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arXiv · 1610.06508

Transverse Momentum Dependent Fragmenting Jet Functions with Applications to Quarkonium Production

Reggie Bain·Yiannis Makris·Thomas Mehen
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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 $J/ψ$ 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 $J/ψ$ 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 $J/ψ$ makes with the jet axis.

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Reggie Bain, Yiannis Makris, Thomas Mehen. 2017-06-08. Transverse Momentum Dependent Fragmenting Jet Functions with Applications to Quarkonium Production. https://doi.org/10.1007/jhep11(2016)144

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