}^{r}(m,\vec{q})$
and $I_{\Gamma}^{t_{i}}(m,\vec{q})$ are functions of $\left|\vec{q}\right|$
only.
We will see later on that this fact actually occurs
in our calculation.

The integrals over $q^{0}$ and $k^{0}$ in
the expressions
$I_{\Gamma}^{r,t_{i}}(\vec{q})$
can be easily evaluated using the poles of the propagators. For instance,
when $\Gamma=V^{0}=\gamma^{0}$ we obtain
\begin{equation}
I_{V^{0}}^{r}(m,\vec{q})=  \bigintss\frac{d^{3}k}{(2\pi)^{3}}\frac{4\left[E_{\left|\vec{k}\right|}^{2}\left(4\,E_{\left|\vec{k}+\vec{q}\right|}^{2}+m_{\pi}^{2}\right)+m_{\pi}^{2}\,\vec{k}\cdot\vec{q}\right]}{E_{\left|\vec{k}\right|}E_{\left|\vec{k}+\vec{q}\right|}\left(4\,E_{\left|\vec{k}\right|}^{2}-m_{\pi}^{2}\right)\left(4\,E_{\left|\vec{k}+\vec{q}\right|}^{2}-m_{\pi}^{2}\right)} \, ,
\end{equation}
where $E_{v}=\sqrt{v^{2}+m^{2}}.$ Now, the angular integration can be
performed, arriving to

\begin{eqnarray}
I_{V^{0}}^{r}(m,q) & = & \bigintsss\frac{dk}{(2\pi)^{2}}\frac{k}{qE_{k}}\left\{ (E_{ k+ q }-E_{k - q})\left(1+\frac{3}{2}\frac{m_{\pi}^{2}}{
4E_{k}^{2}-m_{\pi}^{2}}\right)\right.\nonumber \\
 & + & \left.m_{\pi}\frac{32E_{k}^{2}-2E_{k+ q}^{2}-
 2E_{k-q}^{2}+m_{\pi}^{2}}{8(4E_{ k}^{2}-m_{\pi}^{2})}\ln\frac{(2E_{ k-  q}+m_{\pi})
 (2E_{k+ q}-m_{\pi})}{(2E_{ k-q}-m_{\pi})(2E_{k+ q}+m_{\pi})}\right\} \,,
\end{eqnarray}
where $k=|\vec{k}|$ and $q=\left|\vec{q}\right|.$ In
a similar way we obtain

\begin{eqnarray}
I_{V^{0}}^{t}(m,q) & = & I_{V^{0}}^{t_{1}}(m,q)+I_{V^{0}}^{t_{2}}(m,q)=\nonumber \\
 & = & \int\frac{dk}{(2\pi)^{2}}\left(-\frac{k}{qE_{k}}\right)(E_{k+q}-E_{k-q})\left\{ 1-\frac{1}{3}\frac{(E_{k+q}-E_{k-q})^{2}}{4E_{k}^{2}-m_{\pi}^{2}}\right.\nonumber \\
 & - & \left.\frac{m_{\pi}^{2}}{3(4E_{k}^{2}-m_{\pi}^{2})^{2}}\left[36E_{k}^{2}-2(E_{k+q}-E_{k-q})^{2}-3m_{\pi}^{2}\right]\right\} \,.
\end{eqnarray}

After regularization, the same integrals become

\begin{eqnarray}
\bar{I}_{V^{0}}^{r}(q)=\sum_{i=0}^{2}c_{i}I_{V^{0}}^{r}(M_{i},q)\,,\label{ivb}
\end{eqnarray}

\begin{eqnarray}
\bar{I}_{V^{0}}^{t}(q)=\sum_{i=0}^{2}c_{i}I_{V^{0}}^{t}(M_{i},q)\,.\label{itb}
\end{eqnarray}
One can see that these integrals do not depend on the direction of
$\vec{q}$, as anticipated, and therefore Eqs. \eqref{xyz} become

\begin{eqnarray}
X_{V^{0}}^{r}(q) & = & 4N_{c}(ig_{\pi qq})^{2}[\bar{I}_{V^{0}}^{r}(q)]\,,\nonumber \\
X_{V^{0}}^{t}(q) & = & 4N_{c}(ig_{\pi qq})^{2}[\bar{I}_{V^{0}}^{t}(q)]\,,\nonumber \\
Y_{V^{0}}^{r}(q) & = & Y_{V^{0}}^{t}(q)=Z_{V^{0}}^{t}(q)=0\,.\label{newxyzV0}
\end{eqnarray}

We conclude this section observing that
the above equations define the leading order contributions
to the functions \eqref{ottorel} in the $\Gamma=\gamma^0=V^0$ case:

\begin{eqnarray}
F_{0}({q}) & = & X_{V^0}^{r}({q})+X_{V^0}^{t}({q})\,,\nonumber \\
F_{1}({q}) & = & -X_{V^0}^{r}({q})+X_{V^0}^{t}({q})\,,\nonumber \\
F_{2}(\vec{q}) & = & X_{V^0}^{r}({q})\,,\nonumber \\
iF_{3}({q}) & = & 0 \,,\nonumber \\
G_{1}({q}) & = & 0 \,,\nonumber \\
G_{2}({q}) & = & 0 \,.
\label{summary}
\end{eqnarray}

\subsection{Dressing the vertex and other contributions}

In addition to the contribution
we have just discussed, one has to consider that,
in the present NJL scheme,
the local vertex can be dressed by the chiral interaction through
the diagrams depicted in Fig. \ref{Fig_dressed_local_vertex}. This
dressing, which could produce corrections to the results obtained in the previous subsection,
implies to change the bare vertex $\tau^{\alpha}\Gamma$ as follows, for the  isoscalar and isovector vertices respectively
\begin{align}
\Gamma & \rightarrow\Gamma+\frac{2ig}{1-2g\,\Pi_{S}\left(q^{2}\right)}\left(-2N_{c}\right)\int\frac{d^{4}q_{1}}{\left(2\pi\right)^{4}}\text{tr}\left[iS_{F}\left(q_{1}\right)\,iS_{F}\left(q_{1}-q\right)\,\Gamma\right] \, ,\nonumber \\
\label{Dres_vert_lineal}\\
\tau^{a}\Gamma & \rightarrow\tau^{a}\Gamma+i\gamma_{5}\tau^{a}\frac{2ig}{1-2g\,\Pi_{PS}\left(q^{2}\right)}\left(-2N_{c}\right)\int\frac{d^{4}q_{1}}{\left(2\pi\right)^{4}}\text{tr}\left[iS_{F}\left(q_{1}\right)\,i\gamma_{5}\,iS_{F}\left(q_{1}-q\right)\,\Gamma\right]\, , \nonumber
\end{align}
where $q^{\mu}=p_{1}^{\mu}-p_{2}^{\mu}=\left(0,\vec{q}\right).$

\begin{figure}
\begin{centering}
\includegraphics[scale=0.5]{Diagrama_linea_quark_vestida_local.pdf}
\par\end{centering}
\caption{Dressed local vertex.}
\label{Fig_dressed_local_vertex}
\end{figure}

In the vector current case, only the isoscalar current can
be dressed in principle. However, it is also easily proved that such a contribution vanishes, as
\begin{equation}
\int\frac{d^{4}q_{1}}{\left(2\pi\right)^{4}}\text{tr}\left[iS_{F}\left(q_{1}\right)\,iS_{F}\left(q_{1}-q\right)\,\gamma^{0}\right]=0\,.
\end{equation}
Therefore, in the particular case of the vector current under investigation here, there is no dressing of the vertex.

\begin{figure}
\centering{}
\includegraphics[scale=0.5]{Diagrama_vestido_b_local_AC.pdf}
\caption{Other type of contribution originated by the dressing of the currents. }
\label{Fig_p_diagram}
\end{figure}

