Implications of Lorentz violation on Higgs-mediated lepton flavor violation

Abstract

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 $Y_{\mu \nu }^{AB}$, whereas the latter by a constant Lorentz vector $Y_{\mu }^{AB}$. 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 $H\to {\mu }^{\pm }{e}^{\mp }$ 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.

Updated to essentially match published version

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• Bounds on Lorentz-violating Yukawa couplings via lepton electromagnetic moments
• Constraining dimension-six nonminimal Lorentz-violating electron-nucleon interactions with EDM physics
• Vacuum polarization in Yang-Mills theories with Lorentz violation
• CPT-Odd effects on the electromagnetic properties of charged leptons in the Standard Model Extension
• Constraining EDM and MDM lepton dimension five interactions in the electroweak sector