Higgs boson-μ−τcoupling at high and low energy colliders

Abstract

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 that extra symmetry was imposed. Therefore, FCNC processes are an excellent probe for physics beyond the SM (BSM). In this paper, we study the lepton flavor violated decay processes $h\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\tau}$ and $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ induced by the Higgs boson-$\ensuremath{\mu}\text{\ensuremath{-}}\ensuremath{\tau}$ vertex. For $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$, its branching ratio is also related to the $ht\overline{t}$, $h{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$, and $h{W}^{+}{W}^{\ensuremath{-}}$ vertices. We categorize the BSM into two scenarios for the Higgs boson coupling strengths near or away from the SM. For the latter scenario, we take the spontaneously broken two Higgs doublet model (the Lee model) as an example. We consider the constraints by recent data from the LHC and B factories, and we find that the measurements give weak constraints. At LHC run II, $h\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\tau}$ will be confirmed or will have a stricter limit set on its branching ratio. Accordingly, $\mathrm{Br}(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma})\ensuremath{\lesssim}\mathcal{O}({10}^{\ensuremath{-}10}\ensuremath{-}{10}^{\ensuremath{-}8})$ for general chosen parameters. For the positive case, $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ can be discovered with $\mathcal{O}({10}^{10})$ $\ensuremath{\tau}$ pair samples at the SuperB factory, the Super $\ensuremath{\tau}$-charm factory, and the new Z factory. The future measurements for $\mathrm{Br}(h\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\tau})$ and $\mathrm{Br}(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma})$ will be used to distinguish these two scenarios or set strict constraints on the correlations among different Higgs couplings.