Finally, we consider the diagram depicted in Fig.~\ref{Fig_p_diagram}.
This contribution can be written in the form ---$(p)$ stands for {\it pole contribution},
\begin{equation}
G_{\alpha\beta}^{\left(p\right)ij}\left(\vec{q}\right)=\mathbb{M}_{ij}\,\frac{2ig}{1-2g\,\Pi_{S}\left(0\right)}\,\mathbb{N_{\alpha\beta}} \, ,
\end{equation}
with
\begin{align}
\mathbb{M}_{ij}= & -\int\frac{d^{4}\ell}{\left(2\pi\right)^{4}}\text{Tr}\left[\bar{\phi}_{\pi^{j}}\,iS_{F}\left(P+\ell\right)\,iS_{F}\left(P+\ell\right)\,\phi_{\pi^{i}}\,iS_{F}\left(\ell\right)\right]\nonumber \\
 & -\int\frac{d^{4}\ell}{\left(2\pi\right)^{4}}\text{Tr}\left[\bar{\phi}_{\pi^{j}}\,iS_{F}\left(\ell\right)\,\phi_{\pi^{i}}\,iS_{F}\left(\ell-P\right)\,iS_{F}\left(\ell-P\right)\right]
 \, ,
\end{align}
and
\begin{equation}
\mathbb{N}_{\alpha\beta}=-\int\frac{d^{4}k}{\left(2\pi\right)^{4}}\text{Tr}\left[iS_{F}\left(k\right)\,iS_{F}\left(k\right)\,\tau^{\beta}\Gamma\,iS_{F}\left(k+q\right)\,\tau^{\alpha}\Gamma\right]+\left(q^{\mu}\leftrightarrow-q^{\mu},\alpha\leftrightarrow\beta\right) \, .
\end{equation}
The direct calculation gives, for $\mathbb{M}_{ij}$,
\begin{equation}
\mathbb{M}_{ij}=\delta_{ij}\,16N_{c}g_{\pi qq}^{2}\,m\,\left[m_{\pi}^{2}\,I_{3}\left(m_{\pi}^{2}\right)-I_{2}\left(0\right)\right] \, ,
\end{equation}
with $I_{2}\left(q^{2}\right)$ and $I_{3}\left(q^{2}\right)$ defined
in App. \ref{App.NJL_Basic_Equations}. The two quark intermediate state
is described by the quantity,
\begin{equation}
\frac{2ig}{1-2g\,\Pi_{S}\left(0\right)}=\frac{-i}{4N_{c}\left[m_{\pi}^{2}I_{2}\left(m_{\pi}^{2}\right)+4m^{2}I_{2}\left(0\right)\right]} \, ,
\end{equation}
and for $\mathbb{N}_{\alpha\beta}$ we have
\begin{equation}
\mathbb{N}_{\alpha\beta}=\delta_{\alpha\beta}\,i\,2N_{c}\left[I_{\Gamma}^{p}\left(m,\vec{q}\right)+I_{\Gamma}^{p}\left(m,-\vec{q}\right)\right] \, ,
\end{equation}
with
\begin{equation}
I_{\Gamma}^{p}\left(m,\vec{q}\right)=\int\frac{d^{4}k}{\left(2\pi\right)^{4}}\text{tr}\left[S_{F}\left(k\right)\,S_{F}\left(k\right)\,\Gamma\,S_{F}\left(k+q\right)\,\Gamma\right] \, .
\end{equation}
Putting all these results together, we obtain
\begin{equation}
G_{\alpha\beta}^{\left(p\right)ij}\left(\vec{q}\right)=
\delta_{ij}\delta_{\alpha\beta}\,2N_{c}\, (ig_{\pi qq})^2\,(- 4m^2)\,\frac{\left[m_{\pi}^{2}\,I_{3}\left(m_{\pi}^{2}\right)-I_{2}\left(0\right)\right]}{\left[m_{\pi}^{2}I_{2}\left(m_{\pi}^{2}\right)+4m^{2}I_{2}\left(0\right)\right]}\left[I_{\Gamma}^{p}\left(m,\vec{q}\right)+I_{\Gamma}^{p}\left(m,-\vec{q}\right)\right]
\, .
\label{polo4}
\end{equation}
By comparing to the structures for the isospin amplitudes defined in  Eqs.~(\ref{Iso_descomp}), it is observed that the {\it pole} contributions add to the bare leading-order results in Eqs.~(\ref{ottorel}) in the following manner
\begin{eqnarray}
F_{0}(\vec{q}) & = & X_{\Gamma}^{r}(\vec{q})+X_{\Gamma}^{t}(\vec{q})+X_{\Gamma}^{p}(\vec{q})\,,\nonumber \\
F_{1}(\vec{q}) & = & -X_{\Gamma}^{r}(\vec{q})+X_{\Gamma}^{t}(\vec{q})+X_{\Gamma}^{p}(\vec{q})\,,
\nonumber \\
F_{2}(\vec{q}) & = & X_{\Gamma}^{r}(\vec{q})\,,
\label{ottorel1}
\end{eqnarray}
with

\begin{equation}
X_{\Gamma}^{p}(\vec{q})=8N_{c}g_{\pi qq}^{2}\,m^2\,\frac{\left[m_{\pi}^{2}\,I_{3}\left(m_{\pi}^{2}\right)-I_{2}\left(0\right)\right]}{\left[m_{\pi}^{2}I_{2}\left(m_{\pi}^{2}\right)+4m^{2}I_{2}\left(0\right)\right]}\left[I_{\Gamma}^{p}\left(m,\vec{q}\right)+I_{\Gamma}^{p}\left(m,-\vec{q}\right)\right] \, .
\end{equation}

In the case $\Gamma=\gamma^{0},$
shown in the following as an example, $I_{\Gamma}^{p}\left(m,\vec{q}\right)$
is a function of $q=\left|\vec{q}\right|$,
\begin{align}
I_{V^{0}}^{p}\left(m,q\right) &
=\int\frac{dk}{\left(2\pi\right)^{2}}\frac{-k}{12\,q\,E_{k}^{3}}\left(E_{k+q}-E_{k-q}\right)^{3} \, , \nonumber
\end{align}
and, after regularization, the last integral becomes
\begin{equation}
\bar{I}_{V^{0}}^{\,p}\left(q\right)=\sum_{i=0}^{2}c_{i}\,I_{V^{0}}^{p}\left(M_{i},q\right) \, .
\end{equation}
Putting all these results together we have finally

\begin{equation}
\label{xvp}
X_{V^{0}}^{p}\left(q\right)=16N_{c}g_{\pi qq}^{2}\,m^{2}\,\frac{\left[m_{\pi}^{2}\,I_{3}\left(m_{\pi}^{2}\right)-I_{2}\left(0\right)\right]}{\left[m_{\pi}^{2}I_{2}\left(m_{\pi}^{2}\right)+4m^{2}I_{2}\left(0\right)\right]}\bar{I}_{V^{0}}^{\,p}\left(q\right) \, ,
\end{equation}
and the final result for the functions
under investigation, including all the contributions evaluated so far, can be
summarized as follows
\begin{eqnarray}
F_{0}({q}) & = & X_{V^0}^{r}({q})+X_{V^0}^{t}({q})+
X_{V^0}^{p}({q})\,,\nonumber \\
F_{1}({q}) & = & -X_{V^0}^{r}({q})+X_{V^0}^{t}({q})+X_{V^0}^{p}({q})\,,
\nonumber \\
F_{2}({q}) & = & X_{V^0}^{r}({q})\,.
\label{summ2}
\end{eqnarray}

\begin{figure}
\centering{}
\includegraphics[scale=0.6]{F0-F1_y_pub.pdf}
\caption{The quantities $F_0$ and $F_1$, Eqs.~\eqref{summ2},
in coordinate space, for various choices of the NJL parameters ---given in App.~\ref{App.NJL_PV_regularization}--- corresponding to a different
pion mass, to allow a proper comparison with lattice data~\cite{Bali:2018nde}
(green points with error band), for $\Gamma=\gamma^0$.}
\label{Fig:7}
\end{figure}

\begin{figure}
\centering{}\includegraphics[scale=0.65]{F2_y_pub.pdf} \caption{
Same as in Fig. 4, but for the function
$F_2$ in Eqs. \eqref{summ2}.
}
\label{Fig:10}
\end{figure}

\begin{figure}[htbp]
\centering{}\includegraphics[scale=0.7]{C1-C2_y_pub.pdf} \caption{The functions $C_{1}$ and $C_{2}$, Eq.
\eqref{duerel}, for various choices of the NJL parameters ---given in App.~\ref{App.NJL_PV_regularization}---  corresponding to a different
pion mass to allow a proper comparison with lattice data
\cite{Bali:2018nde}
(green points with error band), for $\Gamma=\gamma^0$, in coordinate space.}
\label{Fig:8}
\end{figure}

\begin{figure}
\centering{}\includegraphics[scale=0.8]{C1-C2_q_pub.pdf} \caption{Same as in Fig.~\ref{Fig:8}, but in
momentum space.}
\label{Fig:9}
\end{figure}

\section{\label{IV} Comparison with lattice data}

The comparison of our results with the lattice evaluation of Ref.~\cite{Bali:2018nde}
in the vector-vector case
is presented in Figs.~\ref{Fig:7}-\ref{Fig:9}.

