1. KIT – Universität des Landes Baden-Württemberg und nationales Forschungszentrum in der Helmholtz-Gemeinschaft Institut für Experimentelle Kernphysik www.kit.edu Constraints on Supersymmetry using the latest data from cosmology, DM searches and LHC C. Beskidt, W. de Boer, D. Kazakov, F. Ratnikov

2. 2 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Introduction to Supersymmetry (SUSY) Predictions of SM of particle physics in good agreement with experimental results BUT: still good arguments for physics beyond the SM No dark matter candidate, that can give the right amount of DM Quadratic divergences on the Higgs mass Higgs mechanism has to be introduced ad hoc Gravitation cannot be included within QFT etc. → need a theory beyond the SM Supersymmetry,…

3. 3 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Introduction to SUSY SUSY = symmetry between fermions and bosons Minimal supersymmetric SM (MSSM): SM particles + SUSY partners + 2 Higgs Doublets (h,H,A,H ± ) SUSY leads to equal masses of superpartners → broken symmetry Soft Breaking would lead to over 100 free parameters → no prediction possible R Parity +1R Parity -1

4. 4 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Introduction to SUSY – Constrained MSSM Assuming unified SUSY masses and couplings at the GUT (~ 10 16 GeV) scale → 4 free parameters and one free sign m 0 : common spin 0 mass m 1/2 : common spin ½ mass tanβ: ratio between the vev’s of the two Higgs fields A 0 : trilinear coupling sign(μ): sign of higgs mixing parameter Which combination of 4 free parameters are allowed?

5. 5 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Outline Find allowed parameter space in CMSSM using a  2 method based on LHC SUSY searches, Higgs discovery, relic density, flavour constraints, electroweak constraints, direct DM searches Problem 1: Free CMSSM parameters are highly correlated Solution 1: Multi-step fitting approach → highly correlated parameters are fitted first for fixed other CMSSM parameters Problem 2: Higgs of 125 GeV and large  BR hard to accommodate in CMSSM Solution 2: go to NMSSM

6. 6 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Constraints used for the  2 -function Relic Density  h 2 = 0.1131 ± 0.0034 B →  BR exp (B→  ) = (1.68 ± 0.31)·10 -4 Myon g-2Δa  =(30.2 ± 6.3 ± 6.1) ·10 -11 b →s  BR exp (b→s  ) = (3.55 ± 0.24)·10 -4 B s →  BR exp (B s →  ) < 4.5·10 -9 Higgs Mass m h m h > 114.4 GeV LHC direct searches  had < 0.001 – 0.03 pb XENON100   N < 1.8·10 -45 - 6·10 -45 cm 2 Pseudo-scalar Higgs m A m A > 510 GeV for tanβ ~ 50 For more details see CB et al., EPJ C

7. 7 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Combination of all constraints  2 =  2 –  min 2 For each 95% CL exclusion contour  2 = 5.99 Best fit point χ min 2 = 4.3 95% CL → Δχ 2 < 5.99 Contour 1 2 3 4 5 68% CL → Δχ 2 < 2.3 LSP For more details see CB et al., EPJ C or backup slides LHC direct searches B s →  m h > 114.4 GeV m A XENON100

8. 8 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Influence of g-2 Preferred region by g-2 if the errors are added quadratically or linearly g-2 gives a light preference for light SUSY masses but light SUSY masses are already excluded by the LHC direct searches → errors underestimated or additional loop contribution Deviation from SM 2-3  : for heavy m SUSY

9. 9 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 (SM?) - Higgs found at the LHC Both the CMS and ATLAS experiment measured a Higgs within the errors of about 126 GeV What does this mean for the allowed CMSSM parameter space? CMS (CMS-PAS-HIG-12-020)ATLAS (ATLAS-CONF-2012-093) (125.3 ± 0.4 (stat) ± 0.5 (syst)) GeV(126.5 ± 0.6 (stat) ± 0.6 (syst)) GeV

