Role of the ρ meson in the description of pion electroproduction experiments

Abstract

We study the $p(e,{e}^{'}{\ensuremath{\pi}}^{+})n$ reaction in the framework of an effective Lagrangian approach including nucleon, \ensuremath{\pi} and \ensuremath{\rho} meson degrees of freedom and show the importance of the \ensuremath{\rho}-meson $t$-pole contribution to ${\ensuremath{\sigma}}_{T}$, the transverse part of cross section. We test two different field representations of the \ensuremath{\rho} meson, vector and tensor, and find that the tensor representation of the \ensuremath{\rho} meson is more reliable in the description of the existing data. In particular, we show that the \ensuremath{\rho}-meson $t$-pole contribution, including the interference with an effective nonlocal contact term, sufficiently improves the description of the recent JLab data at invariant mass $W\ensuremath{\lesssim}2.2$ GeV and ${Q}^{2}\ensuremath{\lesssim}2.5$ GeV${}^{2}/{c}^{2}$. A ``soft'' variant of the strong $\ensuremath{\pi}\mathit{NN}$ and $\ensuremath{\rho}\mathit{NN}$ form factors is also found to be compatible with these data. On the basis of the successful description of both the ${\ensuremath{\sigma}}_{L}$ and ${\ensuremath{\sigma}}_{T}$ parts of the cross section we discuss the importance of taking into account the ${\ensuremath{\sigma}}_{T}$ data when extracting the charge pion form factor ${F}_{\ensuremath{\pi}}$ from ${\ensuremath{\sigma}}_{L}$.