The quantities $F_0$ and $F_1$ in Eqs. \eqref{summ2} ---evaluated using Eqs.
\eqref{newxyzV0} and \eqref{xvp}---
are shown for $\Gamma=\gamma^0$ in Fig. \ref{Fig:7}, in coordinate space, for various choices of the parameters
of the NJL model corresponding to a different
pion mass. The sets of model parameters corresponding to different values of the pion mass are reported in Appendix \ref{App.NJL_Basic_Equations}. The change of the full parameter set allows a proper comparison with lattice data.
The blue dashed curves ---labelled
{\it $m_\pi=$~300~MeV~NJL--Latt}---
have to be compared with the lattice results ---in green. Those lattice data correspond to  Figs. 20 (c)
and (a) of Ref.~\cite{Bali:2018nde}, respectively.
A qualitative agreement is clearly found.
A similar conclusion holds for $F_2$, given in Eqs. \eqref{summ2} and shown in Fig. \ref{Fig:10}.

Besides, the results of the evaluations of the rhombus and trapezoid diagrams in our approach are related, in the calculation scheme of Ref. \cite{Bali:2018nde}, to  lattice contractions called
$C_{1}$ and $C_{2}$. The correspondence formally reads
\begin{eqnarray}
C_{1}(q) & = & \frac{1}{2}X_{\Gamma}^{r}(q)\,,\nonumber \\
C_{2}(q) & = & \frac{1}{4}[X_{\Gamma}^{t}(q)+X_{\Gamma}^{p}(q)]\, .
\label{duerel}
\end{eqnarray}
The latter  quantities can also be directly compared to the findings
of Ref.~\cite{Bali:2018nde}, which will come of useful for the interpretation of contributions from diagrams.
Our results for these functions are shown in Figs.~\ref{Fig:8} and~\ref{Fig:9}, in coordinate and momentum space,
respectively. In particular the
former results
show an encouraging agreement with the lattice data
reported, in coordinate space, in Figs. 11 (a) of Ref. \cite{Bali:2018nde}.
Overall, the NJL scheme seems to tentatively reproduce
the trend of the available lattice results.

Following an argument discussed in Ref.~\cite{Burkardt:1994pw}, it is observed that, in the absence of correlations,
two-current distributions could be computed from the single-current ones. This factorization hypothesis is comparable to an argument that has often
been used more recently for dPDFs
---see, {\it e.g.}, Ref.~\cite{Diehl1}.
This hypothesis is examined
in Ref.~\cite{Bali:2018nde}. In particular, for the isospin combination $\left\langle \pi^+\left(P\right)\right|\mathcal{O}_{n}^{uu}\left(y\right)\mathcal{O}_{n}^{dd}\left(0\right)\left|\pi^+\left(P\right)\right\rangle$, inserting a complete set of intermediate states between the two currents and keeping,
among them, only the pion ground state, it can be shown  that the two-current observable can be expressed in terms of single-current Form Factors.

In the most recent evaluation, the
the full lattice result
for the $C_1$ contraction ---as it dominates the relevant isospin combination--- is compared to
single-current expressions using known results for the charges --{\it i.e.} Form Factors at zero momentum transfer--- as well as a common power law fall-off for the momentum transfer dependence of the Form Factor.
While the results at zero momentum transfer are acceptable, the attempt is found to generally fail to a large extent.

Based on our previous experience with dPDFs~\cite{jhep19}, we have evaluated diagrams of the type shown in Fig.~\ref{Fig_Two_Fem},
where the intermediate  two  quark  state can have the quantum numbers of a $\sigma$ particle
or a pion, as allowed in the present calculation scheme.
After a tedious evaluation
detailed in the Appendix \ref{App.FormFactors}
for $\Gamma=\gamma^0$
and assuming dominance of the pion pole, in agreement with the procedure followed
in Ref.~\cite{Bali:2018nde},
it is found that the only
contribution arising
from these diagrams
can be written
\begin{equation}
X_{\Gamma}^{F_{PS}^{-}}(\vec{q})=4\,\frac{\left(E_{\pi}+m_{\pi}\right)^{2}}{E_{\pi}}\,\left[F_{em}\left(2m_{\pi}^{2}-2m_{\pi}E_{\pi}\right)\right]^{2} \, ,
\label{2ff}
\end{equation}
where $F_{em}$ is the pion electromagnetic form factor and $E_{\pi}=\sqrt{m_{\pi}^2+\vec{q}^2}$.
This expression ---after using the relevant isospin combination from Eq.~(\ref{eq:iso_pionexcha})--- agrees with that
adopted in Ref.~\cite{Bali:2018nde} to approximate the full result given by the function
$C_1$. In the NJL scheme used here
the contributions to $C_1$ arise from the {\it rhombus} diagram only;
such diagram cannot accommodate for
any contribution of the type of Fig.~\ref{Fig_Two_Fem}. Therefore no comparison between the result of
Eq.~(\ref{2ff}) with the contributions coming from $C_1$
---as suggested in Ref.~\cite{Bali:2018nde}---
 can be made according to the spirit of the present paper. Accordingly we do not discuss relations based on that factorization hypothesis any further.

\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.5]{Diagrama_dos_Fem_1.pdf}
\end{center}
\caption{One of the eight diagrams with pion intermediate states.}
\label{Fig_Two_Fem}
\end{figure}
\section{\label{V}Conclusions}

Two-partons correlations represent an elusive non perturbative information, theoretically encoded
in two-current correlations as well as double parton distribution functions.
The latter quantities are under theoretical investigation for the proton. There are  perspectives to observe
them during the LHC operation in the next years. While
a possible access to the same observable for the pion
appears challenging, lattice results have already been
obtained for two-current correlations in the pion,
a quantity that could be related to double parton distribution functions~\cite{Bali:2018nde}. A consistent field-theoretical approach, based
on the Nambu--Jona-Lasinio model with Pauli--Villars
regularization, has been used in this paper for
a systematic analysis
of two-current
correlations in the pion.
We have given explicit expressions
for the time-time component of the vector-vector
two-current correlations in momentum space.
We have compared our results for
two-current correlations with lattice data, obtaining an overall good
qualitative agreement.
As happens in model calculation
of the related quantities double parton distributions, it is found  that, at the low scale relative to the model description,
these functions encode novel non-perturbative information,
not present in one-body quantities. This conclusion is highlighted in the consideration of a possible factorization of the two-current correlation into one-body Form Factors, which is found to be an unconnected contribution in our low-energy model.
It will be interesting to compare our results
for pion double distribution functions with forth-coming lattice data, whose
evaluation is presently in progress
\cite{private}.

