Phenomenology of two-photon interaction at high energies: accessing dilute and high parton density of the photon structure

Abstract

In this work, $\gamma^{(\ast)}\gamma^{(\ast)}$ interactions in electron-positron collisions are studied across both low- and high-energy regimes. The analysis includes contributions from the Vector Meson Dominance (VMD) model (via Reggeon exchange), the Quark Parton Model (via box diagrams), and the gluonic component (described using the dipole formalism), which becomes dominant at high energies. A key feature of the dipole picture is that a photon can fluctuate into a quark-antiquark ($q\bar{q}$) pair, forming a color dipole. The dipole-dipole cross section is modeled using two different prescriptions. We analyze the impact of these models on several key observables: the total cross section for real photons ($\sigma^{\gamma \gamma}$), including heavy quark production $\gamma\gamma \rightarrow c\bar{c}X, b\bar{b}X$; for virtual photons ($\sigma^{\gamma^{\ast}\gamma^{\ast}}$); and the photon structure function ($F_2^\gamma$). Both prescriptions express the dipole-dipole interaction in terms of the dipole-proton scattering amplitude, used in Deep Inelastic Scattering (DIS). This amplitude is obtained by solving the Balitsky-Kovchegov (BK) non-linear evolution equation, incorporating running coupling and various models that differ in their treatment of the transition between the dilute and saturation regimes. These approaches exhibit distinct behaviors in photon-photon interactions at high energies: while one prescription describes the photon as a smaller and denser system, the other treats it as a larger and more dilute configuration. Accordingly, they predict greater and lesser hadron production in the final state, respectively, at the energies of future colliders. These characteristics become more significant with increasing photon virtuality.