Muon conversion to an electron in nuclei in the $B\text{−}L$ symmetric SSM

In a few years, the COMET experiment at J-PARC and the Mu2e experiment at Fermilab will probe the $\mu -e$ conversion rate in the vicinity of $\mathcal{O}({10}^{-17})$ for an Al target with high experimental sensitivity. Within the framework of the minimal supersymmetric extension of the Standard Model with local $B\text{−}L$ gauge symmetry (B-LSSM), we analyze the lepton flavor violating (LFV) process of $\mu -e$ conversion in nuclei. Considering the constraint of the experimental upper limit of the LFV rare decay $\mu \to e\gamma$, the $\mu -e$ conversion rates in nuclei within the B-LSSM can achieve $\mathcal{O}({10}^{-12})$, which is 5 orders of magnitude larger than the future experimental sensitivity at the Mu2e and COMET experiments and may be detected in the near future.

Figure 1

Penguin-type diagrams for the $\mu -e$ conversion processes at the quark level, where the contributions come from neutral fermion ${\chi }_{\eta }^0$ and charged scalar $S_{m,n}^c$ loops.

Figure 2

Box-type diagrams for the $\mu -e$ conversion processes at the quark level, (a) and (b) represent the contributions from neutral fermion ${\chi }_{\eta ,\sigma }^0$, charged scalar $S_m^c$, and squark ${\tilde{q}}_I$ ($q=u,d$ and ${\tilde{u}}_I=U_I^{+}$, ${\tilde{d}}_I=D_I^{-}$) loops.

Figure 3

(a) $\mathrm{CR}(\mu \to e:\mathrm{Ti})$, (b) $\mathrm{CR}(\mu \to e:\mathrm{Au})$, and (c) $\mathrm{CR}(\mu \to e:\mathrm{Al})$ versus the slepton flavor mixing parameter ${\delta }_{12}^{LL}$, where the dashed lines in panels (a) and (b) stand for the upper limits on $\mathrm{CR}(\mu \to e:\mathrm{Ti})$ and $\mathrm{CR}(\mu \to e:\mathrm{Au})$, respectively, and the dot-dashed line in panels (a) and (c) represents the sensitivity of future experiments on $\mathrm{CR}(\mu \to e:\mathrm{Ti})$ and $\mathrm{CR}(\mu \to e:\mathrm{Al})$, respectively. (d) $\mathrm{Br}(\mu \to e\gamma )$ versus slepton mixing parameter ${\delta }_{12}^{LL}$, where the dashed line denotes the present limit of $\mathrm{Br}(\mu \to e\gamma )$ at 90% C.L. as shown in Eq. (1). Here, the red solid line is ruled out by the present limit of $\mathrm{Br}(\mu \to e\gamma )$, and the black solid line is consistent with the present limit of $\mathrm{Br}(\mu \to e\gamma )$.

Figure 4

(a) $\mathrm{CR}(\mu \to e:\mathrm{Ti})$, (b) $\mathrm{CR}(\mu \to e:\mathrm{Au})$, (c) $\mathrm{CR}(\mu \to e:\mathrm{Al})$, and (d) $\mathrm{Br}(\mu \to e\gamma )$ versus the slepton flavor mixing parameter ${\delta }_{12}^{RR}$.

Figure 5

(a) $\mathrm{CR}(\mu \to e:\mathrm{Ti})$, (b) $\mathrm{CR}(\mu \to e:\mathrm{Au})$, (c) $\mathrm{CR}(\mu \to e:\mathrm{Al})$, and (d) $\mathrm{Br}(\mu \to e\gamma )$ versus the slepton flavor mixing parameter ${\delta }_{12}^{LR}$.

Figure 6

(a) $\mathrm{CR}(\mu \to e:\mathrm{Ti})$, (b) $\mathrm{CR}(\mu \to e:\mathrm{Au})$, and (c) $\mathrm{CR}(\mu \to e:\mathrm{Al})$ versus parameters $M_E$, where the dashed lines in panels (a) and (b) stand for the upper limits on $\mathrm{CR}(\mu \to e:\mathrm{Ti})$ and $\mathrm{CR}(\mu \to e:\mathrm{Au})$, respectively, and the dot-dashed lines in panels (a) and (c) represent the sensitivity of future experiments on $\mathrm{CR}(\mu \to e:\mathrm{Ti})$ and $\mathrm{CR}(\mu \to e:\mathrm{Al})$, respectively. (d) $\mathrm{Br}(\mu \to e\gamma )$ versus parameters $M_E$, where the dashed line denotes the present limit of $\mathrm{Br}(\mu \to e\gamma )$ at 90% C.L. as shown in Eq. (1). Here, the red solid line is ruled out by the present limit of $\mathrm{Br}(\mu \to e\gamma )$, and the black solid line is consistent with the present limit of $\mathrm{Br}(\mu \to e\gamma )$.

Figure 7

(a) $\mathrm{CR}(\mu \to e:\mathrm{Ti})$, (b) $\mathrm{CR}(\mu \to e:\mathrm{Au})$, (c) $\mathrm{CR}(\mu \to e:\mathrm{Al})$, and (d) $\mathrm{Br}(\mu \to e\gamma )$ versus parameters $\tan {\beta }^{\prime }$.

Figure 8

(a) $\mathrm{CR}(\mu \to e:\mathrm{Ti})$, (b) $\mathrm{CR}(\mu \to e:\mathrm{Au})$, (c) $\mathrm{CR}(\mu \to e:\mathrm{Al})$, and (d) $\mathrm{Br}(\mu \to e\gamma )$ versus parameters $g_{YB}$.

Figure 9

(a) $\mathrm{CR}(\mu \to e:\mathrm{Ti})$, (b) $\mathrm{CR}(\mu \to e:\mathrm{Au})$, (c) $\mathrm{CR}(\mu \to e:\mathrm{Al})$, and (d) $\mathrm{Br}(\mu \to e\gamma )$ versus ${\delta }_{12}^{LL}$ after randomly scanning Table 2, where the dashed and dot-dashed lines denote the present limits and future sensitivities respectively. Here, the red triangles are ruled out by the present limit of $\mathrm{Br}(\mu \to e\gamma )$, and the black dots are consistent with the present limit of $\mathrm{Br}(\mu \to e\gamma )$.

Figure 10

(a) $\mathrm{CR}(\mu \to e:\mathrm{Ti})$, (b) $\mathrm{CR}(\mu \to e:\mathrm{Au})$, (c) $\mathrm{CR}(\mu \to e:\mathrm{Al})$, and (d) $\mathrm{Br}(\mu \to e\gamma )$ versus ${\delta }_{12}^{RR}$ after randomly scanning Table 2.

Figure 11

(a) $\mathrm{CR}(\mu \to e:\mathrm{Ti})$, (b) $\mathrm{CR}(\mu \to e:\mathrm{Au})$, (c) $\mathrm{CR}(\mu \to e:\mathrm{Al})$, and (d) $\mathrm{Br}(\mu \to e\gamma )$ versus ${\delta }_{12}^{LR}$ after randomly scanning Table 2.