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

Abstract

We calculate the S-matrix element for the Higgs boson decay to a Z-boson and a photon, h → Zγ, at one-loop in the Standard-Model Effective Field Theory (SMEFT) framework and in linear Rξ -gauges. Our SMEFT expansion includes all relevant operators up to dimension-6 considered in Warsaw basis without resorting to any flavour or CP- conservation assumptions. Within this approximation there are 23 dimension-6 operators affecting the amplitude, not including flavour and hermitian conjugation. The result for the on-shell h → Zγ amplitude is gauge invariant, renormalisation-scale invariant and gauge-fixing parameter independent. The calculated ratio of the SMEFT versus the SM expectation for the h → Zγ decay width is then written in a semi-numerical form which is useful for further comparisons with related processes. For example, the h → Zγ amplitude contains 16 operators in common with the h → γγ amplitude and one can draw useful results about its feasibility at current and future LHC data.