Supersymmetry confronts $B_s\to {\mu }^{\mathbf{+}}{\mu }^{\mathbf{-}}$: Present and future status

The purely leptonic rare decay $B_s\to {\mu }^{+}{\mu }^{-}$ is very sensitive to supersymmetric contributions which are free from the helicity suppression of its Standard Model diagrams. The recent observation of the decay by the LHCb experiment and the first determination of its branching fraction motivate a review of their impact on the viable parameter space of supersymmetry (SUSY). In this paper we discuss the implications of the present and expected future accuracy on $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ for constrained and unconstrained scenarios of the minimal supersymmetric extension of the Standard Model, in relation to the results from direct SUSY searches and the Higgs data at the LHC. While the constraints from $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ can be very important in specific SUSY regions, we show that the current result, and even foreseen future improvements in its accuracy, will leave a major fraction of the SUSY parameter space, compatible with the results of direct searches, unconstrained. We also highlight the complementarity of the $B_s\to {\mu }^{+}{\mu }^{-}$ decay with direct SUSY searches.

Figure 1

Dominant $B_s\to {\mu }^{+}{\mu }^{-}$ diagrams in the SM, two Higgs doublet model and MSSM.

Figure 2

$\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ vs the top quark pole mass. The black (lower) line corresponds to the $CP$-averaged branching ratio, while the red (upper) line shows the untagged value.

Figure 3

Distribution of $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-}{)}_{\mathrm{untag}}$ for CMSSM points. The general shape with entries at values below and above the SM expected value of $3.87\times {10}^{-9}$ persists when restricting to the points compatible with the results of LHC SUSY searches.

Figure 4

Expected uncertainty in the branching fraction of $B_s\to {\mu }^{+}{\mu }^{-}$ vs the integrated luminosity recorded by LHCb (solid lines). The red (upper) line refers to an ultimate systematic uncertainty of 5%, and the green (lower) line shows an ultimate systematic uncertainty of 1%. The dashed lines show the precision of LHC combinations, assuming comparable sensitivity for the LHCb and CMS experiments in the same time period.

Figure 5

Untagged $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ vs the CMSSM parameters $m_0$ (upper left panel), $m_{1/2}$ (upper right panel), $A_0$ (lower left panel), and $\tan \beta$ (lower right panel). The solid line corresponds to the central value of the $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ measurement, and the dashed lines correspond to the $2\sigma$ experimental deviations. The green (lighter) points are those in agreement with the Higgs mass constraint.

Figure 6

Fraction of CMSSM points compatible with the current (left panel) and ultimate (right panel) 95% C.L. constraints on $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ in the $(m_{1/2},m_0)$ parameter plane. The continuous line shows the parameter region excluded by the ATLAS SUSY searches at 8 TeV with $5.8{\mathrm{fb}}^{-1}$ of data (from Ref. 51), and the dotted line shows the reach estimated by CMS for searches at 14 TeV with $300{\mathrm{fb}}^{-1}$ (from Ref. 52).

Figure 7

Fraction of CMSSM points obtained through a 4-parameter flat scan passing the LHC SUSY constraints and in agreement with the present $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ measurement of Eq. (3.3) (continuous line), and with the prospective range of Eq. (3.4) (dotted line), as a function of $\tan \beta$.

Figure 8

Untagged $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ vs the parameters $\mu$ (upper left panel), $M_3$ (upper right panel), $A_t$ (middle left panel), $\tan \beta$ (middle right panel), $M_A$ (lower left panel) and $m_{{\tilde{t}}_1}$ (lower right panel). The solid line corresponds to the central value of the $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ measurement, and the dashed lines correspond to the $2\sigma$ experimental deviations. The green points are those in agreement with the Higgs mass constraint.

Figure 9

Variation of the untagged $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ in the plane $(C_{10},C_{Q_1})$. The dotted vertical lines delimit the range of $C_{10}$ in the CMSSM, and dashed lines delimit the range in the pMSSM.

Figure 10

Constraints from $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ in the $(M_A,\tan \beta )$ and $(M_A,m_{{\tilde{t}}_1})$ parameter planes. The black points corresponds to all the valid pMSSM points and those in grey to the points for which $123<M_h<129\mathrm{GeV}$. The dark green points, in addition, are in agreement with the latest $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ range given in Eq. (3.3), while the light green points are in agreement with the prospective LHCb $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ range given in Eq. (3.4). The red line indicates the region excluded at 95% C.L. by the CMS $A/H\to {\tau }^{+}{\tau }^{-}$ searches (from Ref. 57).

Figure 11

Fraction of pMSSM points passing the LHC SUSY and Higgs mass constraints and in agreement with the latest $\mathrm{BR}(B_s\to {\mu }^{+}{\mu }^{-})$ measurement of Eq. (3.3) (continuous line), and with the prospective range of Eq. (3.4) (dotted line), as a function of $\tan \beta$.