Towards a single scale-dependent Pomeron in holographic light-front QCD

Abstract

The Pomeron Regge trajectory underlies the dynamics dependence of hadronic total cross sections and diffractive reactions at high energies. The physics of the Pomeron is closely related to the gluon distribution function and the gluon gravitational form factor of the target hadron. In this article we examine the scale dependence of the nonperturbative gluon distribution in the nucleon and the pion, which was derived in a previous article [G. F. de T\'eramond, H. G. Dosch, T. Liu, R. S. Sufian, S. J. Brodsky, and A. Deur, Gluon matter distribution in the proton and pion from extended holographic light-front QCD, Phys. Rev. D 104, 114005 (2021)] in the framework of holographic light-front QCD and the Veneziano model. We argue that the QCD evolution of the gluon distribution function $g(x,\ensuremath{\mu})$ to large ${\ensuremath{\mu}}^{2}$ leads to a single scale-dependent Pomeron. The resulting Pomeron trajectory ${\ensuremath{\alpha}}_{P}(t,\ensuremath{\mu})$ not only depends on the momentum transfer squared $t$, but also on the physical scale $\ensuremath{\mu}$ of the amplitude, such as the virtuality ${Q}^{2}$ of the interacting photon in inclusive diffractive electroproduction, thus unifying the soft and the perturbative Pomeron. This can explain not only the ${Q}^{2}$ evolution of the proton structure function ${F}_{2}(x,{Q}^{2})$ at small $x$, but also the observed energy and ${Q}^{2}$ dependence of high energy diffractive processes involving virtual photons up to LHC energies.