NNLO vertex corrections in charmless hadronic B decays: Real part

Understand

We compute the real part of the 2-loop vertex corrections for charmless hadronic B decays, completing the NNLO calculation of the topological tree amplitudes in QCD factorization.

• Among the technical aspects we show that the hard-scattering kernels are free of soft and collinear infrared divergences at the 2-loop level, which follows after an intricate subtraction procedure involving evanescent four quark operators.
• The numerical impact of the considered corrections is found to be moderate, whereas the factorization scale dependence of the topological tree amplitudes is significantly reduced at NNLO.
• We in particular do not find an enhancement of the phenomenologically important ratio |C/T| from the perturbative calculation.