$ψ(2S)$ production in jets using NRQCD

TL;DR

The paper addresses constraining the $ψ(2S)$ long-distance matrix elements (LDMEs) in NRQCD by studying $ψ(2S)$ production inside jets. It combines NRQCD factorization with two jet-fragmentation formalisms, the Fragmenting Jet Function (FJF) and Gluon Fragmentation Improved Pythia (GFIP), to predict the jet-internal $ψ(2S)$ distribution and compares against LHCb data at $ ms{\sqrt{s}}=13$ TeV. The results show that both formalisms significantly improve over naive NRQCD+Pythia predictions, with GFIP generally aligning with data across LDME sets and FJF’s performance strongly dependent on the chosen LDME extraction, particularly near the endpoint $z\to1$. The study demonstrates that in-jet observables provide a powerful discriminator among LDME extractions and motivates global fits incorporating jet data to tighten constraints on the $ψ(2S)$ LDMEs, thus advancing our understanding of quarkonium production in QCD.

Abstract

Based on recent data from LHCb, we study $ψ(2S)$ production in jets using non-relativistic QCD (NRQCD) in conjunction with the Fragmenting Jet Function (FJF) and Gluon Fragmentation Improved Pythia (GFIP) formalisms. Similar to previous studies of $J/ψ$ production in jets, our results show that these formalisms offer a much better description of data than the default Pythia+NRQCD prediction. We compare and contrast the predictions from the FJF formalism and the GFIP approach. In addition, our results show that the distribution of $ψ(2S)$ in jets is an excellent discriminator to test different predictions for the $ψ(2S)$ LDMEs from various extractions. We find a large disparity between the predictions from three different collaborations, showing that a more precise extraction of the $ψ(2S)$ LDMEs may be necessary.

Figures (2)

• Figure 1: Comparison of different theoretical treatments for quarkonium production inside jets.
• Figure 2: $z$-distributions of $\psi(2S)$ inside jets. Black dots are measured at the LHCb experiment with collision energy $\sqrt{s}=13$ TeV. The red and blue curves represent the results from the GFIP and FJF methods, respectively. Each row presents the results at a certain $p_T^{\text{jet}}$-bin with three different groups of LDMEs.