Factorization for $J/\psi$ leptoproduction at small transverse momentum

TL;DR

This paper develops a TMD factorization framework for low transverse momentum $J/$ leptoproduction, deriving a new factorization theorem, computing TMD shape functions at NLO, and connecting them to NRQCD LDMEs, with implications for the Electron-Ion Collider.

Contribution

It introduces a TMD factorization approach combining NRQCD and SCET for $J/$ leptoproduction at small transverse momentum, including NLO calculations and evolution of TMD shape functions.

Findings

Derived a factorization theorem for $J/$ leptoproduction at low $q_T$.

Computed TMD shape functions at next-to-leading order.

Established the evolution and matching of TMD shape functions to LDMEs.

Abstract

Nonrelativistic Quantum Chromodynamics (NRQCD) breaks down in the region of low transverse momentum, where the transverse momentum of the produced quarkonium state is sensitive to multiple scattering with the incoming hadron and to soft gluon radiation. In this kinematic regime, the transverse-momentum-dependent (TMD) factorization framework is required, promoting the long-distance matrix elements (LDMEs) of NRQCD to the so-called TMD shape functions (TMDShFs), which encode both the soft gluon radiation and the formation of the heavy-quark bound state. In this work, we apply an effective-field theory approach (combining NRQCD and SCET) to the photon-gluon fusion process in inclusive $J/\psi$ leptoproduction. We derive a factorization theorem for the cross section in terms of TMDShFs, compute these quantities at next-to-leading order, establish their evolution, and study their matching onto the corresponding LDMEs in the high-transverse-momentum region. Our results are particularly relevant to the Electron-Ion Collider, where $J/\psi$ leptoproduction can be used to probe gluon transverse-momentum-dependent parton distribution functions (gluon TMDPDFs).