The decay h \u2192 \u03b3\u03b3 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 Rξ - gauges. We employ a simple renormalisation scheme that is hybrid between on-shell overline{mathrm{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 ℛh→ 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 QφB, QφW, QφW B , and at one-loop level from the dipole operators QuB, QuW. 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.