Completing NLO QCD corrections for tree level non-leptonic ΔF = 1 decays beyond the Standard Model

Abstract

In various extensions of the Standard Model (SM) tree level non-leptonic decays of hadrons receive contributions from new heavy gauge bosons and scalars. Prominent examples are the right-handed W′ bosons in left-right symmetric models and charged Higgs (H ±) particles in models with extended scalar sector like two Higgs doublet models and supersymmetric models. Even in the case of decays with four different quark flavours involved, to which penguin operators cannot contribute, twenty linearly independent operators, instead of two in the SM, have to be considered. Anticipating the important role of such decays at the LHCb, KEKB and Super-B in Rome and having in mind future improved lattice computations, we complete the existing NLO QCD formulae for these processes by calculating ${\mathcal O}$ (α s ) corrections to matching conditions for the Wilson coefficients of all contributing operators in the ${\text{NDR}} - \overline {\text{MS}}$ scheme. This allows to reduce certain unphysical scale and renormalization scheme dependences in the existing NLO calculations. Our results can also be applied to models with tree-level heavy neutral gauge boson and scalar exchanges in ΔF = 1 transitions and constitute an important part of NLO analyses of those non-leptonic decays to which also penguin operators contribute.