The 1 $\rightarrow$ 3 Massive Splitting Functions from QCD Factorization and SCET

TL;DR

This paper derives and verifies analytic triple collinear splitting functions involving a massive parton in QCD using two different methods, enhancing the tools for higher order calculations with heavy quarks.

Contribution

The paper provides the first analytic derivation of triple collinear splitting functions with a massive parton in QCD using matrix elements and SCET, confirming their consistency.

Findings

Analytic triple collinear splitting functions for massive quarks derived.

Results agree with soft-collinear effective theory and factorization predictions.

Provides essential ingredients for higher order calculations involving heavy flavor jets.

Abstract

Splitting functions are universal functions describing the collinear dynamics of gauge theories, and as such are crucial ingredients for a wide variety of calculations in perturbative QCD. We present analytic results for the triple collinear splitting functions in QCD with a single massive parton. We derive the splitting functions using two distinct methods; first by expanding the squared matrix elements in the collinear limit, and secondly by using soft-collinear effective theory with massive quarks. We find agreement between these two approaches, providing a strong check of our results. Additionally, we also check all iterated and soft limits of our results, finding agreement with predictions from factorization. Our results provide an important ingredient for higher order perturbative calculations involving massive partons, and for the description of the collinear dynamics of heavy flavor jets.