Relativistic corrections to the vector meson light front wave function

TL;DR

This paper develops a relativistic light front wave function for heavy vector mesons, incorporating significant corrections that improve the description of experimental data, especially for J/psi production, and highlights the importance of relativistic effects.

Contribution

It introduces a systematic expansion of the vector meson wave function in quark velocity, including relativistic corrections crucial for accurate phenomenology.

Findings

Relativistic corrections are significant for J/psi production.

Wave function dependence affects nuclear vs. proton cross section ratios.

Non-relativistic limit is inadequate even in ratio analyses.

Abstract

We compute a light front wave function for heavy vector mesons based on long distance matrix elements constrained by decay width analyses in the Non Relativistic QCD framework. Our approach provides a systematic expansion of the wave function in quark velocity. The first relativistic correction included in our calculation is found to be significant, and crucial for a good description of the HERA exclusive $\mathrm{J}/\psi$ production data. When looking at cross section ratios between nuclear and proton targets, the wave function dependence does not cancel out exactly. In particular the fully non-relativistic limit is found not to be a reliable approximation even in this ratio. The important role of the Melosh rotation to express the rest frame wave function on the light front is illustrated.