Abstract
We calculate the full set of next-to-leading order (NLO) corrections to h → b overline{b} 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 overline{mathrm{MS}} scheme for some Standard Model parameters (such as the b-quark mass and electric charge) and the on-shell scheme for others.
Highlights
Only recently been observed by the ATLAS and CMS collaborations [9, 10]
Provided the new physics is associated with a scale ΛNP which is much greater than the electroweak symmetry breaking (EWSB) scale and decouples [13], its effect on processes at low energy is captured through non-zero values of these Wilson coefficients
This builds upon our previous next-to-leading order (NLO) Standard Model Effective Field Theory (SMEFT) calculations of weak corrections in the large-mt limit or those related to four-fermion operators [55], and QCD corrections [56]
Summary
Where L(4) denotes the SM Lagrangian, and L(6) depends on the dimension-6 operators Qi. The 2- and 3-body terms involving emissions of gluons or photons contribute to Γg,γ These contain IR divergences, which we regularize by performing the loop integrations and phase-space integrals in d = 4 − 2 dimensions. The most challenging part of the calculation is to obtain the UV-renormalized 2-body matrix element M(1)(h → bb), which is needed to determine Γrem We do this by evaluating the expression. The exact form of the counterterm and bare amplitude depends on the set of independent parameters in terms of which the SMEFT Lagrangian in the mass basis is expressed, and the scheme in which these parameters are renormalized, as discussed in more detail below. The first is that the UV poles in the bare and counterterm matrix elements cancel against each other, and the related fact that the decay rate is independent of the renormalization scale μ up to NLO. We have verified the gauge independence of our results by performing all calculations in both unitary and Feynman gauge
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