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 parametrized 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 purely real or purely 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 $\mathrm{Br}(l_B\to l_A{l}_C{\overline{l}}_C)$ 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 coefficients are purely real, for the $l_B\to l_A{l}_C{\overline{l}}_C$ process it is found that $|{\mathbf{e}}_l^{\mu \tau }|<2.87\times {10}^{-12}$ and $|{\mathbf{b}}_l^{\mu \tau }|<4.05\times {10}^{-12}$. These results offer more restrictive bounds than those previously reported in the literature.

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• Feynman diagrams
• Flavor changing neutral currents
• Leptonic, semileptonic & radiative decays
• Particle decays
• Particle interactions
• Phenomenology
• Yukawa coupling
• Lorentz symmetry