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We calculate a set of one-loop corrections to $h\to b\bar b$ and $h\to\tau\bar \tau$ decays in the dimension-6 Standard Model effective field theory(SMEFT). In particular, working in the limit of vanishing gauge couplings, wecalculate directly in the broken phase of the theory all large logarithmiccorrections and in addition the finite corrections in the large-$m_t$ limit.Moreover, we give exact results for one-loop contributions from four-fermionoperators. We obtain these corrections within an extension of the widely usedon-shell renormalisation scheme appropriate for SMEFT calculations, and showexplicitly how UV divergent bare amplitudes from a total of 21 different SMEFToperators are rendered finite within this scheme. As a by-product of thecalculation, we also compute to one-loop order the logarithmically enhanced andfinite large-$m_t$ corrections to muon decay in the limit of vanishing gaugecouplings, which is necessary to implement the $G_F$ input parameter schemewithin the SMEFT.

the journal of high energy physics/the journal of high energy physics

One-loop corrections to $h\to b\bar b$ and $h\to \tau\bar \tau$ decays  in the Standard Model Dimension-6 EFT: four-fermion operators and the  large-$m_t$ limit