Excess observed in CDF $B_s^0\to {\mu }^{+}{\mu }^{-}$ and supersymmetry at the LHC

The recent excess observed by CDF in $B_s^0\to {\mu }^{+}{\mu }^{-}$ is interpreted in terms of a possible supersymmetric origin. An analysis is given of the parameter space of mSUGRA and nonuniversal SUGRA under the combined constraints from LHC-7 with $1.04{\mathrm{fb}}^{-1}$ of integrated luminosity, under the new XENON-100 limits on the neutralino-proton spin-independent cross section and under the CDF $B_s^0\to {\mu }^{+}{\mu }^{-}$ 90% C.L. limit reported to arise from an excess number of dimuon events. It is found that the predicted value of the branching ratio $B_s^0\to {\mu }^{+}{\mu }^{-}$ for mSUGRA parameter points consistent with all constraints contains the following set of next to lightest particles beyond the standard model: chargino, stau, stop or $CP$ odd (even) Higgs. The lower bounds of sparticles, including those from the LHC, XENON and CDF $B_s^0\to {\mu }^{+}{\mu }^{-}$ constraint, are exhibited and the shift in the allowed range of sparticle masses arising solely due to the extra constraint from the CDF result is given. It is pointed out that the two-sided CDF 90% C.L. limit puts upper bounds on sparticle masses. An analysis of possible signatures for early discovery at the LHC is carried out corresponding to the signal region in $B_s^0\to {\mu }^{+}{\mu }^{-}$. Implications of GUT-scale nonuniversalities in the gaugino and Higgs sectors are discussed.

Figure 1

Example of a diagram giving rise to supersymmetric contributions to the process $B_s^0\to {\mu }^{+}{\mu }^{-}$ producing a scattering amplitude proportional to ${tan}^3\beta$.

Figure 2

(color online) The mSUGRA parameter space in the $m_0$ and $m_{1/2}$ plane allowing for $A_0/m_0$ in the range $(-10,10)$ and $\tan \beta$ in the range $(1,60)$ in the initial scan. Left panels: The grey area is the region which satisfies all the previous experimental constraints prior to the new results from LHC-7, XENON-100 and the CDF $\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})$ result. Specifically it has only the $\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})<4.3\times {10}^{-8}$. The red curve is the 95% C.L. ATLAS exclusion curve based on the 0 lepton search over $1.04{\mathrm{fb}}^{-1}$ of integrated luminosity. In maroon, we show the parameter points excluded by the new XENON-100 results. Finally, we highlight in lime green the unconstrained mSUGRA parameter points within the 90% C.L. CDF signal region as given in Eq. (3), i.e., $4.6\times {10}^{-9}<\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})<3.9\times {10}^{-8}$ and these parameter points correspond to values of $\tan \beta \in (28,58)$ and $A_0\in (-3.0,3.6)m_0$. Relic density consistent with WMAP, i.e., $0.0896<{\Omega }_{\chi }{h}^2<0.1344$ is satisfied over the entire dotted region exhibited in the figure above. Right panels: similar to the left panel, but all parameter points displayed here are consistent with the combined CMS and LHCb one-sided limit; parameter points that are inconsistent with this $\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})$ constraint are not shown in the right panel. The upper (lower) panels consider the ATLAS(CMS) limit.

Figure 3

(color online) An exhibition of the spin-independent neutralino-proton cross section against the neutralino mass. All parameter points shown satisfy the general constraints discussed first in Sec. 2 (see Fig. 2). Left panel: Parameter points in maroon are excluded by the XENON-100 limit. Parameter points in red are excluded by the ATLAS LHC-7 $1.04{\mathrm{fb}}^{-1}$ 0 lepton search. In grey, we have the parameter points satisfying both the LHC-7 and XENON-100, but outside the two-sided 90% C.L. CDF $\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})$ limit. Finally, in lime green we highlight the mSUGRA parameter points passing all constraints and are within the new two-sided bound on $\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})$ i.e. the signal region in the CDF data. Right panel: similar to the left panel, but all parameter points displayed here are consistent with the combined CMS and LHCb one-sided limit; parameter points that are inconsistent with this $\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})$ constraint are not shown in the right panel.

Figure 4

An exhibition of the allowed parameter space of mSUGRA satisfying all constraints including LHC-7, XENON-100 producing a $\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})$ that can lie within the CDF signal region. The parameter points here are labeled by the NLP. The left panel shows parameter points with chargino and $CP$ even or odd Higgs as NLP. Here the ATLAS limit has been applied, as it is more stringent for this case. The right panel shows parameter points with stau or stop as the NLP. The stop NLP parameter points is depleted by the CDF result but can be seen in the far right region of the right panel. We employ the CMS limit here, as it is more severe for low values of $m_0$, where one finds the ${\tilde{\tau }}_1$ as the NLP.

Figure 5

Signature analysis of Benchmark 1 consistent with all constraints including constraints from LHC-7, XENON-100, and $\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})$. A distribution of the effective mass, $M_{\mathrm{eff}}(4,0)$, in 45 GeV bins for $5{\mathrm{fb}}^{-1}$ of integrated luminosity at LHC with $\sqrt{s}=7\mathrm{TeV}$ using Signal 1 described in the text. Exhibited is the signal plus SM background compared to the SM background. The dark region is the SM background and the white region is the sum of the background plus signal.

Figure 6

Exhibited here are cases of SUGRA with nonuniversal boundary conditions on the gaugino sector (left) and the Higgs sector (right) with initial scan allowing the $A_0/m_0$ range $(-10,10)$ and $\tan \beta$ range $(1,60)$. In each case, the parameter points presented satisfy limits from LEP, WMAP, FCNC data, and XENON-100, as well as the new CDF 90% C.L. $\mathcal{B}r(B_s^0\to {\mu }^{+}{\mu }^{-})$ two-sided limit. We readily see that the introduction of nonuniversalities in the gaugino sector presents parameter points with new NLP cases from mSUGRA, as we see parameter points with $\tilde{g}$ and ${\tilde{e}}_R$ NLPs. Note that in both panels, we simply provide the mSUGRA exclusion from the CMS and ATLAS SUSY searches as a reference—this constraint has not been considered for the CDF signal region of the nonuniversal SUGRA models.