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Phenomenological studies of exclusive heavy-quarkonium electroproduction at NLO

Chris A. Flett

TL;DR

The paper tackles exclusive electroproduction of heavy quarkonia, such as $J/ψ$ and $Υ$, in $ep$ collisions within a collinear factorisation framework at NLO to probe small-$x$ gluon structure via GPDs. It computes NLO coefficient functions for γ* p → V p, constructs quark and gluon GPDs with the Shuvaev transform, and compares predictions to HERA data, while providing EIC predictions and highlighting a double-logarithmic enhancement that motivates resummation beyond fixed-order CF. The study finds overall agreement with HERA data across a range of $Q^2$ and $W$, and shows that gluon contributions become increasingly important at larger $Q^2$, suggesting improved constraints on gluon GPDs at intermediate scales with the EIC. It also identifies the need for a dedicated resummation framework to address the large-$Q^2$ logarithms and outlines future directions toward resummation and applications at future colliders like FCC-eh or LHeC.

Abstract

Using the next-to-leading order (NLO) coefficient functions for exclusive electroproduction of heavy vector mesons derived in our previous work, we perform various phenomenological studies of exclusive electroproduction in $ep$ collisions relevant for both the existing measurements from HERA, and the forthcoming Electron-Ion collider (EIC). We compare our cross-section results to HERA data across a broad range of photon virtualities $Q^2$ and $γ^* p$ centre-of-mass energies, provide predictions for upcoming EIC measurements and conclude with a discussion on the necessity of resumming logarithmically enhanced contributions in $J/ψ$ electroproduction.

Phenomenological studies of exclusive heavy-quarkonium electroproduction at NLO

TL;DR

The paper tackles exclusive electroproduction of heavy quarkonia, such as and , in collisions within a collinear factorisation framework at NLO to probe small- gluon structure via GPDs. It computes NLO coefficient functions for γ* p → V p, constructs quark and gluon GPDs with the Shuvaev transform, and compares predictions to HERA data, while providing EIC predictions and highlighting a double-logarithmic enhancement that motivates resummation beyond fixed-order CF. The study finds overall agreement with HERA data across a range of and , and shows that gluon contributions become increasingly important at larger , suggesting improved constraints on gluon GPDs at intermediate scales with the EIC. It also identifies the need for a dedicated resummation framework to address the large- logarithms and outlines future directions toward resummation and applications at future colliders like FCC-eh or LHeC.

Abstract

Using the next-to-leading order (NLO) coefficient functions for exclusive electroproduction of heavy vector mesons derived in our previous work, we perform various phenomenological studies of exclusive electroproduction in collisions relevant for both the existing measurements from HERA, and the forthcoming Electron-Ion collider (EIC). We compare our cross-section results to HERA data across a broad range of photon virtualities and centre-of-mass energies, provide predictions for upcoming EIC measurements and conclude with a discussion on the necessity of resumming logarithmically enhanced contributions in electroproduction.

Paper Structure

This paper contains 4 sections, 6 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Overview of framework
  3. Results
  4. Conclusions

Figures (3)

  • Figure 1: From left to right: Example Feynman diagrams for the LO gluon, NLO quark and NLO gluon-initiated subprocesses. Here, the average of the incoming and outgoing proton momenta, $P^\mu$, defines the collinear direction. The momentum fractions carried by the incoming and outgoing partons along the light-cone component $P^+$ are $X+\xi$ and $X-\xi$, respectively. All diagrams were produced using JaxoDraw Binosi:2003yf.
  • Figure 2: Postdictions for exclusive $J/\psi$ electroproduction as a function of $W$ for $\langle Q^2 \rangle = 16$ GeV$^2$ (left) and $22.4$ GeV$^2$ (right), and compared to experimental measurements from HERA H1:1996gwvZEUS:2004yehH1:2005dtp. The shaded band represents the $\mu_{F,R}$ scale-variation uncertainty about the central scale $\mu^2 = Q^2 + 4m_c^2$, while the hatched band represents the NLO PDF uncertainty.
  • Figure 3: The exclusive $J/\psi$ electroproduction cross section as a function of $Q^2$ for a fixed centre-of-mass energy $W$ = 90 GeV and compared to the data from ZEUS ZEUS:2004yeh and H1 H1:2005dtp, using results in Flett:2021ghh and Shuvaev-transformed input CT18ANLO PDFs Hou:2019efy. The grey shaded band represents the simultaneous $\mu_{F,R}$ scale variation uncertainty of the LO result, the light-red shaded band that of the NLO result, while the hatched band gives the propagation of the NLO PDF uncertainty to the cross-section level.