SMEFT analysis of charged lepton flavor violating $B$-meson decays

Charged lepton flavor violation (cLFV) processes, potentially important for various beyond the Standard Model physics scenarios are analyzed in the Standard Model effective field theory framework. We consider the most relevant two-quark–two-lepton $(2q2\ell )$ operators for the leptonic and semileptonic LFV $B$-decay (LFVBD) processes $B_s\to {\mu }^{+}{e}^{-},B^{+}\to K^{+}{\mu }^{+}{e}^{-},B^0\to K^{*0}{\mu }^{+}{e}^{-}$, and $B_s\to \varphi {\mu }^{-}{e}^{+}$. We analyze the interplay among the Wilson coefficients responsible for these LFVBDs and other cLFV processes, like $\mathrm{CR}(\mu \to e)$, ${\ell }_i\to {\ell }_j\gamma$, ${\ell }_i\to {\ell }_j{\ell }_k{\ell }_m$, and $Z\to {\ell }_i{\ell }_j$, to find the maximal possible LFV effects in $B$-meson decays. We probe the scale of new physics in relation to the constraints imposed by both classes of the LFV decays while considering both the present bounds and future expectations. In view of proposed experiments at LHCb-II and Belle II to study charged LFV processes, we have also provided the upper limits on the indirect constraints on such LFVBDs. For the processes where the $B$ meson is decaying to ${\mu }^{\pm }$ and $e^{\mp }$, we show that new physics can be constrained by an enhancement of 2–4 orders of magnitude on the current sensitivities of the branching ratios of $B^{+}\to K^{+}{\mu }^{+}{e}^{-},B^0\to K^{*0}{\mu }^{+}{e}^{-}$, and $B_s\to \varphi {\mu }^{\pm }{e}^{\mp }$.

Figure 1

Feynman diagrams for $B^{+}\to K^{+}{\ell }^{+}{\ell }^{\prime -}$. Replacing $u$ quark by $d$ quark leads to similar diagrams for $B^0\to K^{*0}{\ell }^{+}{\ell }^{\prime -}$.

Figure 2

Display of values of $\mathrm{\Lambda }$ for (a) $C_{\ell q}^{(1)}$, (b) $C_{\ell q}^{(3)}$, (c) $C_{qe}$ (in the top row) and (d) and (e) $C_{\ell edq}$ (in the bottom row), for $\mu -e$, that are consistent with the present and future experimental bounds of various LFV decays when only one single (perturbative) WC is fixed at unity. Blue and green bars refer to current and possible future bounds of LFV processes, respectively, as described in Table 1. Darker and lighter red shades, starting above the blue shades, represent the assumed enhancement of the BR sensitivity by 2 and 4 orders of magnitude, respectively.

Figure 3

Similar as Fig. 2 for $e-\tau$ (in the top row) and $\mu -\tau$ (in the bottom row).

Figure 4

With $\mathrm{\Lambda }=1\mathrm{TeV}$, contours for $B^0\to K^{*0}\mu e$ as a function of $[C_{\ell q}^{(1)}{]}_{1223}$ and $[C_{\ell q}^{(3)}{]}_{1223}$. Lighter colors show the currently allowed regions for $\mu \to eee$ (brown) and $\mathrm{CR}(\mu \to e)$ (blue) bounds, whereas darker shades represent futuristic limits. For $\mathrm{CR}(\mu \to e)$, the lighter and darker blue shades correspond to phase I ($\mathrm{BR}\sim {10}^{-15}$) and phase II ($\mathrm{BR}\sim {10}^{-17}$), respectively.

Figure 5

With $\mathrm{\Lambda }=1\mathrm{TeV}$, contours of $B_s\to \mu e$ as a function of $[C_{\ell edq}{]}_{1223}$ and $[C_{\ell q}^{(1)}{]}_{1223}$. Color codes are the same as in Fig. 4.

Figure 6

With $\mathrm{\Lambda }=1\mathrm{TeV}$, contours of $B^0\to K^{0*}\mu e$ as a function of $[C_{\varphi \ell }^{(1)}{]}_{12}$ and $[C_{\ell q}^{(1)}{]}_{1223}$ (top) and $[C_{\varphi e}{]}_{12}$ and $[C_{qe}{]}_{2312}$ (bottom). Color codes are the same as in Fig. 4.