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

Understand

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 $\alpha_s^2$.