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Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges

Yuri V. Kovchegov

TL;DR

This work tackles the small-x evolution of the nuclear F2 structure function by deriving a nonlinear evolution equation within Mueller's dipole model that resums all leading-log(1/x) multiple pomeron exchanges in the large-Nc limit. The approach yields an evolution for the forward qq̄–nucleus amplitude N(x01,b0,Y), expressed as a non-linear integral equation tied to the dipole wavefunction, enabling a direct connection to observable F2. In the double logarithmic limit, the equation reduces to the GLR equation for the nuclear gluon distribution xG_A, matching the GLRMQ form for a cylindrical nucleus and clarifying the relation between the dipole framework and conventional parton evolution. The paper also discusses limitations (neglected loop diagrams, large-Nc approximation) and outlines avenues for phenomenological applications and future extensions to higher-order corrections.

Abstract

We derive an equation determining the small-x evolution of the F_2 structure function of a large nucleus which includes all multiple pomeron exchanges in the leading logarithmic approximation using Mueller's dipole model. We show that in the double leading logarithmic limit this evolution equation reduces to the GLR equation.

Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges

TL;DR

This work tackles the small-x evolution of the nuclear F2 structure function by deriving a nonlinear evolution equation within Mueller's dipole model that resums all leading-log(1/x) multiple pomeron exchanges in the large-Nc limit. The approach yields an evolution for the forward qq̄–nucleus amplitude N(x01,b0,Y), expressed as a non-linear integral equation tied to the dipole wavefunction, enabling a direct connection to observable F2. In the double logarithmic limit, the equation reduces to the GLR equation for the nuclear gluon distribution xG_A, matching the GLRMQ form for a cylindrical nucleus and clarifying the relation between the dipole framework and conventional parton evolution. The paper also discusses limitations (neglected loop diagrams, large-Nc approximation) and outlines avenues for phenomenological applications and future extensions to higher-order corrections.

Abstract

We derive an equation determining the small-x evolution of the F_2 structure function of a large nucleus which includes all multiple pomeron exchanges in the leading logarithmic approximation using Mueller's dipole model. We show that in the double leading logarithmic limit this evolution equation reduces to the GLR equation.

Paper Structure

This paper contains 4 sections, 34 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Evolution equation from the dipole model
  3. Double logarithmic limit
  4. Conclusions

Figures (4)

  • Figure 1: Forward amplitude of DIS on a nucleus in the quasi--classical (Glauber) approximation.
  • Figure 2: DIS on a nucleus including the QCD evolution in the quark--antiquark pair in the form of dipole wave function. Each double line represents a gluon in the large--$N_c$ limit.
  • Figure 3: Multiple pomeron exchanges and splittings resummed by Eq. (\ref{['eqN']}). Each pomeron ladder interacts with a nucleus, which is symbolically denoted by $A$.
  • Figure 4: (a) Diagrams which are not included in our analysis. (b) A diagram which is included in Eq. (\ref{['eqN']}).