10. 10 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 125 GeV Higgs within the CMSSM A 125 GeV light Higgs is possible within the CMSSM if the SUSY masses are heavy enough and if the trilinear coupling A 0 is negative The allowed parameter space is largely determined by the assigned error → strong dependence on the theoretical error Exp. ~ 2GeV, theo. ~ 3GeV, non-Gaussian → lin. addition → 5GeV best fit points for different errors (   2 =5.99) 95% C.L. contour 125 123 121 119 Higgs mass contours

11. 11 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Summary so far 125 GeV Higgs hard to accomodate in CMSSM (unless one stretches the errors) In addition, couplings have tendency to deviate from SM (see next slides) Heavier Higgs and non-SM couplings easy to accomodate if mixing between Higgs doublet and additionally singlet, as proposed in NMSSM to solve  -problem (Kim, Nilles Phys. Lett. B 138, 150 (1984))

12. 12 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 NMSSM versus MSSM NMSSM (Next to MSSM): Mixing: larger Higgs mass couplings to up and down type fermions can be different new free parameters:couplings,  trilinear couplings A , A mixing parameter  eff = (in addition to m 0, m 1/2, A 0, tan  ) MSSM NMSSM Higgs content 3 CP even 2 CP odd 1 singlet

13. 13 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Fit to SM couplings (scale factors) C F = scale factor for coupling to fermions C V = scale factor for coupling to vector bosons Best fit point: C F ≈ 0.5 C V ≈ 1.0 SM: C F = C V = 1 (CMS-PAS-HIG-12-020) SM Best fit point

14. 14 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Higgs mass MSSM NMSSM: Mixing with singlet Hall, Pinner, Ruderman, arXiv 1112.2703 loop corrections Increases Higgs mass for large

15. 15 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Benchmark points in NMSSM Analyses have been done e.g. Ellwanger, Hugonie (arXiv:1203.5048 using GUT scale parameters), Mühlleitner et al. (arXiv:1201.2671 using low energy values of parameters) Benchmark points fulfill Higgs mass and couplings, but one needs very specific singlet mixing to obtain simultaneously m H =125 GeV, large branching into , small branching into  M0M0 m 1/2 A0A0 AA A tan  eff 600 -1550-275-6252.400.5450.253120 960525-1140-360-5752.290.6000.321122 E.g. Benchmark points from Ellwanger, Hugonie, arXiv:1203.5048 Input at M SUSY Input at M GUT BM I BM II

16. 16 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Typical Higgs masses and couplings 126 Components of H 2 HdHd 0.260.04 HuHu 0.85-0.54 S-0.450.84 BM I II 100121 Components of H 1 HdHd 0.390.50 HuHu 0.340.74 S0.860.45 BM I II Strong mixing with singlet → R  can be enchanced It is possible that 126 GeV is not the lightest Higgs Lightest Higgs H 1 Second lightest Higgs H 2

17. 17 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012  2 including R , M h and  h 2 constraint Allowed region in  -plane for BM I Parameters strongly constrained by M h =125, R  =1.7,  h 2 =0.11 (all other parameters fixed)  2 including R  and M h constraint

18. 18 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012  2 including R , M h and  h 2 constraints. Parameters,  and  eff have been varied, A 0, A  and A fixed  large allowed region within m 0 m 1/2 -plane Allowed region in m 0 m 1/2 -plane ex. by  h 2 excluded by R 

19. 19 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Allowed region in m 0 m 1/2 -plane Even though other constraints have not been included to the previous fit, the result is in good agreement with b  s , B s , B  and g-2 g-2 B s   b  s  B   Similar to CMSSM: Including g-2 to  2  constant offset at large M susy

20. 20 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Summary 125 GeV Higgs within CMSSM only possible for high SUSY masses Allowed CMSSM parameter space depends on total error of the Higgs mass Within NMSSM one can get a 125 GeV Higgs and in addition an enhancement/reduction in R γγ/ττ “naturally” because of large mixing with additional Higgs singlet Other constraints fulfilled like in CMSSM, e.g.  h 2,b →s , B s → , B → , and g-2 → good starting point to do same minimization as in CMSSM → work in progress…

