Spectator effects in the HQET renormalization group improved Lagrangian at $\mathcal{O}(1/m^3)$ with leading logarithmic accuracy: Spin-dependent case

TL;DR

This paper calculates the effects of massless spectator quarks on the renormalization group improved Wilson coefficients in the spin-dependent heavy quark effective theory at order 1/m^3, achieving leading logarithmic accuracy.

Contribution

It provides the first computation of spectator effects in the RG-improved Lagrangian at this order with leading logarithmic precision.

Findings

Completes the spin-dependent HQET Lagrangian at order 1/m^3 with spectator effects.

Uses Coulomb gauge for the computation.

Achieves leading logarithmic accuracy in the results.

Abstract

The present paper incorporates the effects induced by massless spectator quarks in the renormalization group improved Wilson coefficients associated to the ${\cal O}(1/m^3)$ spin-dependent heavy quark effective theory Lagrangian operators. The computation is carried out in Coulomb gauge with leading logarithmic precision. The result completes the Lagrangian to $\mathcal{O}(1/m^3)$ with that accuracy.