Exact one-loop results for $$l_i \rightarrow l_j\gamma $$ l i → l j γ in 3-3-1 models

Abstract

We investigate the decays l i → l j γ , with l i = e, μ, τ in a general class of 3-3-1 models with heavy exotic leptons with arbitrary electric charges. We present full and exact analytical results keeping external lepton masses. As a by product, we perform numerical comparisons between exact results and approximate ones where the external lepton masses are neglected. As expected, we found that branching fractions can reach the current experimental limits if mixings and mass differences of the exotic leptons are large enough. We also found unexpectedly that, depending on the parameter values, there can be huge destructive interference between the gauge and Higgs contributions when the gauge bosons connecting the Standard Model leptons to the exotic leptons are light enough. This mechanism should be taken into account when using experimental constraints on the branching fractions to exclude the parameter space of the model.

General one-loop formulas for decay $$h\rightarrow Z\gamma $$ h → Z γ

“…where λ(x, y, z) = x 2 + y 2 +z 2 −2x y −2yz −2xz. This formula is also consistent with LoopTools and [48], where notations are changed as…”

“…The Feynman rules used in our calculations are listed in Table 1. We found them to appear commonly in many gauge extensions of the SM, for example in the models constructed from the following electroweak gauge symmetries: [48][49][50][51][52][53], where an important relation g Z γ V i j = e Q g Z V i j is valid. It results in that many compli-cated terms containing dangerous divergences in two contributions from diagrams 5 and 6 in Fig.…”

“…We would like to emphasize now that formula (14) is written in terms of PV functions which are contained in LoopTools and hence it can be easily evaluated numerically. Moreover, analytic expressions for the relevant PV functions have been constructed [10,48], that is enough to implement our results in existing numerical programs or to write a new stand-alone code. We would like comment here about a more general case when couplings of gauge bosons and photon do not obey the relation g Z γ V i j = e Q g Z V i j , which helps us to reduce many divergent terms in M (5+6)μν .…”

“…The C i,i j functions are found based on the reduction technique [83]. Their explicit forms used in this work are [48],…”

Neutral Higgs boson decays H→Zγ,γγ in 3-3-1 models

“…There is another arrangement that the model contains three left-handed lepton triplets, one quark triplet and two other quark anti-triplets. But, it was shown that the two arrangements are equivalent in the sense that they predict the same physics [47,48].…”