# Two-Loop Massive Quark Jet Functions in SCET

## TL;DR

This paper computes second-order corrections to massive quark jet functions in SCET, clarifies their definitions, and explores their role in factorization approaches for accurate jet mass predictions involving massive quarks.

## Contribution

It introduces a new way to define SCET jet functions using collinear-soft matrix elements, avoiding zero-bin subtractions, and compares two approaches for secondary massive quark effects.

## Key findings

- Calculated $ ext{O}( ext{α}_s^2)$ corrections to massive quark jet functions.
- Established the equivalence of two factorization approaches for secondary quark effects.
- Addressed technical issues like rapidity divergences and infrared regularization.

## Abstract

We calculate the $\mathcal O(\alpha_s^2)$ corrections to the primary massive quark jet functions in Soft-Collinear Effective Theory (SCET). They are an important ingredient in factorized predictions for inclusive jet mass cross sections initiated by massive quarks emerging from a hard interaction with smooth quark mass dependence. Due to the effects coming from the secondary production of massive quark-antiquark pairs there are two options to define the SCET jet function, which we call universal and mass mode jet functions. They are related to whether or not a soft mass mode (zero) bin subtraction is applied for the secondary massive quark contributions and differ in particular concerning the infrared behavior for vanishing quark mass. We advocate that a useful alternative to the common zero-bin subtraction concept is to define the SCET jet functions through subtractions related to collinear-soft matrix elements. This avoids the need to impose additional power counting arguments as required for zero-bin subtractions. We demonstrate how the two SCET jet function definitions may be used in the context of two recently developed factorization approaches to treat secondary massive quark effects. We clarify the relation between these approaches and in which way they are equivalent. Our two-loop calculation involves interesting technical subtleties related to spurious rapidity divergences and infrared regularization in the presence of massive quarks.