$B^0-{\bar{B}}^0$ Mixing at Next-to-Leading Order

Abstract

We compute the perturbative corrections to the HQET sum rules for the matrix element of the \Delta B=2 operator that determines the mass shift of $B^0$, ${\bar{B}}^0$ states. Technically, we obtain analytically the non-factorizable contributions at order ${\alpha }_s$ to the bag parameter that first appear at the three-loop level. Together with the known non-perturbative corrections due to vacuum condensates and $1/m_b$ corrections, the full next-to-leading order result is now available. We present a numerical value for the renormalization group invariant bag parameter that is phenomenologically relevant and discuss comparison with recent lattice determinations.

Comments: v2: references updated, small fixes, corresponds to the published version