There is no tree-level flavor changing neutral current (FCNC) in the standard
model (SM) which contains only one Higgs doublet. If more Higgs doublets are
introduced for various reasons, the tree level FCNC would be inevitable except
extra symmetry was imposed. Therefore FCNC processes are the excellent probes
for the physics beyond the SM (BSM). In this paper, we studied the lepton
flavor violated (LFV) decay processes h→μτ and
τ→μγ induced by Higgs-μ-τ vertex. For
τ→μγ, its branching ratio is also related to the
httˉ, hτ+τ− and hW+W− vertices. We categorized the BSM
into two scenarios for the Higgs coupling strengths near or away from SM. For
the latter scenario, we took the spontaneously broken two Higgs doublet model
(Lee model) as an example. We considered the constraints by recent data from
LHC and B factories, and found that the measurements gave weak constraints. At
LHC Run II, h→μτ will be confirmed or set stricter limit on
its branching ratio. Accordingly,
Br(τ→μγ)≲O(10−10−10−8)
for general chosen parameters. For the positive case,
τ→μγ can be discovered with O(1010)τ
pair samples at SuperB factory, Super Ï„-charm factory and new Z-factory.
The future measurements for Br(h→μτ) and
Br(τ→μγ) will be used to distinguish these two
scenarios or set strict constraints on the correlations among different Higgs
couplings, please see Table II in the text for details.Comment: 18 pages, 10 figures, 2 table; more references added; more
discussions about cancellation in the amplitude added accoeding to the
referee's suggestion