Physical limits in the Color Dipole Model Bounds

TL;DR

This paper explores the theoretical limits of the color dipole model in high-energy photon-hadron scattering, analyzing how gluon distribution behaviors influence model bounds and their validity at small dipole sizes.

Contribution

It investigates the dependence of color dipole bounds on gluon distribution behavior using expansion and Laplace transform methods, comparing with DGLAP-based gluons.

Findings

Color dipole bounds depend on gluon distribution behavior.

Numerical analysis indicates the model's validity at small dipole sizes.

Comparison with DGLAP gluons clarifies the model's applicability range.

Abstract

The ratio of the cross sections for the transversely and longitudinally virtual photon polarizations, $\sigma^{\gamma^{*}p}_{L/T}$, at high photon-hadron energy scattering is studied. I investigate the relationship between the gluon distribution obtained using the color dipole model and standard gluons obtained from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution and the Altarelli-Martinelli equations. It is shown that the color dipole bounds are dependent on the gluon distribution behavior. This behavior is considered by the expansion and Laplace transform methods. Numerical calculations and comparison with the color dipole model (CDM) bounds can indicate the range of validity of this method at small dipole sizes, $r\sim 1/Q{\ll}1/Q_{s}$.