Implications of Lorentz violation on Higgs-mediated lepton flavor violation

The lepton flavor violating decay of the Higgs boson $H\to l_A{l}_B$ is studied within two qualitatively different extensions of the Yukawa sector: one renormalizable and the other nonrenormalizable; both incorporating Lorentz violation in a model-independent fashion. These extensions are characterized by Yukawa-like matrices, the former by a constant Lorentz 2-tensor $Y^{AB}{\mu \nu}$,whereasthelatterbyaconstantLorentzvector$Y^{AB}\mu$. It is found that the experimental constraints on the decays $l_A\to l_B\gamma$ severely restrict lepton flavor violating Higgs signals in the renormalizable scenario. In this context, it is found that $BR(H\to {\mu }^{\pm }{e}^{\mp })$ and $BR(H\to {\tau }^{\pm }{\mu }^{\mp })$ cannot be larger than ${10}^{-18}$ and ${10}^{-11}$, respectively. In the nonrenormalizable scenario, transitions mediated by the Higgs or the $Z$ gauge boson are induced at tree level, and we find mild restrictions on lepton flavor violation. Using the experimental limits on the three-body decays $l_A\to l_B{\bar{l}}_C{l}_C$ to constraint the vector $Y_{\mu }^{AB}$, it is found that the branching ratio for the decays $H\to \mu^\pm e^\mp$isofabout$4\times 10^{-9}$,moreimportant,abranchingratioof$7\times 10^{-4}$isfoundforthe$\tau^\pm \mu^\mp$ mode. Accordingly, the decay $H\to {\tau }^{\pm }{\mu }^{\mp }$ could be at the reach of future measurements. The lepton flavor violating decays of the $Z$ gauge boson were also studied. In the renormalizable scenario, it was found the undetectable branching ratios $BR(Z\to {\mu }^{\pm }{e}^{\mp })<5.7\times {10}^{-21}$ and $BR(Z\to \tau^\pm \mu^\mp)<2.0\times 10^{-12}$. In the nonrenormalizable scenario, it was found that $BR(Z\to {\mu }^{\pm }{e}^{\mp })<0.67\times {10}^{-12}$ and $BR(Z\to \tau^\pm \mu^\mp)<1.12\times 10^{-7}$. Although the latter branching ratio is relatively large, it still could not be within the range of future measurements.