Constrained MSSM favoring new territories: The impact of new LHC limits and a 125 GeV Higgs boson

We present an updated and extended global analysis of the constrained MSSM (CMSSM) taking into account new limits on supersymmetry from $\sim 5/\mathrm{fb}$ data sets at the LHC. In particular, in the case of the razor limit obtained by the CMS Collaboration we simulate detector efficiency for the experimental analysis and derive an approximate but accurate likelihood function. We discuss the impact on the global fit of a possible Higgs boson with mass near 125 GeV, as implied by recent data, and of a new improved limit on $\mathrm{BR}({\mathrm{B}}_{\mathrm{s}}\to {\mu }^{+}{\mu }^{-})$. We identify high posterior probability regions of the CMSSM parameters as the stau-coannihilation and the $A$-funnel region, with the importance of the latter now being much larger due to the combined effect of the above three LHC results and of dark matter relic density. We also find that the focus point region is now disfavored. Ensuing implications for superpartner masses favor even larger values than before, and even lower ranges for dark matter spin-independent cross section, ${\sigma }_p^{\mathrm{SI}}\lesssim {10}^{-9}\mathrm{pb}$. We also find that relatively minor variations in applying experimental constraints can induce a large shift in the location of the best-fit point. This puts into question the robustness of applying the usual ${\chi }^2$ approach to the CMSSM. We discuss the goodness-of-fit and find that, while it is difficult to calculate a $p$-value, the $(g-2{)}_{\mu }$ constraint makes, nevertheless, the overall fit of the CMSSM poor. We consider a scan without this constraint, and we allow $\mu$ to be either positive or negative. We find that the global fit improves enormously for both signs of $\mu$, with a slight preference for $\mu <0$ caused by a better fit to $\mathrm{BR}(\mathrm{b}\to s\gamma )$ and $\mathrm{BR}({\mathrm{B}}_{\mathrm{s}}\to {\mu }^{+}{\mu }^{-})$.

Figure 1

(a) Our approximation of the CMS razor $4.4/\mathrm{fb}$ likelihood map as described in the text. $\tan \beta$ and $A_0$ are fixed to the values in the legend. The thick solid line shows the 95.0% CL ($2\sigma$) bound. It approximates the CMS 95% CL exclusion contour, shown by the dashed black line. The thin solid line and the thin dashed line show our calculations of the 68.3% CL ($1\sigma$) and 99.73% CL ($3\sigma$) exclusion bound, respectively. The dotted gray line shows the ATLAS 95% CL exclusion bound. (b) Our calculation of the CMS razor 95% CL exclusion line for $\mu >0$ (red) and $\mu <0$ (blue).

Figure 2

Marginalized posterior pdf in (a) the $(m_0,m_{1/2})$ plane and (b) the $(A_0,\tan \beta )$ plane of the CMSSM, constrained by the experiments listed in Table 3. The solid black line shows the CMS razor 95% CL exclusion bound.

Figure 3

One-dimensional marginalized posterior pdf for the mass of (a) the lightest stop, (b) the ${\tilde{u}}_L$ squark, (c) the gluino, and (d) the lightest neutralino in the CMSSM constrained by the experiments listed in Table 3.

Figure 4

One-dimensional marginalized posterior pdf for the supersymmetric spectrum constrained by the experiments listed in Table 3.

Figure 5

Marginalized posterior pdf in the $(A_0,m_h)$ plane, in the CMSSM constrained by the experiments listed in Table 3. (b) Marginalized posterior pdf in the $(m_A,\tan \beta )$ plane for the same constraints.

Figure 6

(a) Marginalized posterior pdf of the experimental observables $\delta (g-2{)}_{\mu }^{\mathrm{susy}}$ versus $\mathrm{BR}(\overline{\mathrm{B}}\to {\mathrm{X}}_{\mathrm{s}}\gamma )$ in the CMSSM constrained by the experiments listed in Table 3. (b) Marginalized posterior pdf of the experimental observables $\delta (g-2{)}_{\mu }^{\mathrm{susy}}$ versus $\mathrm{BR}(\overline{\mathrm{B}}\to {\mathrm{X}}_{\mathrm{s}}\gamma )$ under the same constraints.