\section*{Acknowledgments}

We thank M. Rinaldi for useful discussions and C. Zimmermann for sending us the lattice data of Ref. \cite{Bali:2018nde} relative to the quantities of interest here.
This work was supported in part by the Mineco
under contract FPA2016-77177-C2-1-P, {by the
STRONG-2020 project of the European Union's Horizon 2020 research and innovation programme under grant agreement No 824093,}  and by UNAM through the PIIF project Perspectivas en F\'isica de Part\'iculas y Astropart\'iculas as well as  Grant No. DGAPA-PAPIIT IA101720.
A.C. and S.S. thank the Department of Theoretical Physics of the
University of Valencia for warm hospitality and support.

redpajama_set_name: RedPajamaArXiv


text:
UK government deletes tweet about Russian spy's poisoning
By James Masters, Sheena McKenzie, Gianluca Mezzofiore and Katie Polglase, CNN
Updated 1348 GMT (2148 HKT) April 4, 2018
The UK Foreign Office deleted a tweet blaming Russia for the nerve agent attack.
London (CNN) Britain's claim that Moscow was behind the poisoning of a former Russian spy faced fresh scrutiny Wednesday when it emerged the UK government had deleted a tweet blaming Russia for producing the nerve agent used in the attack.
The UK Foreign Office acknowledged it had removed the social media post, which stated that British chemical weapons experts believed Russia made the nerve agent, Novichok, used to poison Sergei Skripal and his daughter Yulia in the English city of Salisbury on March 4.
A Foreign Office spokesperson told CNN that the tweet was removed because it was "truncated and did not accurately report" a briefing by the British ambassador to Moscow last month.
The revelation came as the UK government was already on the defensive on the issue. On Tuesday, the chief executive of the Porton Down defense laboratory in the UK said scientists could not confirm where the nerve agent was made. The British government insisted that additional material from intelligence sources led it to the conclusion that Russia was behind the attack.
Russia, which has repeatedly denied involvement in the attack and has sought to blame Britain instead, seized on the developments. The Russian embassy in London tweeted: "Why would @foreignoffice delete this tweet from 22 March?"
The controversy centered on a briefing on the Salisbury poisoning given by the British ambassador to Moscow, Laurie Bristow, on March 22. In it, he said "the analysts at Porton Down, the Defense Science and Technology Laboratory in the UK, established and made clear that this was a military-grade chemical weapon. One of the Novichok series; a nerve agent as I said produced in Russia."
A tweet, which the Foreign Office said was published in "real time", paraphrased the comments, saying: "Analysis by world-leading experts at the Defence Science and Technology Laboratory at Porton Down made clear that this was a military-grade Novichok nerve agent produced in Russia."
The tweet was deleted sometime before March 27. An identical tweet by the UK embassy in Russia, was also deleted.
The Foreign Office spokesperson said the decision to delete the tweets did not change the UK government's assessment that Russia was responsible for the "brazen and reckless act" of poisoning the Skripals.
Britain and its allies, including the US, France and Germany, have expelled more than 100 Russian diplomats from their countries over the poisoning, prompting a series of reciprocal expulsions of foreign diplomats from Russia.
Porton Down contradicts Johnson
News of the deleted tweets came a day after Gary Aitkenhead, the head of the Porton Down laboratory said that while scientists were sure that only a "state actor" could have accessed the nerve agent, they could not say definitively where it was made.
"We have not identified the precise source, but we have provided the scientific info to government, who have then used a number of other sources to piece together the conclusions you have come to," Aitkenhead told Sky News.
He added: "It is our job to provide the scientific evidence of what this particular nerve agent is. We identified that it is from this particular family and that it is a military grade, but it is not our job to say where it was manufactured."
His comments contradicted remarks made by Foreign Secretary Boris Johnson, who was asked last month how the government was able to quickly conclude that Russia was the source of the nerve agent.
"When I look at the evidence, the people from Porton Down, the laboratory, they were absolutely categorical," Johnson told the German broadcaster Deutsche Welle.
"I asked the guy myself, I said: 'Are you sure?' And he said: 'There's no doubt.' So we have very little alternative but to take the action that we have taken," said Johnson.
UK chemical weapons representative slams Russia
The brewing controversy over the tweets threatened to overshadow an emergency summit of the world's chemical weapons watchdog in The Hague on Wednesday to discuss the poisoning of the Skripals.
The British delegation to the Organization for the Prohibition of Chemical Weapons (OPCW) slammed a Russian proposal for a joint investigation into the incident as "perverse," describing it as a "diversionary tactic" aimed at evading questions over Moscow's alleged role in the attack.
Speaking at the meeting, called at Russia's request, the UK said the Kremlin's response to the Skripal case, as well as chemical weapons attacks allegedly committed by the Syrian regime, were proof of its disdain for international monitors.
"It seems clear that Russia will never accept the legitimacy of any investigation into chemical weapons use unless it comes up with an answer Russia likes," said John Foggo, the UK representative to the OPCW.
The European Union's representative at the chemical weapons meeting, Krassimir Kostov, also backed the UK's assessment that it was "highly likely" Russia was behind the attack, telling delegates of the EU's "shock at the offensive use of any military-grade nerve agent, of a type developed by Russia, for the first time in European soil in over 70 years."
CNN's Sheena McKenzie contributed to this report.

