Implications of Lorentz violation on Higgs-mediated lepton flavor violation

The lepton flavor violating decay of the Higgs boson $H\to l_Al_B$ 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 $Y^{AB}_{\mu \nu}$, whereas the latter by a constant Lorentz vector $Y^{AB}_\mu$. 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 $l_A \to l_B \bar{l}_Cl_C$ to constraint the vector $Y^{AB}_\mu$, it is found that the branching ratio for the decays $H\to \mu^\pm e^\mp$ is of about $4\times 10^{-9}$, more important, a branching ratio of $7\times 10^{-4}$ is found for the $\tau^\pm \mu^\mp$ 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.