Setting the scale of the p p and p bar p total cross sections using AdS/QCD

TL;DR

This paper refines the calculation of the Pomeron-proton coupling in AdS/QCD, specifically using the Sakai-Sugimoto model, to better match experimental total cross section data for proton-proton and proton-antiproton scattering.

Contribution

It provides a detailed computation of the Pomeron-proton coupling constant within the Sakai-Sugimoto model, improving the theoretical understanding of scattering processes in AdS/QCD.

Findings

Calculated the Pomeron-proton coupling constant as approximately 6.38 GeV^{-1}.

Found this value to be in reasonable agreement with the phenomenologically fitted value of 8.28 GeV^{-1}.

Enhanced the theoretical modeling of total cross sections in proton scattering using holographic QCD.

Abstract

This paper is an addendum to our earlier paper \cite{pom} where we computed the Pomeron contribution to $p ~ p$ and $p ~ \bar p$ scattering in AdS/QCD. The model of \cite{pom} depends on four parameters: the slope and intercept of the Pomeron trajectory $\alpha'_c, \alpha_c(0)$, a mass scale $M_d$ which determines a form factor entering into matrix elements of the energy-momentum tensor, and a coupling $\lambda_{\cal P}$ between the lightest spin $2$ glueball and the proton which sets the overall scale of the total cross section. Here we perform a more detailed computation of $\lambda_{\cal P}$ in the Sakai-Sugimoto model using the construction of nucleons as instantons of the dual 5d gauge theory and an effective 5d fermion description of these nucleons which has been successfully used to compute a variety of nucleon-meson couplings. We find $\lambda_{\cal P,{\rm SS}} \simeq 6.38 ~ {\rm GeV}^{-1}$ which is in reasonable agreement with the value $\lambda_{{\cal P},{\rm fit}} = 8.28 ~ {\rm GeV}^{-1}$ determined by fitting single Pomeron exchange to data.