Anomalous dimension of subleading-power ${N}$-jet operators II

TL;DR

This paper extends the analysis of anomalous dimensions for subleading-power N-jet operators in QCD, focusing on fermion-number-one operators and their renormalization effects due to soft loops, providing explicit anomalous dimension matrices.

Contribution

It presents the one-loop mixing and anomalous dimension matrix for fermion-number-one N-jet operators, advancing understanding of power-suppressed SCET interactions.

Findings

Computed the one-loop anomalous dimension matrix for fermion-number-one N-jet operators.

Analyzed the effects of soft loops on operator mixing and renormalization.

Provided explicit Feynman rules for power-suppressed SCET interactions.

Abstract

We continue the investigation of the anomalous dimension of subleading-power $N$-jet operators. In this paper, we focus on the operators with fermion number one in each collinear direction, corresponding to quark (antiquark) initiated jets in QCD. We investigate the renormalization effects induced by the soft loop and compute the one-loop mixing of time-ordered products involving power-suppressed SCET Lagrangian insertions into $N$-jet currents through soft loops. We discuss fermion number conservation in collinear directions and provide explicit results for the collinear anomalous dimension matrix of the currents. The Feynman rules for the power-suppressed SCET interactions in the position-space formalism are collected in an appendix.