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

TL;DR

This paper computes one-loop corrections to Higgs decays into bottom quarks and tau leptons within the Standard Model effective field theory, focusing on large top mass effects and four-fermion operators, providing precise finite and logarithmic results.

Contribution

It presents the first comprehensive calculation of one-loop SMEFT corrections to Higgs decay processes including four-fermion operators and large-$m_t$ effects, extending the on-shell renormalisation scheme.

Findings

Explicit finite corrections for $h o b\bar{b}$ and $h\to \tau\bar{\tau}$ decays.

Exact large-$m_t$ corrections for these decays.

One-loop large-$m_t$ corrections to muon decay in SMEFT.

Abstract

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, we calculate directly in the broken phase of the theory all large logarithmic corrections and in addition the finite corrections in the large-$m_t$ limit. Moreover, we give exact results for one-loop contributions from four-fermion operators. We obtain these corrections within an extension of the widely used on-shell renormalisation scheme appropriate for SMEFT calculations, and show explicitly how UV divergent bare amplitudes from a total of 21 different SMEFT operators are rendered finite within this scheme. As a by-product of the calculation, we also compute to one-loop order the logarithmically enhanced and finite large-$m_t$ corrections to muon decay in the limit of vanishing gauge couplings, which is necessary to implement the $G_F$ input parameter scheme within the SMEFT.