[Paper Review] Saturation model in the non-Glauber approach

Andrey Kormilitzin|ArXiv.org|Jul 15, 2007

High-Energy Particle Collisions Research26 references3 citations

TL;DR

This paper presents a new saturation model in the non-Glauber approach using the generating functional method to describe parton saturation in high-energy deep inelastic scattering. It successfully fits HERA data for the proton structure function $F_2$, diffractive structure function $F_2^D$, and charm quark structure function $F_2^{c\bar{c}}$, achieving a $χ^2/\text{d.o.f.} \approx 1.04$, demonstrating that the model captures saturation effects without relying on the eikonal approximation.

ABSTRACT

In this paper a new saturation model is presented. This model is based on the theoretical solution for the generating functional, and it is quite different and not more complicated than the Glauber-like approach used before. The model describes the structure function F_{2} of the proton, as well as the diffractive structure function F_{2}^{D}. We show the difference between our model, and the eikonal approach by calculating the multiplicity distribution, using the AGK cutting rules strategy.

Motivation & Objective

• To develop a saturation model based on a self-consistent theoretical framework that avoids the eikonal approximation used in prior models.
• To describe the proton structure function $F_2$ and the diffractive structure function $F_2^D$ across a wide kinematic range using a single set of parameters.
• To incorporate QCD evolution via the DGLAP equation and account for heavy quark contributions in structure functions.
• To test the model’s predictive power by comparing its results on diffractive dissociation with ZEUS experimental data using the same parameters fitted to inclusive DIS data.
• To distinguish the model from eikonal-based saturation models through multiplicity distribution analysis using AGK cutting rules.

Proposed method

• Uses the generating functional approach to solve a simplified evolution equation for dipole probability $P_n$, assuming constant dipole size during interaction.
• Derives the interaction amplitude $N(y; b, r)$ from the generating functional $Z(y, u)$, leading to a closed-form expression involving the saturation scale $\gamma(r)$.
• Applies the relation $N(y; b, r) = 1 - Z(y, u(r))$ to obtain a non-linear, unitary amplitude that incorporates parton saturation effects.
• Redefines Bjorken-$x$ in the saturation region to account for transverse momentum effects, introducing a physical saturation scale.
• Integrates the DGLAP evolution equation to describe the energy dependence of the initial gluon density.
• Uses the AGK cutting rules strategy to compute multiplicity distributions and compare with eikonal models, highlighting differences in behavior.

Experimental results

Research questions

• RQ1 Can a generating functional-based saturation model describe inclusive and diffractive deep inelastic scattering data without relying on the eikonal approximation?
• RQ2 How does the multiplicity distribution in the non-Glauber model differ from that in eikonal-based saturation models, and what does this imply about parton dynamics?
• RQ3 To what extent can the same set of parameters from inclusive $F_2$ fits describe diffractive dissociation data?
• RQ4 What is the role of transverse momentum and recombination effects in defining the saturation scale in the small-$x$ regime?
• RQ5 How well does the model describe the charm quark structure function $F_2^{c\bar{c}}$ and the slopes $dF_2/d(\ln Q^2)$ and $d\ln F_2/d(\ln 1/x)$?

Key findings

• The model achieves a good fit to HERA data for $F_2$ with $\chi^2/\text{d.o.f.} = 354/341 \approx 1.04$, indicating high consistency with experimental data.
• The model successfully describes the diffractive structure function $F_2^{D(3)}$ across multiple $M_X$ and $Q^2$ bins using the same parameters fitted to inclusive DIS data.
• The multiplicity distribution in the non-Glauber model shows distinct behavior from eikonal models, especially at high multiplicities, as revealed by AGK cutting rules analysis.
• The saturation scale is significant up to $Q^2 \sim 3-4\,\text{GeV}^2$, where non-linear effects dominate the evolution.
• The model accounts for heavy quark contributions to $F_2$ and accurately describes the $F_2^{c\bar{c}}$ structure function.
• The redefinition of Bjorken-$x$ in the saturation region, based on transverse momentum effects, improves the physical consistency of the model.