The decay h → γγ in the Standard-Model Effective Field Theory
Journal of High Energy Physics
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
... nt 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_φ B, Q_φ W, Q_φ WB, 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 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.