The decay h → γγ in the Standard-Model Effective Field Theory

Abstract

Assuming that new physics effects are parametrized by the Standard-Model Effective Field Theory (SMEFT) written in a complete basis of up to dimension-6 operators, we calculate the CP-conserving one-loop amplitude for the decay h → γγ in general R ξ -gauges. We employ a simple renormalisation scheme that is hybrid between on-shell SM-like renormalised parameters and running MS Wilson coefficients. The resulting amplitude is then finite, renormalisation scale invariant, independent of the gauge choice (ξ) and respects SM Ward identities. Remarkably, the S-matrix amplitude calculation resembles very closely the one usually known from renormalisable theories and can be automatised to a high degree. We use this gauge invariant amplitude and recent LHC data to check upon sensitivity to various Wilson coefficients entering from a more complete theory at the matching energy scale. We present a closed expression for the ratio R h→γγ , of the Beyond the SM versus the SM contributions as appeared in LHC h → γγ searches. The most important contributions arise at tree level from the operators Q ϕB , Q ϕW , Q ϕW B , and at one-loop level from the dipole operators Q uB , Q uW . Our calculation shows also that, for operators that appear at tree level in SMEFT, one-loop corrections can modify their contributions by less than 10%. Wilson coefficients corresponding to these five operators are bounded from current LHC h → γγ data -in some cases an order of magnitude stronger than from other searches. Finally, we correct results that appeared previously in the literature. *

The Higgs width in the SMEFT

“…One loop calculations of this process in the SMEFT were reported in Refs. [28][29][30][31][32]. Such corrections are important, but they the same order (in the SMEFT expansion and the loop expansion) as the scheme dependent corrections to the SM results, which introduces scheme dependence that is only removed once a full one loop improvement of SMEFT predictions is obtained.…”

The decay h → Zγ in the Standard-Model Effective Field Theory

“…Our definitions and conventions follow directly those of refs. [14] and [23]. We introduce the unrenormalised, but regularised, self-energies, that is 1PI diagrams for scalars s 1,2 (= h), and vector bosons V 1,2 (= W ± , Z, γ), q s 1…”

“…(A.6) of ref. [14]. Note that A SM Zγ (0) is a function of the SMEFT couplings, the VEV and the W -boson mass.…”

“…(4.10) with δR h→γγ taken from ref. [14] but translated into the {G F , M W , M Z } input scheme. We have, One can draw interesting remarks by comparing eqs.…”

“…The large scheme dependence can be understood by comparing (4.12) with the first line of eq. (5.1) of ref [14]…”