Details of a recent calculation of O(αₛ²) corrections to the decay b→cνₗ, taking into account the c-quark mass, are described. Construction of the expansion in the mass ratio mc/mb as well as the evaluation of new four-loop master integrals are presented. The same techniques are applicable to the muon decay, μ→eν_μνₑ. Analytical results are presented, for the physical cases as well as for a model with purely-vector couplings.
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Pak et al. (2008) studied this question.
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