$J/ψ$ Production Within Jets at the EIC

TL;DR

This work addresses the challenge of constraining NRQCD long-distance matrix elements governing $J/\psi$ production by proposing differential observables for $J/\psi$ within jets at the EIC. It develops a theoretical framework based on semi-inclusive fragmenting jet functions (FJFs), combining NLO partonic cross sections with NRQCD-structured fragmentation functions and resumming both collinear and threshold logarithms at LL accuracy, to predict distributions in the quarkonium momentum fraction $z_{J/\psi}$ across jet-$p_T$ and $J/\psi$-$p_T$ bins. The analysis emphasizes the enhanced role of quark-initiated fragmentation in electron-proton photoproduction, examines three representative LDME sets, and investigates the impact of jet radius $R$ and muon-identification cuts on the predicted spectra. The results indicate that quarkonium-in-jet observables at the EIC can discriminate between LDME scenarios and provide complementary information to LHC measurements, advancing our understanding of heavy quarkonium formation and offering a pathway to tighter LDME constraints using future EIC data.

Abstract

We present theoretical predictions for the transverse-momentum distribution of $J/ψ$ produced within jets at the upcoming Electron-Ion Collider (EIC). Utilizing the semi-inclusive fragmenting jet function (FJF) framework, our calculation achieves next-to-leading order (NLO) accuracy in the strong coupling and leading-logarithmic (LL) accuracy by resumming both collinear and threshold logarithms. In contrast to the gluon-dominated regime of the LHC, EIC photoproduction is characterized by an enhanced quark-initiated component, offering a complementary probe into the charmonium production mechanism governed by nonperturbative long-distance matrix elements (LDMEs). We examine the impact of representative LDME sets, demonstrating the EIC's distinct discriminating power for the mechanisms. We find that quark contributions are particularly significant in the small momentum fraction region. This region is also shown to be sensitive to both the jet radius $R$ and the experimental muon identification criteria for the $J/ψ\to μ^+μ^-$ decay channel. These findings establish quarkonium-in-jet observables at the EIC as a vital, independent probe for constraining the production mechanisms and advancing our understanding of heavy quarkonium formation.

Figures (6)

• Figure 1: LO and NLO PPCSs for quark singlet ($i=q$) and gluon ($i=g$) channels as a function of the momentum fraction $z$, comparing the EIC (left) and LHCb (right).
• Figure 2: The PPCSs for quark singlet ($i=q$) and gluon ($i=g$) channels at the EIC, illustrating the decomposition into direct and resolved components at low $p_T\text{(jet)}=7$ GeV (left) and high $p_T\text{(jet)}=20$ GeV (right) as a function of the momentum fraction $z$.
• Figure 3: The muon acceptance, $\mathcal{A}$, as a function of the momentum fraction $z_{J/\psi}$ calculated for LHCb and CMS kinematic regions.
• Figure 4: Predicted $z_{J/\psi}$ distributions for three sets of LDMEs in Table \ref{['tab:ME']}, with the upper and lower panels displaying results in jet-$p_T$ bin and $J/\psi$-$p_T$ bin respectively.
• Figure 5: Predicted $z_{J/\psi}$ distributions and octet-state fractions for the EIC (upper panel) and LHCb (lower panel).