A ‘BPS expansion’ for B and D mesons

Abstract

We analyze consequences of the approximation μπ2−μG2⪡μπ2 (a ‘BPS’ limit) for B and D mesons. It is shown that neglecting perturbative effects many power corrections would vanish to all orders in 1/mQ, in particular, those violating heavy flavor symmetry. Among them are corrections to B→D formfactors. A number of relations receive corrections only to second order expanding around the BPS limit to any order in 1/mQ, including both f+ and f− at zero recoil. This allows an accurate evaluation of F+ for B→Dℓν. Its perturbative renormalization is computed analytically in the required Wilsonian scheme, yielding the dominant 3% enhancement.