# Towards a Next-to-Next-to-Leading Order analysis of matching in $B^0$-$\bar{B}^0$ mixing

## TL;DR

This paper calculates advanced two-loop perturbative corrections to the matching coefficients between QCD and HQET for the $B^0-ar{B}^0$ mixing, improving precision in theoretical predictions.

## Contribution

It provides the first analytical two-loop correction results for the matching coefficients relevant to $B^0-ar{B}^0$ mixing in the QCD-HQET framework.

## Key findings

- Analytical two-loop corrections at order α_s^2 obtained.
- Clarified operator basis choice in HQET.
- Enhanced precision in $B^0-ar{B}^0$ mixing calculations.

## Abstract

We compute perturbative corrections to matching coefficients of QCD to HQET for the matrix element of the $\Delta B=2$ operator that determines the mass difference in $B^0-\bar{B}^0$ system of states. This involves the technical point of choosing the operator basis in HQET, separating physical operators from evanescent ones. We obtain an analytical result for some of the two-loop corrections at order $\alpha_s^2$.