Renormalization of dimension-six operators relevant for the Higgs decays h → γγ, γZ

Abstract

The discovery of the Higgs boson has opened a new window to test the SM through the measurements of its couplings. Of particular interest is the measured Higgs coupling to photons which arises in the SM at the one-loop level, and can then be significantly affected by new physics. We calculate the one-loop renormalization of the dimensionsix operators relevant for h → γγ, γZ, which can be potentially important since it could, in principle, give log-enhanced contributions from operator mixing. We find however that there is no mixing from any current-current operator that could lead to this log-enhanced effect. We show how the right choice of operator basis can make this calculation simple. We then conclude that h → γγ, γZ can only be affected by RG mixing from operators whose Wilson coefficients are expected to be of one-loop size, among them fermion dipole-moment operators which we have also included.

The effective Standard Model after LHC Run I

“…These are related to the coefficients at the new physics scale through RGE equations [110][111][112][113][114][115][116][117].…”

Light top partners and precision physics

“…In refs. [77,78] an effective approach was used in which only the SM fields are retained and all the composite resonances are integrated out. In this framework it was shown that two effective operators…”

“…[77,78], in our approach the resonances are included in the effective theory and the effective operators O Hq and O Hq are not present directly in our Lagrangian. At low energy, however, they are generated through the exchange of resonances of mass m with a coefficient y 2 /m 2 .…”

“…[77,78] do not appear as real divergences but rather correspond to corrections that scale as y 2 /m 2 log(m 2 /m 2 t ). Terms of this form can be recognized, for example, in the explicit analytic result for S given in eq.…”

Sensitivities of prospective future e + e − colliders to decoupled new physics

“…We note that the coefficients constrained in our fit correspond to those defined at the electroweak scale, c i ≡ c i (v), which can be related to c i (Λ) at the matching scale by RGE running [45][46][47][48][49][50][51][52]. We neglect dimension-8 operators in our analysis, as well as four-fermion operators (other thanc (3)l LL that modifies the input parameter G F ), whose effects on Z-pole measurements are formally of the same order as dimension-8 operators due to the lack of linear interference terms with the SM amplitudes [16].…”