NLO corrections to h → b$$ \overline{b} $$ decay in SMEFT

Abstract

We calculate the full set of next-to-leading order (NLO) corrections to h → bb decay in the dimension-6 Standard Model Effective Field Theory (SMEFT). Our calculation forms the basis for precision studies of this decay mode in effective field theory, providing analytic and numerical results for contributions of the 45 dimension-6 operators appearing at NLO. On the technical side, we discuss several complications in NLO SMEFT computations which have not yet been addressed in the literature. These include subtleties in Higgs-Z mixing, electric charge renormalization, and especially the treatment of tadpoles in SMEFT. In particular, we highlight the role of decoupling relations in eliminating potentially large tadpole corrections to the decay rate in hybrid renormalization schemes which employ the MS scheme for some Standard Model parameters (such as the b-quark mass and electric charge) and the on-shell scheme for others.

Singlet night in Feynman-ville: one-loop matching of a real scalar

“…In our diagrammatic calculation, as well as in the UOLEA approach described in Appendix A, we renormalise φ tadpoles minimally [44,45] and (3.9), (3.11), (A.8) and (A.9) therefore correspond to the MS scheme. Notice that in the MS scheme the effective one-loop scalar potential contains a term linear in the φ field, which by definition would be absent in the on-shell scheme where the tadpole counterterm is fixed such that all tadpole diagrams vanish [46] -see also [47][48][49] for excellent discussions of the different treatments of tadpoles.…”

The geometric Standard Model Effective Field Theory

“…The SMEFT weak/mass eigenstate dynamical fields 5 and related couplings are then given by [10] (see also Refs. [26][27][28][29])…”

Electroweak and QCD corrections to Z and W pole observables in the standard model EFT

“…The SMEFT QCD corrections to gauge boson pair production [11,12] and top quark production and decay [13][14][15][16] are known. The electroweak SMEFT corrections to Higgs decays to bb [17][18][19], γγ [20][21][22][23], Zγ [24,25], ZZ [24], and W W [20] have also been computed, along with partial corrections to the Drell Yan process [26]. The SMEFT NLO corrections to Z pole decays at NLO are also only partially known [27][28][29].…”