redpajama_set_name: RedPajamaCommonCrawl


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NexPoint Makes Three New Sales and Marketing Appointments to Support Investment Platform Growth
By Highland CapitalMay 7, 2020May 26th, 2020FEATURED, PRESS RELEASE
Distribution Team Adds 17 New Hires in Past Year
DALLAS, May 7, 2020 — NexPoint, a multibillion-dollar alternative investment platform, today announced the addition of three new sales and marketing professionals. The new hires are part of an ongoing expansion of the firm's distribution capabilities designed to support real estate investment offerings and reflect growth across the platform. Including the latest appointments, NexPoint added 17 members to its distribution team in the last year across a range of roles.
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Other new hires announced today include a marketing manager and an internal sales consultant.
"The additions to the team over the last year align our distribution capabilities with the investment opportunities available on the NexPoint platform," said Kirby Noel, managing director and national sales manager. "As a result, we can better serve financial advisers and their clients, building a broader understanding of investors' evolving needs and bringing them a range of investment solutions from NexPoint.
NexPoint is an alternative investment platform comprised of a group of investment advisers and sponsors, a broker-dealer, and a suite of related investment vehicles. NexPoint's platform provides differentiated access to alternatives through a range of investment solutions, including public and private real estate investment trusts, tax-advantaged real estate vehicles, other private real estate investments, closed-end funds, interval funds, and a business development company. NexPoint is based in Dallas, Texas and is part of a network of affiliates with expertise across the asset management and financial services spaces. For more information visit www.nexpointfunds.com.
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Evolving Air Power Paradigms
Posted on June 13, 2011 | by Caroline Teames
The Emergence of the Three Dimensional Warriors
By Robbin Laird
06/16/2011 – As we look forward to the next decade of air power, the question of how best to understand the way forward is rooted in an understanding that past is not prologue. The leveraging of new technologies in preparing for the technologies after next is the most cost-effective as well as operational viable approach.
In broad terms, modern air power has been shaped over the past thirty years by what emerged as air-land battle doctrine. Here the Army was asked to move to a new maneuver concept with air power delivering decisive blows against enemy forces on the battlefield, at the rear, and against moving logistical support elements. This required the acquisition of air superiority, after which air elements engaged with a mobile ground force could seek destruction of enemy forces.
The air-land approach shaped to deal with the Soviet forces facing Europe was executed in the first Gulf War. Here the decisive impact of U.S. and allied forces against the fourth largest army in the world was game changing. Competitors looking at the results noted the need to re-shape their approaches.
Such a re-shaping first started in Bosnia, as the Serbs began to mask and catalogue forces. And to try various techniques to unmask stealth and to use mobile systems to strike air assets. The air campaign was remarkably successful; but only to the point of needing to insert ground forces to shape outcomes. Indeed, the core lesson of air-land battle was the need to combine air power with maneuvering ground forces. This lesson was simply reinforced by the Bosnia experience. With Gulf War II, a new variant of air land battle was implemented, with a significant expansion of the ground maneuvering capability of the USMC and the US Army. In the case of the USMC, they took their airpower with them, in shaping an ability to encircle and destroy Iraqi forces. The USMC began to demonstrate distributed operations enabled by air power, a template that is central to the next age of air power.
The decade of COIN first in Iraq and then in Afghanistan has inverted for many the meaning of airpower. For this generation, air power is largely a support function. The air arm delivers supplies and support to the disbursed ground forces. An air dropping revolution has facilitated an ability for the ground forces to operate without needing to build Walmarts everywhere they go. Aeromedivac has progressed to the point that on average soldiers can be brought back stateside in only three days compare to more than 40 in Vietnam.
Remotely piloted vehicles have been able to create asymmetrical strike options against adversaries who use Pakistani territory. Individual ground units can deploy their own ISR assets to support operations. Indeed, for many RPAs are the future of airpower, but the limitations of these assets are so profound that there is little credibility in making this assumption. But clearly, RPAs are part of the future of air power.
When looking at the decade ahead is the continuation of the COIN model with its assumption of air superiority really a realistic assumption?
A large part of the answer is how innovative U.S. leadership can be. There is a troubling trend to keep buying aircraft the Indians don't want. They answer in large part is how effectively one leverages fifth generation aircraft and changes strategy, doctrine and tactics to take advantage of what they aircraft bring to the table. The next age could clearly be of what we have called the Three Dimensional Warrior. Here the ability to use air assets to provide for 360-degree situational awareness and flying combat systems becomes a key element for any ground or surface operation. US forces do not want to be in a far fight; moving a COIN force to Three Dimensional Warriors is a core element of ensuring that the US is not seeking equality in warfare.
In many ways, the shift in air power is from a consideration of the air element as operating as the strategic hammer to considering air power as the enabler of multi-spectrum, multi mission operations in the 21st century. The much greater capabilities of individual platforms and of fleets operating with such capabilities in mind enable the ground and surface forces to operate with greater range and effectiveness. A new approach to power projection is possible, whereby the U.S. can link its forces much more effectively, with greater lethality and greater range.
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Hey bookworms! We haven't talked in a bit, so I thought why not give you guys my plans for the weekend. No adventures out for me though because work forgot to include P (pay) in PTO. They plan to pay me on this check, but it ruins all the plans I had set. I am already eager to go back to Vancouver, 3.5 days was not enough.
I still want to go to Vancouver Island, go whale watching, maybe see the orchestra, go to the museum. Get a better place to stay next time for sure. My back is still aching from the beds. I didn't take many pictures… I am the worst at that… I like to consider myself a live in the moment kind of girl. Commit to memory rather than pause to get the perfect shot if that makes sense?
Hopefully I have more to tell and show you next time, but know I was happy and content with my trip.
I am currently binging this on Netflix and loving it! It makes me want to explore the setting even more than before. The cast of children really bring the characters to life and it makes me want to continue reading the books. It is an amazing series! Can't wait for season 2!
Tomorrow is going to be a mushy day except for one movie on the list if you can't tell and I love the friendship this movie starts out with and I think it is exactly what I need.
Honestly one of my favorite movies and love stories and to me one of the most realistic (also one of my favorite books). When life gets a little rough it is one of the things that makes it easier is watching this.
My current audio book listen and I'm only a few minutes in so I don't have thoughts yet, but I was really inspired by the first one. Needless to say I have high hopes for the sequel and I may be a bit biased because she is one of my favorite authors.
I haven't picked it up since before I left on my trip, but I feel it is a good time to pick it back up and I feel like it will keep me from getting lost in my own thoughts.
Because I think everyone should read children's classics no matter how old they are. They can hold more more truth than that of adult fiction. I think I will read a few tales and see what I can learn..
Well bookworms I think that is all that is on my agenda this weekend and maybe an ebook if I decide to turn on my nook tonight. What is on your holiday weekend agenda? Any great books or movies? Let me know in the comments and I hope you all have fun! Happy Reading!


When it appears in December, CLICK on the Pegasus Ponies Below for GREAT Savings for 2019 !
Buckaroo Camp is an exciting week filled with horses, games, crafts and FUN! Buckaroo Camp is a DAY CAMP where campers begin each day at 9:00 am and conclude each day at 4:00 pm. On each Wednesday of Buckaroo Camps many campers will elect to stay at BPS for an overnight camp out. Every Wednesday our Campers will have the option to bring their sleeping bags and other essentials so that they may spend the night the same as our Horse Lovers Campers do! That evening they will participate in a camp cookout- Hot Dogs, Hamburgers, Potato Chips and/or Potato Salad, Baked Beans and S'mores Pizza! Plus a campfire jamboree including songs and stories. The cost of Buckaroo Camp is only $425/week. The Wednesday overnight option is $490/week.
All deposits are non-refundable. All deposits should be made as early as possible in order to insure your reservation in the preferred camp of your choice.
All additional clerical fees charged in any circumstance are NON refundable.
Canceling – The camp's paid deposit portions are non-refundable and are non-transferable to other campers. All other moneys paid in advance and in excess of the minimum deposit may be refunded. There are some exceptions to this cancellation policy. If we are able to fill your camper's space with another camper that may be on the waiting list; your deposit moneys and any additional payments will be refunded, MINUS a $45.00 additional office and clerical fee charge. Otherwise, if we are not able to fill your campers space your deposit amount will be forfeited and NOT refunded.


Being a Costco Wholesale member has its perks, especially when it comes to deals and discounts. This month, they're taking hundreds off their best appliances, electronics, bulk food, and personal care products. With only three days left in the sale, you don't want to miss out.
Each month, the Costco member-only savings just keep getting better and better. If you visit before May 21, 2017, you'll find jaw-dropping deals on products from some of your favorite brands. For instance, save $40 off the new, state-of-the-art Philips® Norelco Shaver. Of, if electronics are what you're after, check out this Asus® 17-inch Laptop, now $200 off the original price. No matter what items you're eyeing, you can feel confident that you're getting a great deal.
You only have three more days before these member-only savings expire, so visit your nearest Costco today! Not a member? Visit their website to purchase your wholesale membership.


