$\gamma^* \gamma$ and $\gamma^* p$ scattering in IHQCD

TL;DR

This paper models $\gamma^* \gamma$ and $\gamma^* p$ scattering using improved holographic QCD, fitting experimental data across various processes and kinematic ranges, and extracting gravitational couplings and parton distributions.

Contribution

It introduces a holographic QCD framework to simultaneously fit multiple scattering processes and extract couplings and parton distributions, extending previous models.

Findings

Good fit to data with $\chi^2$ close to 1.07 and 1.40.

Extracted gravitational couplings of gauge fields and protons.

Estimated gluon distribution inside the proton at NLO QCD.

Abstract

We perform joint fits using measurements of the proton structure functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$, of the photon structure function $F_2^\gamma(x,Q^2)$ and of the total cross-sections $\sigma\left( \gamma p \rightarrow X\right)$ and $\sigma \left( \gamma \gamma \rightarrow X\right)$. The data is gathered from several sources including HERA and LEP. The kinematical range considered is wide with a photon virtuality $Q^2 \leq400 \, {\rm GeV}^2$, Bjorken variable $x<0.01$ and $\sqrt{s} > 4 \, {\rm GeV}$. This is done by considering a $U\left(1\right)$ vector gauge field minimally coupled to the graviton Regge trajectory in improved holographic QCD. We find good agreement with the data for a joint fit of $F_2^\gamma$ and $\sigma\left(\gamma \gamma \rightarrow X\right)$ with a $\chi_{d.o.f.}^2 = 1.07$. For a joint fit of $F_2$, $F_L$ and $\sigma\left( \gamma p \rightarrow X\right)$ we find $\chi_{d.o.f.}^2 = 1.40$. A joint fit of all observables for both processes $\gamma^* \gamma$ and $\gamma^* p$ gives a $\chi_{d.o.f.}^2 = 1.38$. The gravitational couplings of the $U\left(1\right)$ vector gauge field and of the proton with the Reggeons of the graviton Regge trajectory are given as an output of the fitting procedure. An approximate relation between the structure functions, valid at NLO QCD, is used to estimate the parton distribution function of the gluon inside the proton.