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Shadowing Corrections in Diffractive QCD Leptoproduction of Vector Mesons

E. Gotsman, E. Levin, U. Maor

TL;DR

The paper develops a perturbative QCD framework to quantify shadowing corrections in diffractive vector meson leptoproduction, introducing a damping factor that encapsulates the reduction of cross sections due to multiple scatterings.It employs a dipole (r_perp) representation to connect vector-meson production to the gluon density and to the DIS structure function $F_2$, and extends the formalism to gluon shadowing using Mueller's Glauber-like approach with possible fan-diagram corrections.Numerical results show that shadowing significantly suppresses cross sections, especially at moderate $Q^2$ and high energy, with sizable but uncertain contributions from gluon-shadowing; comparisons with HERA data provide a testbed for small-x dynamics and the underlying vector-meson wave functions.Overall, the work offers a practical, testable framework to incorporate shadowing into diffractive vector-meson production and to refine our understanding of the proton's gluon density and nonlinear small-x evolution.

Abstract

The formulae for shadowing corrections in deep inelastic leptoproduction of vector mesons are presented. These formulae are also applicable for photoproduction of vector mesons constituted of heavy quarks. Our results are conveniently presented by the definition of a damping factor giving the reduction of the calculated cross sections due to shadowing. Our calculated cross sections are compared with those obtained with no shadowing and with the available experimental data including the recent data from HERA. We have also investigated the importance of shadowing on the relationship between $\frac{\pa F_2(Q^2,x)}{ \pa ln Q^2}$ and the cross section for virtual photoproduction of vector mesons. A discussion of shadowing corrections to the proton's gluon density is presented and numerical estimates are given.

Shadowing Corrections in Diffractive QCD Leptoproduction of Vector Mesons

TL;DR

The paper develops a perturbative QCD framework to quantify shadowing corrections in diffractive vector meson leptoproduction, introducing a damping factor that encapsulates the reduction of cross sections due to multiple scatterings.It employs a dipole (r_perp) representation to connect vector-meson production to the gluon density and to the DIS structure function $F_2$, and extends the formalism to gluon shadowing using Mueller's Glauber-like approach with possible fan-diagram corrections.Numerical results show that shadowing significantly suppresses cross sections, especially at moderate $Q^2$ and high energy, with sizable but uncertain contributions from gluon-shadowing; comparisons with HERA data provide a testbed for small-x dynamics and the underlying vector-meson wave functions.Overall, the work offers a practical, testable framework to incorporate shadowing into diffractive vector-meson production and to refine our understanding of the proton's gluon density and nonlinear small-x evolution.

Abstract

The formulae for shadowing corrections in deep inelastic leptoproduction of vector mesons are presented. These formulae are also applicable for photoproduction of vector mesons constituted of heavy quarks. Our results are conveniently presented by the definition of a damping factor giving the reduction of the calculated cross sections due to shadowing. Our calculated cross sections are compared with those obtained with no shadowing and with the available experimental data including the recent data from HERA. We have also investigated the importance of shadowing on the relationship between and the cross section for virtual photoproduction of vector mesons. A discussion of shadowing corrections to the proton's gluon density is presented and numerical estimates are given.

Paper Structure

This paper contains 18 sections, 76 equations.

Table of Contents

  1. Introduction
  2. Vector meson production in DIS without shadowing corrections
  3. Notations
  4. The amplitude in the $r_{\perp}$ representation
  5. $\sigma(r_{\perp},q^2_{\perp})$ at $q_{\perp}$ = 0
  6. $\sigma(r_{\perp},q^2_{\perp})$ at $q_{\perp}$ = 0
  7. The amplitude of vector meson production at $q_{\perp}$ = 0
  8. The $b_{\perp}$ dependence of the amplitude
  9. Shadowing corrections to diffractive leptoproduction of vector mesons
  10. Percolation of a $\bar{q} q$-pair through the target.
  11. Damping factor for diffractive production of vector meson
  12. The relation between DIS diffractive production of vector mesons and $F_2(Q^2,x)$.
  13. Shadowing corrections for the gluon distribution
  14. Numerics and comparison with experiment
  15. Vector meson production in DIS without SC
  16. ...and 3 more sections