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November 2016 • Volume 104 • Number 11 • Page 12
Thank you for viewing this Illinois Bar Journal article. Please join the ISBA to access all of our IBJ articles and archives.
LawPulse
Illinois Appellate Court overturns forfeiture on Eighth Amendment grounds
By Matthew Hector
The Illinois fifth appellate district invalidated seizure by law enforcement of a Harley Davidson trike, basing its ruling on the Eighth Amendment's excessive fines clause.
Civil forfeiture, the process of the state seizing assets used in the commission of, or related to a crime, has been a topic of public debate in recent years. The Chicago Reader recently published an article about the use of civil forfeiture in Chicago, noting that civil forfeiture generates billions of revenue every year for law enforcement agencies across the country. See http://www.chicagoreader.com/chicago/police-department-civil-forfeiture-investigation/Content?oid=23728922.
In many situations, a person who is not being charged with a crime is faced with the risk of losing assets to forfeiture laws. In some situations, individuals can recover their property. A recent ruling from the Illinois fifth appellate district has taken a new approach to civil forfeiture by invalidating a seizure based on the Eighth Amendment's excessive fines clause.
In People v. 2010 Harley-Davidson, 2016 IL App (5th) 150035, the fifth district held that the civil forfeiture of a $35,000 Harley-Davidson trike was a violation of the Eighth Amendment. The vehicle's owner, Petra Henderson, was a passenger when her husband, Mark, was arrested and charged with aggravated DUI while driving the vehicle.
Petra raised two issues on appeal: 1) whether she had consented to the use of the motorcycle and 2) whether the forfeiture violated the excessive fines clause. If an individual can demonstrate that a vehicle was used without the knowledge and consent of the owner, then it may not be subject to forfeiture.
In this case, the fifth district found that the weight of the evidence demonstrated that Petra had consented to Mark driving the vehicle. Most observers, however, find the Eight Amendment analysis to be the most compelling aspect of the opinion.
DuPage County attorney Donald J. Ramsell says that the fifth district's ruling is a "breakthrough case" and, to his knowledge, the first in Illinois to find a forfeiture excessive under the Eighth Amendment's excessive fine clause. Ramsell says that there is no "innocent owner defense" to a forfeiture action - even the owner of a stolen car may risk forfeiture if that car is used to commit a crime. "This case spells out that even if the state proves up its statutory right to forfeiture, it can be overridden by the fact that the fine itself is excessive," he says.
On the other hand, David J. Robinson, an Illinois Appellate Prosecutor, says the case is "unique." He notes that while there have been some opinions from the fourth district that found a forfeiture excessive, none were decided on an Eighth Amendment basis. While Robinson doesn't find the result surprising, he is surprised by the court's rationale.
A three-prong forfeiture test
The court's opinion lays out a three-prong test for determining whether a forfeiture is constitutionally excessive. The test, adopted by the Illinois Supreme Court, looks at "(i)the inherent gravity of the offense compared with the harshness of the penalty; (ii) whether the property was an integral part of the commission of the crime; and (iii) whether the criminal activity involving the defendant property was extensive in terms of time and/or spatial use." Id., ¶ 28.
As to the first prong, the court stated that driving erratically, as well as under the influence, poses a serious public safety concern. What's more, Mark's license was revoked at the time that he was arrested. "Illinois courts have long recognized that driving with a revoked license is 'one of the most serious driving offenses one can commit absent bodily injury when the underlying revocation stems from a DUI conviction.'" Id., ¶ 30.
However, the court also pointed out that Petra, while culpable for allowing Mark to drive, was not the person who committed the crime. "We also believe that in nearly all cases, the acquiescing owner will be less culpable than the actual offender." Id., ¶ 31.
Turning to the harshness of the penalty, the court found that the seizure of a $35,000 vehicle was "particularly harsh" even though there was no evidence in the record concerning Petra's overall financial situation. Id., ¶ 35. Given the value of her vehicle and the fact that she did not commit the offense, the court found that the first prong of the test weighed in her favor.
As to the second and third prongs, the court noted that Petra's vehicle was clearly central to Mark's offense of driving under the influence, which satisfies the second prong of the test. Turning to the third factor, the court stated that whether the criminal conduct involving the motorcycle was pervasive in time and space "concerns more than simply how long and how far Mark drove the motorcycle." Id., ¶ 39. The court stated that the third factor also involves an inquiry into whether the property "played an extensive or pervasive role in the commission of the crime." Id. But, because that same factor satisfied the second prong of the test, the court declined to find that aspect of the third factor to be relevant to the case.
Instead, the court noted that Mark drove the vehicle about 12 blocks, which likely only took a few minutes. As such, the third factor weighed slightly against forfeiture. In sum, the court found that the harshness of the penalty "was grossly disproportionate to [Petra's] conduct," making the penalty a violation of the Eight Amendment. Id., ¶ 41.
Robinson says that the appellate prosecutor's office has filed a petition for rehearing in this case. For more on the Harley Davidson case, see "Wanna drive drunk? Borrow a Bentley" in the September 29 Illinois Times. For more on civil forfeiture generally, see Hon. Anthony W. Vaupel, "Civil Asset Forfeitures: A Step-by-Step Guide," in last month's Journal.
Matthew Hector is a senior associate at Woerthwein & Miller.
November 2016 LawPulse
Illinois Supreme Court overturns six-person-jury statute
Court rejects right-of-publicity claim against Avvo
Judging judges


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Q: Is it possible: Using Blazor serverside as a client app There is a ready azure microservices that I need to build a client app against. There are 2 choices blazor server side and client side. Because the client side is not ready yet and has limited debugging capabilities I want to use blazor server side.
My question is if calling services from blazor server side is possible and if it is a good idea. To use it as a client app?
And also if it is possible to host blazor next to the microservices in azure?

A: I believe what you are asking is if it's acceptable to use the Blazor server side as a proxy to a microservice?
Technically, there's no reason that you couldn't. You would simply create an HttpClient to call your Microservice assuming that it exposes a REST API.
I'm not sure what you mean by, "..if it is possible to host blazor next to microservices in azure?" If you're using an Azure Web App to host your microservice, you would probably want to create a new Web App for your blazor server side app, otherwise you aren't really getting the benefit from the app service.
There are other options for configuring this type of architecture, but it all depends on your goals. Additionally, you might want to check out the following project:
https://github.com/Suchiman/BlazorDualMode
It will let you run blazor client and server side together. I've used it to help debug client side blazor apps.

redpajama_set_name: RedPajamaStackExchange


The metrical system is based on all worldwide valid surfaces Dimensions, In addition, in many European countries, some very old measures are still in use. In viticulture in Europe are usually hectares (Hectar), in the Anglo-American area mostly Acres for the size of vineyards common. The old measures used to be based on the use of land. The names or Sizes were due to labor - whether a vineyard dug up, sown or plowed a field, or a meadow was mowed. The area that a man could pierce with a spade on a vineyard in one day yielded a grave. The morning and the yoke were the size of arable land that could be plowed up one morning. A daymah or man's maiden corresponded to the area a mower managed to mow in one day.
In addition to the workload, seed and harvest were also used as a criterion for area determination. In the case of fields, it was the amount of seed given by a measure (Metzen, Mutt, Star), in the case of meadows it was the yield unit (Fuder, Heufuder). The area sizes were often different and differed from region to region. They were not exact sizes, but rough approximations. Even within one country, there was no great need for standardization, as basic traffic was handled locally. It was not until the end of the 18th century that precisely measured sizes were introduced on the basis of standard dimensions. Such was the square fathom before the introduction of the metric system.
See also other measure-related statements under drum types. bottles. capacity measures. units. wine vessels and Wine production volumes (all wine-growing countries with wine and vineyards).
This page was last modified at 26 February 2019 at 16:14.


Businesses exist to make a profit, and if they are public they are also accountable to their shareholders for how they spend their money. However, despite being driven by the bottom line, many businesses make substantial donations to charity. How can this be justified, and what is the return on a company doing this?
One of the most important reasons for doing this is to raise internal morale. If employees feel that their company actually cares about worthy causes, they're more likely to form a good opinion of the company and believe that they are part of something worthwhile. This in turn makes them less likely to leave because of the bonds this creates, reducing staff turnover and driving profitability over longer periods of time. Given the cost of recruiting and training new employees when compared to retaining existing ones, this makes eminent sense. In addition, employees who feel good about their company and what it does tend to be more creative and productive, which again has a direct positive impact on the company's operations and balance sheet.
The next reason that companies should give to charity is the one we think about most. Companies need the support of the communities that they are in – as well as all the customers that they do business with – in order to be successful. By working with charities and making this known, they build a strong reputation for caring about things that matter, especially if they choose the right charities. Of course, this must not be done in a cynical manner. Company leaders need to believe in the charities they support – for example, Francesco Corallo worked in Central America during the early years of his career, and continues to support charities there. You can find out more info on Francesco Corallo online.
Clearly, the overriding reason why businesses should give to charity is that it is the right thing to do. However, it is good to know that there are sound business reasons for it as well, making it easier for managers to justify charitable giving to shareholders.


