Complete NLO QCD corrections for tree level Δf = 2 FCNC processes: Colourless gauge bosons and scalars

Anticipating the important role of tree level FCNC processes in the indirect search for new physics at distance scales as short as 10 ^-19-10 ^-21 m, we present complete NLO QCD corrections to tree level ΔF = 2 processes mediated by heavy colourless gauge bosons and scalars. Such contributions can be present at the fundamental level when the GIM mechanism is absent as in numerous Z' models, gauged flavour models with new very heavy neutral gauge bosons and Left-Right symmetric models with heavy neutral scalars. They can also be generated at one loop in models having GIM at the fundamental level and Minimal Flavour Violation of which Two-Higgs Doublet models with and without supersymmetry are the best known examples. In models containing vectorial heavy fermions that mix with the standard chiral quarks and models in which Z and SM neutral Higgs H mix with new heavy gauge bosons and scalars in the process of electroweak symmetry breaking also tree-level Z and SM neutral Higgs H contributions to ΔF = 2 processes are possible. In all these extensions new local operators absent in the SM are generated having Wilson coefficients that are generally much stronger affected by renormalization group QCD effects than it is the case of the SM operators. The new aspect of our work is the calculation of O(α _s) corrections to matching conditions for the Wilson coefficients of the contributing operators in the NDR-MS scheme that can be used in all models listed above. This allows to reduce certain unphysical scale and renormalization scheme dependences in the existing NLO calculations. We show explicitly how our results can be combined with the analytic formulae for the so-called P ^a _i QCD factors that include both hadronic matrix elements of contributing operators and renormalization group evolution from high energy to low energy scales. For the masses of heavy gauge bosons and scalars O(1)TeV the remaining unphysical scale dependences for the mixing amplitudes M ₁₂ are reduced typically from 10-25%, depending on the operator considered, down to 1-2%.