Transverse Momentum Dependent Fragmenting Jet Functions with Applications to Quarkonium Production

TL;DR

This paper introduces the TMDFJF within SCET, providing a framework for analyzing jet fragmentation with identified hadrons, and applies it to quarkonium production, revealing differences in distributions for various production mechanisms.

Contribution

The paper derives the TMDFJF in SCET, incorporating rapidity resummation, and applies it to quarkonium production, offering new insights into hadronization within jets.

Findings

TMDFJF formalism derived with NLL' resummation.

Differences observed in $p_T$ and $z$ distributions for NRQCD mechanisms.

Average angle of $J/\psi$ with jet axis varies by production process.

Abstract

We introduce the transverse momentum dependent fragmenting jet function (TMDFJF), which appears in factorization theorems for cross sections for jets with an identified hadron. These are functions of $z$, the hadron's longitudinal momentum fraction, and transverse momentum, $\boldsymbol{\mathrm{p}}_{\perp}$, relative to the jet axis. In the framework of Soft-Collinear Effective Theory (SCET) we derive the TMDFJF from both a factorized SCET cross section and the TMD fragmentation function defined in the literature. The TMDFJFs are factorized into distinct collinear and soft-collinear modes by matching onto SCET$_+$. As TMD calculations contain rapidity divergences, both the renormalization group (RG) and rapidity renormalization group (RRG) must be used to provide resummed calculations with next-to-leading-logarithm prime (NLL') accuracy. We apply our formalism to the production of $J/\psi$ within jets initiated by gluons. In this case the TMDFJF can be calculated in terms of NRQCD (Non-relativistic quantum chromodynamics) fragmentation functions. We find that when the $J/\psi$ carries a significant fraction of the jet energy, the $p_T$ and $z$ distributions differ for different NRQCD production mechanisms. Another observable with discriminating power is the average angle that the $J/\psi$ makes with the jet axis.