Dear Readers, Daily Current Affairs Questions Quiz for bank exam SBI RRB SSC PO & Clerk Exam 2019 of 08th February 2019. Daily GK quiz online for bank & competitive exam. Here we have given the Daily Current Affairs Quiz based on the previous days Daily Current Affairs updates. Candidates preparing for RRB SSC PO and Clerk Exam 2019 & competitive exams can make use of these Current Affairs Quiz.
1. 5th India-Bangladesh Joint Consultative Committee Meet held in which city?
2. State-run power giant NTPC has signed an agreement with which private sector Bank for a Rs 2,500 crore loan to part finance capital expenditure?
3. Who was conferred the Légion d'Honneur (Legion of Honour) the highest civilian award of France in recognition of his work for specially-abled children?
Francois Laborde, a 92-year-old priest, from Bengal, was conferred the Légion d'Honneur (Legion of Honour) the highest civilian award of France in recognition of his work for specially-abled children.He is the third person from the state to have been awarded the Legion of Honor after film maestro Satyajit Ray and actor Soumitra Chatterjee. Father Francois Laborde has set up the Howrah South Point, an organisation working for the development of specially-abled children, the destitute and the most deprived sections of the society.
4. Parmanu Tech 2019' conference held in which city?
5. Digicop a mobile application developed by Nasscom launched by which city police?
Tamil film actor Vijay Sethupathi launched the mobile App 'DigiCop' of the Chennai police department. The application was developed by Nasscom. Using the App, people can track the status of stolen two-wheelers and cell phones.The details of 18,000 stolen mobile phones are stored in the App. So next time someone is buying a phone from a second hand shop they can verify if the phone is stolen or genuine.Using DigiCop App, people can verify IMEI, report lost two-wheelers and phones, know the nearest police station, police news and traffic alerts.
6. Who has taken over as General Manager of Integral Coach Factory (ICF)?
Rahul Jain has taken over as General Manager of Integral Coach Factory (ICF).Jain, was former Assistant General Manager at Western Railway. He belongs to the Indian Railway Service of Mechanical Engineer (IRSME) cadre and his appointment comes after former ICF GM Sudhanshu Mani retired on December 31.Mani is regarded as the architect of India's first self-propelled long distance "Train 18", which was later named "Vande Bharat Express".
7. What is Indias' rank in the recently released US Chamber's global IP index?
India has jumped eight places to 36th position on the International Intellectual Property (IP) Index, which analyses the IP climate in 50 global economies. India's eight-point jump in 2019 from 44th position in 2018 is the highest increase among 50 nations mapped by the index. The US, the UK, Sweden, France and Germany remained the top five economies on the intellectual property index in 2019 retaining their spots from the last year. The index brought out by the US Chamber of Commerce's Global Innovation Policy Center (GIPC) ranks countries based on 45 indicators that are critical to an innovation-led economy supported by robust patent, trademark, copyright, and trade secrets protection.
8. With which statutory body of the Government of India, did the Government e Marketplace (GeM)entered into a Memorandum of Understanding to enable a fair and competitive environment in the e-Marketplace?
Government e Marketplace (GeM) and Competition Commission of India (CCI) entered into a Memorandum of Understanding to enable a fair and competitive environment in the e-Marketplace. GeM is a state-of-the-art national public procurement platform of Ministry of Commerce and Industries, which has used technology to remove entry barriers for bonafide sellers and has created a vibrant e-marketplace with a wide range of goods and services.Competition Commission of India is a statutorybody of the Government of India, responsible for enforcing the Competition Act, 2002 throughout India and to prevent activities that have an adverse effect on competition.
9. Which team won the recently concluded Ranji Thropy?
Vidharbha lifted the Ranji Trophy for the second time in a row, defeating Saurashtra by 78 runs at Nagpur. Vidarbha became the sixth team to win back to back Ranji Trophy titles. Left arm spinner, Sarwate was adjudged man of the match.
10. 9th Hockey India Senior Women National Championship 2019 Begins In which state?
11. Name the campaign launched by Swachh Bharat Mission Grameen focuses on sustaining the open defecation free status of villages across India?
12. India's fiscal deficit has touched what percent of the FY19 Budget target of Rs. 6.24 lakh crore during the period of 9 months from April to December 2018?
India's fiscal deficit has touched 112% of the FY19 Budget target of Rs. 6.24 lakh crore during the period of 9 months from April to December 2018. The data was presented by the Controller General of Accountant (CGA) which manifested that fiscal deficit of previous fiscal was 13.6%. Fiscal deficit was at 7 lakh crores during this financial year. This is 112.4% of the Budget estimates for FY19, while for exact figures, it was 113.6% for 2017-2018. Fiscal Deficit is the gap between income and expenditure of the government.
1) 5th India-Bangladesh Joint Consultative Committee Meet held in which city?
2) State-run power giant NTPC has signed an agreement with which private sector Bank for a Rs 2,500 crore loan to part finance capital expenditure?
3) Who was conferred the Légion d'Honneur (Legion of Honour) the highest civilian award of France in recognition of his work for specially-abled children?
4) Parmanu Tech 2019' conference held in which city?
5) Digicop a mobile application developed by Nasscom launched by which city police?
6) Who has taken over as General Manager of Integral Coach Factory (ICF)?
7) What is Indias' rank in the recently released US Chamber's global IP index?
8) With which statutory body of the Government of India, did the Government e Marketplace (GeM)entered into a Memorandum of Understanding to enable a fair and competitive environment in the e-Marketplace?
9) Which team won the recently concluded Ranji Thropy?
10) 9th Hockey India Senior Women National Championship 2019 Begins In which state?
11) Name the campaign launched by Swachh Bharat Mission Grameen focuses on sustaining the open defecation free status of villages across India?
12) India's fiscal deficit has touched what percent of the FY19 Budget target of Rs. 6.24 lakh crore during the period of 9 months from April to December 2018?


