Heavy Quark Jet Fragmentation

TL;DR

This paper investigates the effects of heavy quark masses on jet fragmentation functions, providing next-to-leading order calculations and a factorization theorem to resum large logarithms, with applications to b-jet production.

Contribution

It introduces a systematic approach to include heavy quark mass effects in jet fragmentation functions and formulates a factorization theorem for heavy quark jet production.

Findings

Heavy quark mass effects significantly alter jet fragmentation functions.

The formulated factorization theorem enables resummation of large mass logarithms.

Application to b-jet production shows notable phenomenological implications.

Abstract

In this paper we study the fragmentation of a parton into a jet containing a heavy quark. When heavy quarks are involved in a jet, the quark mass can lead to a numerically significant correction to the jet cross section and its substructure. With this motivation, we calculated the heavy quark mass effects to next-to-leading order in $\alpha_s$ on the fragmentation functions to a jet (FFJs) and the jet fragmentation functions (JFFs), where the former describes fragmentation of parton into a jet and the latter describes fragmenting processes inside a jet. The finite size of the heavy quark mass does not change the ultraviolet behaviors, but it can give significant corrections to the finite contributions. When we take the zero mass limit, we find that the FFJs and the JFFs reproduce established results for massless partons. If we define the heavy quark jet as one that include at least one heavy (anti-)quark, the tagged heavy quark jet production is sensitive to the heavy quark mass and produces large logarithms of the mass. Taking advantage of the FFJs and JFFs, we formulate a factorization theorem for heavy quark jet production in order to resum these large logarithms systematically. As an application, we study inclusive $b$-jet production and show phenomenological implications due to keeping a non-zero quark mass.