Nt1330 Unit 3 Numerical Analysis

To obtain a numerical result for the form factors, first one needs the expressions for the distribution amplitudes for the $N$ baryon.
The distribution amplitudes for the nucleon are studied in \cite{Braun:2006hz}.
The DAs depend on various non-perturbative parameters which are also estimated in \cite{Braun:2006hz}.
In Table \ref{parameter_table} we present the values of the input parameters using the DAs of $N$.
%In this section, we will only consider the central values of these parameters.
\begin{table}[t]
\addtolength{\tabcolsep}{10pt}
\begin{tabular}{ccccccc}
\hline\hline
% baryon DA parameters & $f_B$~(GeV$^2$) & $\lambda_1$~(GeV$^2$)& $\lambda_2$~(GeV$^2$)& \\[0.5ex] \hline & 0.005 $\pm$ 0.0005 &-0.027$\pm$ 0.009 & 0.054$\pm$

This means that the baryon mass correction contribution to this form factors even changes the sign of the form factor and hence can not be neglected.

In Figs (\ref{fig:NC3Mont.eps}-\ref{fig:NC6Mont.eps}), we present the $Q^2$ dependence of the form factors obtained using two different types of analysis.
The results of the traditional sum rules analysis is presented with lines and in this analysis we used $s_0=2.5\pm 0.5~GeV^2$ and $M^2=3.0~GeV^2$.
And the circles and squares with bars are the results of the Monte Carlo analysis.
We have modelled continuum contribution double(DE) and triple(TE) exponentials for Monte Carlo analysis.
In Figs. (\ref{fig:NC3Mont.eps}-\ref{fig:NC6Mont.eps}), the results of the Monte Carlo analysis is presented along with the result obtained for the central values of the parameter. It is observed that for the form factors $C_3^{N \Delta}(Q^2)$, $C_4^{N \Delta}(Q^2)$ and $C_6^{N \Delta}(Q^2)$,
Monte Carlo analysis and the prediction for the central values agree at large values of $Q^2$, but deviate from each other for small values of

Also, it is seen that although with the traditional sum rules analysis , one obtains almost zero value for form factor $C_3^{N \Delta}(Q^2)$, the Monte Carlo analysis shows that this form factor is consistent with significant non-zero values.
In the case of $C_4^{N \Delta}(Q^2)$, although the traditional sum rules analysis leads to a value that is significantly away from