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Australia: Significant change included in pastoral bill
by Anthony Kelly
Mellor Olsson Lawyers
Your LinkedIn Connections
with the authors
In SA, there are in excess of 300 pastoral leases, with this land occupying more than 40 per cent of the state.
The use of pastoral land has, for many years, been controlled by the Pastoral Land Management and Conservation Act 1989.
The state government has been undertaking a major review of the act and has put proposed new legislation to replace the act – the Pastoral Lands Bill 2020 – out for public consultation.
Existing leases are proposed to roll over at the commencement of the bill. But, they will be subject to a review by the Pastoral Board within five years to ensure their conditions are consistent with the requirements under the proposed legislation.
There are a number of major changes proposed as a consequence of the bill. The first of these proposed changes is to increase the maximum possible lease term from 42 years to 100 years. This will allow greater certainty of tenure and, with it, mean that pastoral lessees will be able to take a longer term outlook when it comes to investigating in the business operations of the land.
In addition to the longer lease terms, there is express provision made for alternative, non=pastoral land uses and for the grazing of species other than sheep or cattle. This broadens the scope of activities potentially permitted on pastoral land.
A significant change proposed is the removal of maximum stock numbers. It is proposed that there will be no limit on the maximum stock numbers and pastoral lessees will be able to make their own decisions on the number of stock being run on the land. But, there are further amendments which have an effect on the actual stock numbers – there are provisions relating to the condition of the land and ensuring that it is maintained to a certain condition, with various consequences if it is not.
There is also provision in the new legislation for the relevant Minister to develop policies and guidelines. While these policies and guidelines will not attract the scrutiny of Parliament, any policies or guidelines adopted will have to be complied with and will be enforceable. For example, the guidelines could set out specific requirements for fencing or maintenance and, if not complied with, the pastoral lessees could be pursued.
A further change is the obligations in respect of items like fencing. The new provisions set out a need to maintain 'adequate infrastructure'. This means that the lease holder is only required to maintain infrastructure that is required for the particular pastoral use being undertaken on their land, rather than there being a blanket standard which applies across the board for all pastoral land irrespective of its use.
These are some significant changes and it will be interesting to see what finds its way into the new legislation following the consultation process.
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sat07may7:30 PMLisbon, ND - Eagles ClubFascinating Rhythms of the World w/ the Alex Meixner BandEagles Club, 6540 Hwy. 32, Lisbon, ND
2/1/16 – Due to a scheduling conflict, the AMB show has been moved to the Eagles Club 6540 Hwy. 32, Lisbon, ND Contact Allied Concert Services for details and available ticket information 763-559-8019 Fascinating
2/1/16 – Due to a scheduling conflict, the AMB show has been moved to the Eagles Club 6540 Hwy. 32, Lisbon, ND
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Fascinating Rhythms of the World w/ the Alex Meixner Band: Accordionist Alex Meixner is equally at home playing a traditional Oktoberfest or amped up Rocktoberfest, while also having the ability to meld into swinging jazz, gypsy world-beat, authentic European folk or smoking blues at the drop of a hat. His talents in music and comedy were featured on The Tonight Show and most recently he received a Grammy nomination for his Polka Freak Out CD.
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Argentine election looms over EU-Mercosur deal
National elections in Argentina could spell the triumphant return of protectionist policies in South America's second-largest economy | Paula Ribas/Getty Images
Brazil and EU officials are concerned Buenos Aires could return to protectionism.
Hans von der Burchard
10/25/19, 6:00 AM CET
Updated 10/27/19, 7:27 AM CET
The EU's landmark trade accord with Mercosur has met opposition in France, Austria and Ireland — but an even more immediate threat to the deal is now emerging in South America.
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National elections in Argentina this Sunday could spell the triumphant return of protectionist policies in the continent's second-largest economy, as polls predict a comeback for the left-wing politician Cristina Kirchner, who governed the country from 2007 to 2015.
During her presidency, which was plagued with corruption charges that are still pending (and which she strongly denies), Kirchner embraced a militant protectionist agenda and allied the country to other far-left Latin American leaders in Bolivia and Venezuela, among others.
Officially, she is the running-mate of the Peronist party's presidential candidate Alberto Fernández, but if they beat the conservative, pro-business incumbent Mauricio Macri and she is installed as vice president, Kirchner would likely become the real power-broker in Argentina.
The latest polls predict that Fernández and Kirchner could win by a lead of 18-20 percentage points, raising concerns that Argentina could soon reverse the market openings created under Macri and flip back to the protectionist policies championed by Kirchner during her previous tenure. The business-friendly incumbent has sought to lead the country out of economic isolation by pushing reforms and forcefully promoted the free trade deal with the EU.
The ratification of the agreement has already been thrown into doubt by European concerns about deforestation and rainforest fires, a lack of enforceability of environmental clauses as well as a veto by Austrian lawmakers. The accord needs to be approved by EU governments, the European Parliament, some 40 national parliaments across Europe as well as national assemblies in the Mercosur bloc.
But the Argentine election has the potential to derail the accord much sooner, before it even gets to the ratification phase, which is supposed to start in the second half of 2020.
Brazilian President Jair Bolsonaro sounded the alarm this week that Kirchner's comeback could not only jeopardize the trade deal but the whole Mercosur bloc, which in addition to Argentina and Brazil includes Paraguay and Uruguay.
"We know that the return of … Cristina Kirchner's class to the Argentine government can indeed endanger the entire Mercosur," he told reporters on Wednesday during a state visit to Japan, according to Brazilian media.
"What we want is that Argentina continues the trade policies of Macri in case the opposition wins," Bolsonaro said. "If not, we may get together with Paraguay and Uruguay to make a decision," he added, alluding to a potential scenario under which Brazil and allies could seek to either exclude Argentina from Mercosur, or leave the bloc themselves.
"If you are possibly putting the entire Mercosur at risk, you have to have an alternative in your pocket," he said.
The warning from Brazil highlights the latest trouble for the deal, which was concluded in June and is supposed to crack open the highly defensive South American market for European exports, from cars to machinery, while lowering EU agricultural tariffs for Mercosur exports such as beef, sugar and ethanol.
In Argentina, Fernández and Kirchner have criticized the trade deal as surrendering the country's industrial sector to powerful European competitors for the price of turning Argentina into a simple exporter of agricultural commodities. During a televised election debate last week, Fernández alluded to his previous calls for renegotiating the trade deal: "I'm not afraid of re-opening [the agreement]," he said.
The divergences on trade policy further fuel concerns about the overall economic and financial crisis in Argentina. Many Argentinians who once supported Macri now feel disappointment with his promises of reforms because he didn't manage to stop the Argentine peso from crashing in recent years, and the country now looks likely to request another bailout from the International Monetary Fund.
Officials, diplomats and lawmakers in Brussels are observing the situation with concern.
"It's clear that these are crucial elections," said Nicola Danti, the vice chair of the European Parliament's delegation for relations with Mercosur. "Argentina is a significant country in the Mercosur bloc … [and] if it was to return to protectionist policies, this would put our agreement in a very fragile situation."
Danti added that the EU-Mercosur accord was not just a trade deal but also "very important from the political perspective, it defines our strategic partnership with the region."
One EU diplomat said there were "some serious concerns" about whether the Mercosur deal, which is currently under legal review, could even move into the ratification phase next year if Argentina changes its position on the deal. The diplomat noted that Fernández and Bolsonaro had a "pretty poisonous" relationship, which could make it more difficult for Mercosur to agree on a common position.
Fernández, in last week's debate, said he wanted "to unite Latin America and improve Mercosur" to "defy the challenges of globalization."
Another EU diplomat noted that Bolsonaro has already discussed a bilateral trade deal with U.S. President Donald Trump, and warned Brazil could turn toward Washington if political changes in Argentina were to throw a spanner into the works of the EU deal.
MEP Sven Simon, the spokesperson for the center-right European People's Party on the Mercosur deal, said that because it took 20 years to negotiate the agreement in the first place, it would be "difficult" for the EU to re-open the pact, as Fernández and Kirchner want.
"If we unroll the deal, we face the challenge that nothing is negotiated until everything is negotiated," he said. Brazil would come up with its own demands, and so could France, he added. "It would unravel a carefully struck balance."
Some observers predict that Fernández and Kirchner will moderate their tone on the Mercosur deal if they get into office.
Shunko Rojas, a former Argentine undersecretary for trade, told POLITICO that a Kirchner government would face pressure from various sectors that stand to benefit from the trade deal — especially if Brazil decided to push ahead and enact the agreement without Argentina.
"If Brazil ratifies the deal and benefits from increased exports to Europe, for example in the beef sector, then Argentina cannot allow itself to lose out," he said. "I'm sure once Fernández takes office and sees the fine print [of the agreement], he'll support it."
MEP Danti said he also remained cautiously optimistic: "I think, nowadays, even a Peronist government cannot return that easily to a protectionist policy."
This article is part of POLITICO's premium policy service Pro Trade. From transatlantic trade wars to the U.K.'s future trading relationship with the EU and rest of the world, Pro Trade gives you the insight you need to plan your next move. Email pro@politico.eu for a complimentary trial.


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Pulitzer-Winning Photographer Made Charlottesville Photo On His Last Day On The Job Photographer Ryan Kelly, was just finishing four years at The Daily Progress when he captured the image of a car plowing into a crowd of counterprotesters in Charlottesville, Va.
Pulitzer-Winning Photographer Made Charlottesville Photo On His Last Day On The Job
Pulitzer-Winning Photographer Made Charlottesville Photo On His Last Day On The Job 3:29
April 17, 20184:25 PM ET
Ailsa Chang
People fly into the air as a vehicle drives into a group of protesters demonstrating against white nationalists in Charlottesville, Va. on Aug. 12, 2017. Kelly won a Pulitzer Prize for the image. Ryan M. Kelly/The Daily Progress via AP hide caption
Ryan M. Kelly/The Daily Progress via AP
Last summer, on August 12, photographer Ryan Kelly arrived at a far-right rally in Charlottesville, Va., to take pictures for the city's newspaper, The Daily Progress.
It was his last day on the job — and it was a memorable one. A photo he took of a car plowing through a crowd of counterprotesters became the defining image of the chaos that day.
On Monday, Kelly was awarded a Pulitzer Prize for breaking news photography for the photo he took.
The photo shows a car careening into a massive crowd, with bodies flying through the air.
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"You see sunglasses and shoes and cellphones that aren't connected to people's hands or feet or heads. You see water spraying. There's just a lot of violent, violent details that are coming through in ways that you don't normally experience in everyday life," Kelly says.
The scene shown in Kelly's photo is the same incident in which 32-year-old Charlottesville resident Heather Heyer was killed, and in which 19 others were hospitalized.
"I'm honestly shocked that more people weren't affected by that," Kelly says. "It was such a violent collision. He was traveling so fast down the road when he collided with the crowd. It's amazing to me that more people didn't die, but I'm very thankful for that."
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Kelly says his role as a photojournalist is to bear witness to the events around him, but that prior to the far-right rally, he hadn't "covered anything remotely as dramatic or intense" in his four years at the newspaper.
"There's not normally that sort of emotional wrestling that I have to do with an assignment, so this was something new and something more intense than I was used to dealing with," Kelly says. "But that's part of the job. That's news and this was absolutely news."
In Kelly's case, the news of the Charlottesville rally became a global story.
"I'm just happy I could have done my job in that moment despite the fact that I wish it had never happened to begin with," he says.
Kelly left journalism and now works for a brewery managing its social media. On his career shift, he says, "I love journalism. I believe passionately in its importance ... but I was just burnt out after four years and I needed a change."
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Noah Caldwell and Emily Kopp edited and produced the audio for this story. Wynne Davis adapted it for the Web.