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A systematic study of one-loop contributions to the decay channels$h\rightarrow l\bar{l}\gamma$ with $l=\nu_{e,\mu, \tau}, e, \mu$, performed inHiggs extended versions of the Standard Model, is presented in the 'tHooft-Veltman gauge. Analytic formulas for one-loop form factors are expressedin terms of the logarithm and di-logarithmic functions. As a result, these formfactors can be reduced to those relating to the loop-induced decay processes$h\rightarrow \gamma\gamma, Z\gamma$, confirming not only previous resultsusing different approaches but also close relations between the three kinds ofthe loop-induced Higgs decay rates. For phenomenological study, we focus on thetwo observables, namely the enhancement factors defined as ratios of the decayrates calculated between the Higgs extended versions and the standard model,and the forward-backward asymmetries of fermions, which can be used to searchfor Higgs extensions of the SM. We show that direct effects of mixing betweenneutral Higgs bosons and indirect contributions of charged Higg boson exchangescan be probed at future colliders.

One-loop expressions for $h\rightarrow l\bar{l}\gamma$ in Higgs extensions of the Standard Model