Proton-neutron mass difference, electroproduction, and photoabsorption in an analytic model of the virtual Compton amplitude

Abstract

An analytic model of the forward (virtual) Compton amplitude is proposed which satisfies $v$ plane analyticity, $s\ensuremath{-}u$ crossing symmetry, Regge behavior, and Bjorken scale invariance in appropriate limits. The model is constructed using the method of conformal mapping. Very good fits are obtained to the electroproduction data on $v{W}_{2}^{p}$, $2m{W}_{1}^{p}$, $v{W}_{2}^{p}\ensuremath{-}v{W}_{2}^{n}$, $\frac{v{W}_{2}^{n}}{v{W}_{2}^{p}}$, $v{R}_{p}$, and $1+v\frac{{W}_{2}^{n}}{v{W}_{2}^{p}}$, and to the photoabsorption data on ${\ensuremath{\sigma}}_{T}(\ensuremath{\gamma}p)$, ${\ensuremath{\sigma}}_{T}(\ensuremath{\gamma}n)$, and ${\ensuremath{\sigma}}_{T}(\ensuremath{\gamma}p)\ensuremath{-}{\ensuremath{\sigma}}_{T}(\ensuremath{\gamma}n)$. The scale-invariance breaking at finite ${Q}^{2}$ as exhibited by the data on $v{W}_{2}^{p}$ plotted as a function of ${Q}^{2}$ with $\ensuremath{\omega}$ fixed is also successfully reproduced. The $p\ensuremath{-}n$ mass difference calculated using the Cottingham formula is finite. In particular, it is shown that a set of parameters exists for which the general condition for no logarithmic divergence even in the presence of Bjorken scaling given by $limit of\text{}{Q}^{4}\ensuremath{\Delta}{t}_{1}^{I}(\ensuremath{-}{Q}^{2},0)\text{as}{Q}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}=(\frac{\ensuremath{\alpha}m}{\ensuremath{\pi}})\ensuremath{\int}{0}^{1}dx[\ensuremath{\Delta}{F}_{2}(x)+2x\ensuremath{\Delta}{F}_{1}(x)]$ can be realized consistent with theoretical consideration and experimental data. The final result of our calculation of the mass difference is (-1.96 \ifmmode\pm\else\textpm\fi{} 0.52) MeV, which is to be compared with the experimental value of -1.293 MeV.