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.
Highlights
Are consistent with the SM prediction, with the error margin expected to be reduced in the near future
We sum all contributions to Rh→γγ found in section 4, leaving as unknowns, the renormalisation group running Wilson coefficients, C = C(μ), the renormalisation scale μ divided by the W -boson mass and the energy scale Λ
It is suggested from eq (1.2) that the corrections to δRh→γγ should be at most 15%
Summary
In EFT, an effect from the decoupling of heavy particles with masses of order Λ is captured by the running parameters of the low energy theory influenced by higher dimensional operators added to SM renormalisable Lagrangian L(S4M). The operator Qφ cancels out completely after adding all contributions This leaves 17 CP-conserving operators (or Wilson coefficients) relevant to the h → γγ amplitude. Another classification of various d = 6 operators can be devised alongside with their strength [40, 41]. The division is between operators that are potentially tree level generated (PTG operators) and those that are loop generated (LG operators) by the more fundamental theory at high energies (UV-theory) under the assumption that the latter is perturbatively decoupled Under this classification, operators relevant for h → γγ am-.
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