B0−B¯0mixing at next-to-leading order

Abstract

We compute the perturbative corrections to the HQET sum rules for the matrix element of the ∆B = 2 operator that determines the mass difference of B 0 ,B 0 states. Technically, we obtain analytically the non-factorizable contributions at order α 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 compare it with recent lattice determinations.

Towards a next-to-next-to-leading order analysis of matching in B0−B¯0 mixing

“…This makes the computation rather cumbersome as the renormalized physical operators in such a scheme have no meaning without an explicit form of the evanescent ones. We show that our choice of evanescent operators coordinated with the standard ones in QCD does not affect our calculation of the three-loop correction to the bag parameter in HQET [36].…”

“…This analysis is important for our computation of bag parameters with three-loop correlator in [36]. In the previous section we established that E QCD matches to evanescent operators in HQET provided the basis is chosen as in (2.25) which implies that only physical operators O l , O s should be considered in SR analysis.…”

“…Note in passing that with the NNLO accuracy of the leading term one may need to account also for nonleading terms of HQE [46]. We have revisited the calculation of the bag parameter in sum rules at three-loop level [36]. We stress that the form of the Hamiltonian in the physical sector is not sufficient: for any computation of ME (or Green functions) one needs to know the set of related evanescent operators.…”

“…Thus, the calculation in ref. [36] is not affected by the presence of evanescent operators as soon as they are defined according to the standard rules used for the computation of the Wilson coefficients. This fact has not been explicitly mentioned in ref.…”

“…In a recent paper [36] we have discussed the matrix element (5.1) for a B d meson, using a QCD sum rule within HQET. While in a lattice calculation the decomposition of the matrix element into decay constant and bag parameter is irrelevant, it is important in the sum-rule calculation, since the contributing Feynman diagrams can be uniquely attributed to either f Bq or B Bq .…”