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

Abstract

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 $\mathrm{Br}(l_B\to \gamma l_A)$ and $\mathrm{Br}(l_B\to l_A{l}_C{\bar{l}}_C)$ are estimated. Thus, the $l_B\to \gamma l_A$ decay provides the following upper bounds: $|{\mathbf{e}}_l^{\mu \tau }|<1.51\times 10^{-11}$ , $|{\mathbf{e}}_l^{e\tau }|<1.34\times 10^{-11}$, $|{\mathbf{e}}_l^{e\mu }|<3.65\times 10^{-18}$, $|{\mathbf{b}}_l^{\mu \tau }|<1.95\times 10^{-11}$, $|{\mathbf{b}}_l^{e\tau }|<1.73\times 10^{-11}$, $|{\mathbf{b}}_l^{e\mu }|<4.71\times 10^{-18}$. 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 $|{\mathbf{e}}_l^{\mu \tau }|<3.05\times 10^{-12}$ and $|{\mathbf{b}}_l^{\mu \tau }|<4.31\times 10^{-12}$. These results offer more restrictive bounds than those previously reported in the literature.

Comments: 18 pages, 8 figures