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 $(Y_{f})_{μν}^{AB}$ tensor, with $μ$ and $ν$ 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 $F_{μν}$, $(Y_{f})_{μν}^{AB}$ 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 $\mathrm{Br}(l_B\rightarrow γl_A)$ and $\mathrm{Br}(l_B\rightarrow l_A l_C \bar{l}_C)$ are estimated. Thus, the $l_B\rightarrow γl_A$ decay provides the following upper bounds: $\lvert \mathbf{e}_l^{μτ} \lvert < 1.51\times 10^{-11}$ , $\lvert \mathbf{e}_l^{eτ} \lvert < 1.34 \times 10^{-11}$, $\lvert \mathbf{e}_l^{eμ} \lvert < 3.65 \times 10^{-18}$, $\lvert \mathbf{b}_l^{μτ} \lvert < 1.95\times 10^{-11}$, $\lvert \mathbf{b}_l^{eτ} \lvert <1.73\times 10^{-11}$, $\lvert \mathbf{b}_l^{eμ} \lvert < 4.71\times 10^{-18}$. Conversely, by assuming that the Lorentz-violating parameters are purely real, for the $l_B\rightarrow l_A l_C \bar{l}_C$ process it is found that $\lvert \mathbf{e}_l^{μτ}\lvert< 3.05 \times 10^{-12}$ and $\lvert \mathbf{b}_l^{μτ}\lvert< 4.31 \times 10^{-12}$. These results offer more restrictive bounds than those previously reported in the literature.

Figures (8)

• Figure 1: Feynman rules derived from the MEY sector. On the left, the two-point $f_B f_A$ vertex function. On the right, the $H f_A f_B$ three vertex.
• Figure 2: First-order LV corrections to the $f_{B}f_{A}\gamma$ vertex.
• Figure 3: Reference frame conformed by the unitary vectors along the real or imaginary parts of the $\mathbf{e}^{AB}_{f}$, $\mathbf{b}^{AB}_{f}$, and $\mathbf{e}^{AB}_{f}\times\mathbf{b}^{AB}_{f}$ vectors. The $\theta_\gamma$ and $\phi_\gamma$ correspond to the polar and azimuthal angles of the three-momentum of the final photon, respectively.
• Figure 4: Allowed regions for $\lvert\mathbf{b}^{AB}_{l}\lvert$, $\lvert\mathbf{e}^{AB}_{l}\lvert$ stem from current experimental bounds for: (a) $\tau\rightarrow\mu\gamma$, (b) $\tau\rightarrow e \gamma$, and (c) $\mu\rightarrow e\gamma$.
• Figure 5: First-order LV corrections to the $f_B \rightarrow f_{A} f_C \bar{f}_C$ decay.