%\documentclass[landscape,A4,12pt]{article}

\documentclass[a4paper,12pt]{article}

%\usepackage{psfig,float}



%\hoffset -1.5cm


\begin{document}

\setlength{\columnseprule}{1pt}

%\setlength{\textwidth}{5.5cm}
%\setlength{\textheight}{16.5cm}


%\frenchspacing

\newcommand{\ep}{\epsilon}
\newcommand{\la}{\lambda}
\newcommand{\La}{\Lambda}
\newcommand{\prd}{\partial}

\large



%\vspace*{-3cm}



\renewcommand{\arraystretch}{1.35}


The file \texttt{AnomDim.m} contains anomalous dimensions and the $\beta$-function.
Notations are  as follows.
\medskip
\medskip

 \begin{tabular}{|c|c|c|c|c|c|}
    \hline
    \tt  as & \tt nf & \tt z2, z3, \dots &\tt QQ \\\hline
    $\frac{\alpha_s}{\pi}$ & $n_f$& $\zeta_2,\
    \zeta_3,\ \dots$  &    $Q^2$\\\hline
  \end{tabular}




\vspace{6mm}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\texttt{gV4l} & \texttt{gS4l} & \texttt{gT4l} & \texttt{gSS5l} & \texttt{gVV5l} & \texttt{g1TT4l}
& \texttt{g2TT4l} & be4l 
\\ \hline\hline
 $\gamma^V$  & $\gamma_S$ & $\gamma^T$ &  $\gamma^{SS}$  & $\gamma^{VV}$ & $\gamma^{(1)TT}$
& $\gamma^{(2)TT}$   & $\beta$ 
\\
\hline
\end{tabular}
\vspace{6mm}


The files \verb+ CorrelatorsQ.m + and \verb+ CorrelatorsX.m + contain
the results for the scalar, vector and tensor correlators in  the momentum 
and  the position spaces respectively. 
Notations are  as follows.


\medskip
\medskip

 \begin{tabular}{|c|c|c|c|c|c|}
    \hline
     \tt lmu2Q & \tt lmu2X &\tt trans  \\\hline
     $\log(\mu^2/Q^2)$&$\log(\mu^2X^2/4)+2\gamma_E$  & $-\delta_{\mu\nu}+Q_\mu Q_\nu/Q^2$ 
\\
\hline
  \end{tabular}


\medskip
\medskip

  \begin{tabular}{|c|c|c|}
\hline
     \tt X[mu], X[nu]& \tt d[mu,nu]&\tt T1\\\hline
$X_\mu,\ X_\nu$&$\delta_{\mu\nu}$&
    $\delta_{\mu\rho}\delta_{\nu\sigma}-\delta_{\mu\sigma}\delta_{\nu\rho}$\\\hline
  \end{tabular}

\medskip

  \begin{tabular}{|c|}
\hline
     \tt T2[X]\\\hline
    $\frac{X_\mu
      X_\rho}{X^2}\delta_{\nu\sigma}
     -\frac{X_\mu    X_\sigma}{X^2}\delta_{\nu\rho}
     -\frac{X_\nu  X_\rho}{X^2}\delta_{\mu\sigma}
     +\frac{X_\nu X_\sigma}{X^2}\delta_{\mu\rho}
$
   \\
  \hline
  \end{tabular}

\medskip

  \begin{tabular}{|c|}
\hline
     \tt  \tt T2[Q]\\\hline
     $\frac{Q_\mu Q_\rho}{Q^2}\delta_{\nu\sigma}
     -\frac{Q_\mu  Q_\sigma}{Q^2}\delta_{\nu\rho}
     -\frac{Q_\nu  Q_\rho}{Q^2}\delta_{\mu\sigma}
     +\frac{Q_\nu  Q_\sigma}{Q^2}\delta_{\mu\rho}
$ \\\hline
  \end{tabular}


\medskip

\vspace{6mm}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\texttt{PiS5l} & \texttt{PiV5l} & \texttt{PiT4l} & \texttt{xPiS5l} & \texttt{xPiV5l} & \texttt{xPiT4l} 
\\ \hline
 $\Pi^S$  &  $\Pi^V$  & $\Pi^T$ & $\tilde{\Pi}^S$  & $\tilde{ \Pi}^V$  & $\tilde{\Pi}^T$   
\\
\hline
\end{tabular}




In addition, we factorize the common factors $\frac{1}{16\pi^2}$ in all (momentum space)
 correlators  and $\frac{1}{16\pi^4}$ in all position  space ones. Technically it is 
done with   a new function \verb+ NF[x]+. If the  reader wants  to include these factors
explicitly, he(she) should use the command 
\begin{verbatim}
                     NF[x_] := x
\end{verbatim}
or, better to apply the following substitution rule:
\begin{verbatim}
             PiV5l= PiV5l/.NF[x_] :> x
\end{verbatim}


Finally, the file \verb+ FTtable.m+ contains the Fourier transformation of all combinations
\[ \log\left(\frac{\mu^2}{Q^2}\right)^i/Q^{2j}\] 
for all values of $(i,j) = (0\dots 5,-1 \dots 4)$.
Note, that for the case of $j \ge 2$ we have  displayed no  non-logarithmical pieces as they depend on the specific 
way of regularization of the singularities appearing in the region of $Q^2 \sim 0$. 


\end{document}

