SUSY Constraints from Accelerators and Cosmology using a Multi-step - PowerPoint PPT Presentation

SUSY Constraints from Accelerators and Cosmology using a Multi-step Fitting Approach (MFA) C. Beskidt , W. de Boer, D. Kazakov, F. Ratnikov, V. Zhukov, E. Ziebarth Institut für Experimentelle Kernphysik KIT – Universität des Landes Baden-Württemberg und www.kit.edu nationales Forschungszentrum in der Helmholtz-Gemeinschaft

Outline Problem: different groups get different excluded regions χ 2 -based method Buchmueller et al. arXiv: 0907.5568v1 allowed MCMC sampling at 95% CL allowed Trotta et al. at 95% CL arXiv: 0809.3792v2 Genetic Algorithms Akrami et al. arXiv: 0910.3950 Multinest Feroz et al. arXiv: 0807.4512 Possible reasons: by strong correlations some regions may be missed different error treatments 2 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Outline Problem: different groups get different excluded regions χ 2 -based method Buchmueller et al. arXiv: 0907.5568v1 allowed MCMC sampling at 95% CL allowed Trotta et al. at 95% CL arXiv: 0809.3792v2 Genetic Algorithms Akrami et al. LHC excluded arXiv: 0910.3950 Multinest Feroz et al. arXiv: 0807.4512 Possible reasons: by strong correlations some regions may be missed different error treatments 3 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Start with Relic Density Constraint m ~ Problem: for excluded first diagram too small. Last diagram also q small → can get correct relic density by m A s-channel annihilation β 2 tan σν ∝ 4 m A ⇒ ∝ ∝ m A 2 m m χ 1 / 2 m A can be tuned with tanβ for any m 1/2 → tanβ ≈ 50 (see next slide) 4 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Relic Density Constraint – Dependence on tanβ ( ) ′ + 2 2 2 g g g ( ) ( ) 2 2 2 2 2 2 + − = + − + + − + 2 2 2 V tree H , H m H m H m H H h . c . H H H H 1 2 1 1 2 3 1 2 1 2 1 2 8 2 2 = + 2 2 2 m A m m (Tree Level) 1 2 ∝ h m 1 running t ∝ h m 2 running b running < 0 → if h t and h b similar → small m A for tan β = m t /m b ≈ 50 Fit of Ωh 2 determines m A and tanβ tan β ≈ 50 m A ∝ m 1/2 Co-annihilation arXiv:1008.2150 5 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

What about Higgs m A limit? tanβ ≈ 50 (CMS PAS HIG-11-009) Atlas similar For tanβ ≈ 50 m A > 440 GeV 6 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

CMSSM – electroweak and other Constraints Higgs Mass m h m h > 114.4 GeV • ( ) ∆ = − = ± ⋅ − exp theo 10 • Myon g-2 a a a 30 . 2 12 . 4 10 µ µ µ • b→sγ BR exp (b→sγ) = (3.55 ± 0.24)·10 -4 B s →μμ BR exp (B s →μμ) < 1.1·10 -8 • • B→τν BR exp (B→τν) = (1.68 ± 0.31)·10 -4 • Finding consistent points by minimizing a χ 2 -function 2   χ − χ   mod exp χ 2 =   σ   exp • Minimization by Minuit Problem: 3 of 4 free CMSSM parameters are HIGHLY correlated 7 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Examples for high correlation For given tan β only very For given m 0 only very specific values of A 0 specific values of tan β focus point region χ 2 for B s → μμ and Ωh 2 m A exchange co-annihilation region Both strongly B s → μμ Origin of correlation: dependent on Ωh 2 tanβ 8 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Origin of correlation exp. Value Ωh 2 Upper Limit for B s → μμ (LHCb, CMS) A 0 =0 Upper limit for tanβ for Best tanβ for Ωh 2 upper limit on B s → μμ 9 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Origin of correlation exp. Value Ωh 2 Upper Limit for B s → μμ A 0 =1580 GeV Common tanβ can only be found for specific A 0 value Best tanβ for B s → μμ and Ωh 2 simultaneously 10 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Reason for strong A 0 dependence of B s → μμ arXiv:hep-ph/0203069v2 ~ ~ t ≈ t Becomes small, if 1 2 can be achieved by adjusting A t , Stop mass difference till mixing term ~ (A t – μ/tanβ) becomes small. Important only for light SUSY masses (see blue region) 11 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

How to treat theoretical errors? • Theoretical errors can be treated as nuisance parameters and integrated over in the probability distribution (=convolution for symm. distr.) • If errors Gaussian, this corresponds to adding the experimental and theoretical errors in quadrature Assume σ theo ~ σ exp (only then important) • Convolution of Gaussian + “flat top Gaussian” Convolution of 2 Gaussians (expected if theory errors indicate a range) σ σ + σ σ = σ + σ 2 2 2 ~ + + theo exp theo exp Adding errors linearly more conservative approach for theory errors. 12 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Difference between linear and quadratic error addition mainly important for g-2, where theory and exp. allowed Errors are similar and deviation from SM 3σ, so very sensitive for exclusion limit Errors for g-2 dominated by QCD LO- and NLO Corrections and light-by-light Contributions 95% CL (quad. Add.) → not necessarily 95% CL (lin. Add.) Gaussian error distribution 13 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

95% CL exclusion from cosmology/EW Allowed parameter space (95% CL contour) in the m 0 -m 1/2 plane including all constraints g-2 + b→sγ m h all constraints 14 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

95% C.L. ( ∆χ 2 =5.99) exclusion contours allowed 15 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

95% C.L. ( ∆χ 2 =5.99) exclusion contours Cosmo/EW allowed 16 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

95% C.L. ( ∆χ 2 =5.99) exclusion contours Cosmo/EW allowed LHC direct Searches (CMS-SUS-11-003) (Atlas similar) 17 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

95% C.L. ( ∆χ 2 =5.99) exclusion contours Cosmo/EW allowed LHC direct Searches (CMS-SUS-11-003) (Atlas similar) LHC Higgs combined with cosmology (p. 6) 18 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Including Direct Dark Matter Search Problem: χ N scattering cross sections depends on form factors Lattice has strange quark in nucleus similar to light quarks ( arXiv:0806.4744v3) To be conservative use this smaller form factor-> excluded region small! arXiv:0803.2360v2 minimum maximum p = p = f 0 . 02 ; f 0 . 023 ; u u preliminary allowed = = p p f 0 . 026 ; f 0 . 033 ; d d p = p = f 0 . 02 ; f 0 . 26 ; s s m u m i x a m = = n n f 0 . 014 ; f 0 . 018 ; u u minimum = = p p f 0 . 036 ; f 0 . 042 ; d d = = p p f 0 . 02 ; f 0 . 26 ; s s arXiv:0806.4744v3 arXiv:1006.4811v2 Red=95% C.L. excluded by combined LHC/COSMO/EW 19 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Conclusion Strong correlations between at least 3 of the 4 CMSSM parameters requires careful fitting strategies The multi-step strategy, which fits highly correlated parameters first, works efficiently The allowed region of CMSSM parameter space depends on the error assumptions → non-Gaussian errors more conservatively treated by linear addition of errors The relic density constraint requires large tan β ( ≈ 50) outside co- annihilation regions Tension at large tan β from B s →µµ can be removed by large A 0 No sign for SUSY yet, but lots of parameter space still allowed 20 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Effect of LHC limit on allowed region If added to χ 2 → not much changed (in contrast to case when we would have added errors quad. → large shifts in allowed region by adding LHC to SHALLOW χ 2 (since minimum χ2 is increasing) arXiv:1106.2529 21 Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011