Supersymmetry in Light of 1/fb of LHC Data

TL;DR

This work updates global frequentist fits of the CMSSM and NUHM1 by incorporating ~1/fb of LHC data, XENON100 direct-detection limits, and B-physics observables. The analyses reveal a shift toward heavier SUSY spectra, with best-fit points at $(m_0, m_{1/2})$ around $(450,780)$ GeV for the CMSSM and $(150,730)$ GeV for the NUHM1, and p-values near $15$–$16\%$ when including $(g-2)_\mu$, rising to ~38% if $(g-2)_\mu$ is omitted. The results remain sensitive to the treatment of BR$(B_s \to \mu^+\mu^-)$, $b\to s\gamma$ uncertainties, and the $\ ilde{g}$ mass prediction, with $m_{\tilde{g}}$ around 1.6 TeV and $\sigma^{\rm SI}_p$ near $10^{-45}$ cm$^2$, dependent on the $\,\Sigma_{\pi N}$ uncertainty. Overall, CMSSM and NUHM1 survive current constraints as viable, albeit increasingly fine-tuned, frameworks, with future LHC data and Higgs measurements poised to further delineate their viability.

Abstract

We update previous frequentist analyses of the CMSSM and NUHM1 parameter spaces to include the public results of searches for supersymmetric signals using ~1 /fb of LHC data recorded by ATLAS and CMS and ~0.3/fb of data recorded by LHCb in addition to electroweak precision and B-physics observables. We also include the constraints imposed by the cosmological dark matter density and the XENON100 search for spin-independent dark matter scattering. The LHC data set includes ATLAS and CMS searches for jets + missing ET events and for the heavier MSSM Higgs bosons, and the upper limits on B_s to mu^+ mu^- from LHCb and CMS. The absences of jets + missing ET signals in the LHC data favour heavier mass spectra than in our previous analyses of the CMSSM and NUHM1, which may be reconciled with (g-2)_mu if tan beta ~ 40, a possibility that is however under pressure from heavy Higgs searches and the upper limits on B_s to mu^+ mu^-. As a result, the p-value for the CMSSM fit is reduced to ~ 15 (38)%, and that for the NUHM1 to ~ 16 (38)%, to be compared with ~ 9 (49)% for the Standard Model limit of the CMSSM for the same set of observables (dropping (g-2)_mu), ignoring the dark matter relic density in both cases. We discuss the sensitivities of the fits to the (g-2)_mu and b to s gamma constraints, contrasting fits with and without the (g-2)_mu constraint, and combining the theoretical and experimental errors for b to s gamma linearly or in quadrature. We present predictions for m_gluino, B_s to mu^+ mu^-, M_h and M_A, and update predictions for spin-independent dark matter scattering, stressing again the importance of taking into account the uncertainty in the pi-nucleon sigma term, Sigma_{pi N}. Finally, we present predictions based on our fits for the likely thresholds for sparticle pair production in e^+e^- collisions in the CMSSM and NUHM1.

Figures (15)

• Figure 1: The $(m_0, m_{1/2})$ planes in the CMSSM (left) and the NUHM1 (right). In each plane, the best-fit point after incorporation of the LHC$_{\rm 1/fb}$ constraints is indicated by a filled green star, and the pre-LHC fit mc4 by an open star. The $\Delta \chi^2= 2.30$ and $5.99$ contours, commonly interpreted as the boundaries of the 68 and 95% CL regions, are indicated in red and blue, respectively, the solid lines including the LHC$_{\rm 1/fb}$ data and the dotted lines showing the pre-LHC fits.
• Figure 2: The $(m_0, m_{1/2})$ planes in the CMSSM (left) and the NUHM1 (right), for the pre-LHC data set (upper) and LHC$_{\rm 1/fb}$ data set (lower). In each plane, different regions are colour-coded according to the $p$-values found in our global fits. We note that in the LHC$_{\rm 1/fb}$ analysis the regions with $p > 0.05$ extend up to $m_{1/2} \sim 2000 \,\, \mathrm{GeV}$ in each case.
• Figure 3: The $(m_0, m_{1/2})$ planes in the CMSSM (left) and the NUHM1 (right). In each plane, different regions are colour-coded according to the values of $p_F$ found by applying the F-test to our global fits. We note that the regions with $p_F > 0.8$ extend up to $m_{1/2} \sim 1500 \,\, \mathrm{GeV}$ in each case.
• Figure 4: The $(m_0, m_{1/2})$ planes in the CMSSM (left) and the NUHM1 (right), with shading displaying the contribution to the global $\chi^2$ function from $(g-2)_\mu$ as calculated using low-energy $e^+ e^-$ data to evaluate the SM contribution. These contributions are evaluated for the parameter sets that minimize $\chi^2$ at each point in the planes.
• Figure 5: The $(m_0, m_{1/2})$ planes in the CMSSM (left) and the NUHM1 (right). Here we show as solid lines the 68% and 95% CL contours obtained by dropping the $(g-2)_\mu$ constraint. The contours obtained applying the $(g-2)_\mu$ constraint as in Fig. \ref{['fig:6895']} are shown here for comparison as dotted lines.