[Paper Review] J/ψPhoto- and DIS Production via Nonlinear Evolution

E. Gotsman, E. Levin+3 more|arXiv (Cornell University)|Feb 3, 2003

Quantum Chromodynamics and Particle Interactions1 references3 citations

TL;DR

This paper applies a nonlinear evolution equation (BK equation) to describe J/ψ photoproduction and deep-inelastic scattering (DIS) on protons and nuclei, incorporating unitarity and shadowing effects via a Glauber-like resummation. It achieves good agreement with HERA data using only the uncertainty in the J/ψ wave function normalization as a free parameter, and predicts significant suppression in J/ψ production on gold nuclei due to nonlinear effects at low x, with effects dominating for x ≤ 10⁻³.

ABSTRACT

We apply our solution of the nonlinear evolution equation to the case of $J/ψ$ photo and DIS production on nucleons and nuclei targets. The uncertainty in the $J/ψ$ wave function normalization due to Fermi motion is treated as a free parameter. We obtain good reproduction of the HERA experimental data on a proton target. Calculations of $J/ψ$ mesons coherent production on nuclei targets are presented and discussed. Our analysis supports the conclusions reached in our previous studies, stressing the importance of nonlinear evolution in the kinematical domain of high-density QCD.

Motivation & Objective

• To extend the nonlinear evolution equation (BK equation) to describe J/ψ production in photoproduction and DIS processes.
• To investigate the role of unitarity and parton saturation effects in J/ψ production at high energies and low x.
• To model coherent J/ψ production on nuclear targets using a Glauber-based approach to account for multiple scattering and shadowing.
• To determine whether the nonlinear evolution framework can reproduce HERA data without additional fitting parameters beyond wave function normalization.
• To assess the impact of real part of amplitude and skewed gluons on the cross section predictions.

Proposed method

• Solves the nonlinear BK equation for the dipole-nucleon scattering amplitude, incorporating both linear evolution and nonlinear recombination at high parton density.
• Uses a dipole-based formalism where the J/ψ wave function is represented as a superposition of q̄q and q̄qg Fock states, with the amplitude evolved via the BK equation.
• Applies a Glauber-like multiple scattering formalism to compute the nuclear cross section, including all rescattering contributions and shadowing corrections.
• Extracts the impact parameter (b) dependence from the electromagnetic form factor of the J/ψ, introducing a profile function that decreases near b=0 due to nonlinear effects.
• Introduces a free parameter to account for uncertainty in the J/ψ wave function normalization due to Fermi motion of the c̄c pair.
• Compares results from a full resummation of rescatterings (Eq. 29) with a simplified two-term approximation (Eq. 4), quantifying normalization differences via a ratio R.

Experimental results

Research questions

• RQ1 Can the nonlinear evolution equation (BK equation) successfully describe J/ψ photoproduction and DIS data on proton targets without additional fitting parameters?
• RQ2 How do unitarity and shadowing effects modify the J/ψ cross section on nuclear targets compared to the proton case?
• RQ3 What is the role of the J/ψ wave function normalization uncertainty due to Fermi motion in fitting experimental data?
• RQ4 How do the real part of the amplitude and skewed gluons influence the predicted cross sections?
• RQ5 At what value of x do nonlinear effects (unitarity taming) become dominant in J/ψ production on nuclei?

Key findings

• The model successfully reproduces HERA data for J/ψ photoproduction and DIS on protons using only the uncertainty in the J/ψ wave function normalization as a free parameter.
• The impact parameter dependence of the amplitude exhibits a suppression near b=0, which is interpreted as a signature of nonlinear evolution and unitarity taming.
• For J/ψ production on gold nuclei (A ≈ 200), the full resummation of rescatterings leads to a suppression factor of approximately 0.4 compared to a two-term approximation, indicating significant shadowing effects.
• The characteristic exponent δ in the energy dependence of the cross section is nearly identical between the full and simplified calculations, indicating that the energy dependence is robust, but the normalization is sensitive to rescattering structure.
• Unitarity taming effects dominate for x ≤ 10⁻³, suggesting that future eRHIC experiments are well-suited to test these predictions.
• The predictions for nuclear targets are robust, with minimal sensitivity to the b-dependence uncertainty, as the initial conditions for the BK equation are fixed by proton DIS data alone.