Abstract
We review and clarify computational issues about theW-gauge boson one-loop contribution to theH→γγdecay amplitude, in the unitary gauge and in the Standard Model. We find that highly divergent integrals depend upon the choice of shifting momenta with arbitrary vectors. One particular combination of these arbitrary vectors reduces the superficial divergency down to a logarithmic one. The remaining ambiguity is then fixed by exploiting gauge invariance and the Goldstone Boson Equivalence Theorem. Our method is strictly realised in four dimensions. The result for the amplitude agrees with the “famous” one obtained using dimensional regularisation (DR) in the limitd→4, wheredis the number of spatial dimensions in Euclidean space. At the exact equalityd=4, a three-sphere surface term appears that renders the Ward Identities and the equivalence theorem inconsistent. We also examined a recently proposed four-dimensional regularisation scheme and found agreement with the DR outcome.
Highlights
Today one of the main focal points at the Large Hadron Collider (LHC) is to search for the Higgs boson (H) [1,2,3] through its decay into two photons, H → γγ
The outline of the paper is as follows: in Section 2 we present the calculation of the W-loop contribution
We insist on doing the calculation of (24) in d = 4 with symmetric integration, like in [32, 33], we find that gauge invariance (see (23)) is not satisfied
Summary
Today one of the main focal points at the Large Hadron Collider (LHC) is to search for the Higgs boson (H) [1,2,3] through its decay into two photons, H → γγ (for reviews see [4, 5]). In the SM [8,9,10], this particular decay process goes through loop-induced diagrams involving either charged fermions or W-gauge bosons. Their calculation was first performed in [11] in the limit of light Higgs mass mH ≪ mW, using dimensional regularisation in the ’t HooftFeynman gauge. The amplitude should be consistent with the Goldstone Boson Equivalence Theorem (GBET) [20,21,22] since the SM is a renormalizable, spontaneously broken, gauge field theory
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
