Enhancement of $\mathrm{Br}(B_d\to {\mu }^{+}{\mu }^{-})/\mathrm{Br}(B_s\to {\mu }^{+}{\mu }^{-})$ in supersymmetric unified models

We explain the $2.3\sigma$ deviation in the recent measurements of the neutral $B$ meson decays into muon pairs from the standard model prediction in the framework of supersymmetric grand unified models using antisymmetric coupling as a new source of flavor violation. We show a correlation between the $B_d\to {\mu }^{+}{\mu }^{-}$ decay and the $CP$ phase in the $B_d\to J/\psi K$ decay and that their deviations from the standard model predictions can be explained after satisfying constraints arising from various hadronic and leptonic rare decay processes, $B\text{−}\overline{B}$, $K\text{−}\overline{K}$ oscillation data, and electric dipole moments of electron and neutron. The allowed parameter space is typically represented by pseudoscalar Higgs mass $m_A\le 1\mathrm{TeV}$ and $\tan {\beta }_H(\equiv v_u/v_d)\lesssim 20$ for squark and gluino masses around 2 TeV.

Figure 1

$B_s\to {\mu }^{+}{\mu }^{-}$ and $B_d\to {\mu }^{+}{\mu }^{-}$ induced by the antisymmetric FCNC source are shown. The setup is detailed in the text. The blue points correspond to the case of a randomly generated $a,b,c$ (with phases) using the antisymmetric coupling, and the green points satisfy $K\text{−}\overline{K}$ mixing data ($\mathrm{\Delta }{M}_K$ and ${\epsilon }_K$). The red point shows the SM prediction.

Figure 2

The illustration of the SM and SUSY contribution of the mixing amplitude of $B\text{−}\overline{B}$ mixing in the complex plane. The detail is explained in the text.

Figure 3

We show the correlation between $B_d\to {\mu }^{+}{\mu }^{-}$ and $B_d\text{−}{\overline{B}}_d$ mixing for the choice of SUSY parameters described in the text. The blue plots are for the randomly generated $a,b,c$ in the antisymmetric coupling, and the green points satisfy all the experimental data, such as $K\text{−}\overline{K}$ mixing, $B_s\text{−}{\overline{B}}_s$ mixing, and $b\to d\gamma$, $b\to s\gamma$. The red point shows the SM prediction. The dashed lines show the $2\sigma$ region of the experimental measurement of $\sin 2\beta$.