$B^0$-$\bar{B}^0$ mixing: matching to HQET at NNLO

Understand

We compute perturbative matching coefficients to the Heavy Quark Effective Theory representation for the QCD effective local $\Delta B=2$ Hamiltonian that determines the mass difference in $B^0-\bar{B}^0$ system of states.

• We report on the results at NNLO in the strong coupling constant for matching coefficients of two physical operators in HQET.
• Our results provide the firm confirmation that the recent NLO sum rules analysis of the bag parameter $B_q$ is stable with regard of inclusion of higher order radiative corrections.
• As a by-product of our calculation we give a fully analytical solution for the one loop QCD-to-HQET matching problem: we present the explicit formulas for the renormalization of four quark operators of the full bases in both QCD and HQET and the expressions for matching coefficients in a closed form.