Figure 7

(a) Marginalized 1D posterior pdf of $m_h$ in the CMSSM constrained by the experiments listed in Table 3. (b) Scatter plot showing the distribution of the total ${\chi }^2$ of the points in our chain versus the Higgs mass.

Figure 8

(a) Scatter plot showing the value of $m_h$ in the $(m_0,m_{1/2})$ plane of the CMSSM. (b) Marginalized posterior pdf in the parameters $X_t$ versus $M_{\mathrm{SUSY}}$, relevant for the loop corrections to the Higgs mass.

Figure 9

(a) Marginalized posterior pdf in the $(m_0,m_{1/2})$ plane for the constraints listed in Table 3 except $(g-2{)}_{\mu }$, for $\mu >0$. (b) Marginalized posterior pdf in the $(m_0,m_{1/2})$ plane for the same constraints as in (a) and $\mu <0$. (c) Marginalized posterior pdf in the $(A_0,\tan \beta )$ plane for the same constraints as in (a). (d) Marginalized posterior pdf in the $(A_0,\tan \beta )$ plane for the same constraints as in (a) and $\mu <0$.

Figure 10

Marginalized posterior pdf in the $(m_A,\tan \beta )$ plane, in the CMSSM constrained by all the experiments listed in Table 3 except $(g-2{)}_{\mu }$. (a) $\mu >0$, (b) $\mu <0$.

Figure 11

Marginalized posterior pdf of the experimental observables $\mathrm{BR}(\overline{\mathrm{B}}\to {\mathrm{X}}_{\mathrm{s}}\gamma )$ versus $\mathrm{BR}({\mathrm{B}}_{\mathrm{s}}\to {\mu }^{+}{\mu }^{-})$ in the CMSSM constrained by all the experiments listed in Table 3 except $(g-2{)}_{\mu }$. (a) $\mu >0$, (b) $\mu <0$.

Figure 12

(a) Marginalized 1D posterior pdf of $m_h$ for $\mu <0$, constrained by the experiments listed in Table 3 except $(g-2{)}_{\mu }$. (b) Scatter plot distribution of the Higgs mass in the $(m_0,m_{1/2})$ plane without the $(g-2{)}_{\mu }$ constraint, $\mu <0$.

Figure 13

1D marginalized posterior pdf for the supersymmetric spectrum constrained by the experiments listed in Table 3 except $(g-2{)}_{\mu }$. (a) $\mu >0$. (b) $\mu <0$.

Figure 14

Marginalized posterior pdf in (a) the $(m_0,m_{1/2})$ plane and (b) the $(A_0,\tan \beta )$ plane of the CMSSM for $\mu >0$ and $\mu <0$ combined, constrained by the experiments listed in Table 3 except $(g-2{)}_{\mu }$. The dashed black line shows the CMS razor 95% CL exclusion bound.

Figure 15

Marginalized posterior pdf on the $(m_{\mathcal{X}},{\sigma }_p^{\mathrm{SI}})$ plane in the CMSSM constrained by the experiments listed in Table 3, for the case (a) with $(g-2{)}_{\mu }$ and positive $\mu$, and (b) without $(g-2{)}_{\mu }$ and with a combination of the $\mu >0$ and $\mu <0$.

Figure 16

A bar chart showing the breakdown of the main contributions to the ${\chi }^2$ of the best-fit points of our four different likelihood scans.

Figure 17

(a) Scatter plot distribution of the total ${\chi }^2$ versus $m_0$ for the points along two narrow strips of the $(m_0,m_{1/2})$ plane parametrized by (in blue) $m_{1/2}=1.15m_0+485\mathrm{Gev}$ and (in red) $m_{1/2}=0.38m_0+562\mathrm{GeV}$, with $\mu >0$, $(g-2{)}_{\mu }$. (b) $\mu >0$, no $(g-2{)}_{\mu }$ and $m_h=125\mathrm{GeV}$. $m_0$, $m_{1/2}$ parametrized by $m_{1/2}=0.34m_0+697\mathrm{GeV}$.