Three-loop HQET vertex diagrams for B^0 -\bar{B}^0 mixing

TL;DR

This paper develops an algorithm to reduce complex three-loop HQET vertex diagrams to master integrals, calculates these integrals exactly in d dimensions, and provides their epsilon expansions, advancing theoretical tools for B^0 - ar{B}^0 mixing analysis.

Contribution

The paper introduces a new reduction algorithm for three-loop HQET vertex diagrams and computes all master integrals exactly in d dimensions with epsilon expansions.

Findings

Successfully reduced three-loop diagrams to master integrals.

Calculated master integrals exactly in d dimensions.

Provided epsilon expansions for the integrals.

Abstract

Three-loop vertex diagrams in HQET needed for sum rules for B^0 - \bar{B}^0 mixing are considered. They depend on two residual energies. An algorithm of reduction of these diagrams to master integrals has been constructed. All master integrals are calculated exactly in d dimensions; their epsilon expansions are also obtained.