Lepton-flavor violating decays induced by Lorentz violation in the Yukawa sector of the Standard Model Extension

Tree-level lepton-flavor-violating decays induced by Lorentz-violating effects within the Yukawa sector of the Standard Model Extension are studied. These new physics effects are parameterized by the $(Y_f{)}_{\mu \nu }^{AB}$ tensor, with $\mu$ and $\nu$ denoting Lorentz indices and $A$, $B$ being indices in the flavor space. Since this tensor is antisymmetric under the interchange of Lorentz indices, in analogy with the electromagnetic tensor $F_{\mu \nu }$, $(Y_f{)}_{\mu \nu }^{AB}$ can be expressed in terms of six components associated with two complex three-vectors denoted by ${\mathbf{e}}_l^{AB}$ and ${\mathbf{b}}_l^{AB}$. On the assumption that these three-vectors are pure real or pure imaginary and mutually orthogonal, constraints on their magnitudes via experimental bounds on lepton-flavor-violating processes $\mathrm{B}\mathrm{r}(l_B\to \gamma l_A)$ and $\mathrm{B}\mathrm{r}(l_B\to l_A{l}_C{\bar{l}}_C)$ are estimated. Thus, the $l_B\to \gamma l_A$ decay provides the following upper bounds: $\mid {\mathbf{e}}_l^{\mu \tau }\mid <1.51\times {10}^{-11}$ , $\mid {\mathbf{e}}_l^{e\tau }\mid <1.34\times {10}^{-11}$, $\mid {\mathbf{e}}_l^{e\mu }\mid <3.65\times {10}^{-18}$, $\mid {\mathbf{b}}_l^{\mu \tau }\mid <1.95\times {10}^{-11}$, $\mid {\mathbf{b}}_l^{e\tau }\mid <1.73\times {10}^{-11}$, $\mid {\mathbf{b}}_l^{e\mu }\mid <4.71\times {10}^{-18}$. Conversely, by assuming that the Lorentz-violating parameters are purely real, for the $l_B\to l_A{l}_C{\bar{l}}_C$ process it is found that $\mid {\mathbf{e}}_l^{\mu \tau }\mid <3.05\times {10}^{-12}$ and $\mid {\mathbf{b}}_l^{\mu \tau }\mid <4.31\times {10}^{-12}$. These results offer more restrictive bounds than those previously reported in the literature.