21. 21 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 BACKUP

22. 22 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Details on χ 2 -function Relic Density B →τν Myon g-2 b →sγ B s →μμBR exp (B s →μμ) < 4.5·10 -9 Higgs Mass m h m h > 114.4 GeV LHC direct searches σ had < 0.003 – 0.03 pb DDMSσ χN < 8·10 -45 - 2·10 -44 cm 2 Pseudo-scalar Higgs m A m A > 480 GeV for tanβ ~ 50 Experimental Values Defined in a straight forward way:

23. 23 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Details on χ 2 -function? Relic Density Ωh 2 = 0.1131 ± 0.0034 B →τνBR exp (B→τν) = (1.68 ± 0.31)·10 -4 Myon g-2Δa μ =(30.2 ± 6.3 ± 6.1) ·10 -11 b →sγBR exp (b→sγ) = (3.55 ± 0.24)·10 -4 B s →μμ Higgs Mass m h LHC direct searches σ had < 0.003 – 0.03 pb DDMSσ χN < 8·10 -45 - 2·10 -44 cm 2 Pseudo-scalar Higgs m A m A > 480 GeV for tanβ ~ 50 95% CL only added if X SUSY > X 95% X SUSY = model value of BR(B s →μμ) or m h X 95% can be determined from requirement Δχ 2 =5.99 at 95% CL exclusion limit

24. 24 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Details on χ 2 -function? Relic Density Ωh 2 = 0.1131 ± 0.0034 B →τνBR exp (B→τν) = (1.68 ± 0.31)·10 -4 Myon g-2Δa μ =(30.2 ± 6.3 ± 6.1) ·10 -11 b →sγBR exp (b→sγ) = (3.55 ± 0.24)·10 -4 B s →μμBR exp (B s →μμ) < 4.5·10 -9 Higgs Mass m h m h > 114.4 GeV LHC direct searches DDMS Pseudo-scalar Higgs m A 95% CL exclusion contours Define χ 2 =(X SUSY - X 95% ) 2 /σ 95% 2 X SUSY = model value of m A or hadronic cross section or χN elastic scattering cross section σ 95% can be determined from 1σ band given by experiments X 95% determined from requirement Δχ 2 =5.99 at 95% CL exclusion contour

25. 25 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Typical Sparticle masses and LSP mixing (NMSSM) Components of 0.200.25 -0.16-0.20 0.480.52 -0.70 0.460.37 0.10 BM I II Sparticle masses 13881254 13181397 359463 10011060 528900 108 7778 BM I II

26. 26 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Start with Relic Density Constraint Problem: for excluded first diagram too small. Last diagram also small → can get correct relic density by m A s-channel annihilation m A can be tuned with tanβ for any m 1/2 → tanβ ≈ 50 (see next slide)

27. 27 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 tan   50 Co-annihilation Relic Density Constraint – Dependence on tanβ arXiv:1008.2150 (Tree Level) running < 0 → if h t and h b similar → small m A for tan  = m t /m b  50 Fit of Ωh 2 determines m A and tanβ m 1 running m 2 running m A  m 1/2

28. 28 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 tanβ ≈ 50 (CMS PAS HIG-11-009) Atlas similar For tanβ ≈ 50 m A > 440 GeV What about Higgs m A limit?

29. 29 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Examples for high correlation χ 2 for B s → μμ and Ωh 2 co-annihilation region m A exchange focus point region Origin of correlation: Both strongly dependent on tanβ B s → μμ Ωh 2 For given m 0 only very specific values of tan  For given tan  only very specific values of A 0

30. 30 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Origin of correlation Upper Limit for B s → μμ (LHCb, CMS) exp. Value Ωh 2 Upper limit for tanβ for upper limit on B s → μμ Best tanβ for Ωh 2 A 0 =0

31. 31 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Origin of correlation Upper Limit for B s → μμ exp. Value Ωh 2 A 0 =1580 GeV Best tanβ for B s → μμ and Ωh 2 simultaneously Common tanβ can only be found for specific A 0 value

32. 32 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Reason for strong A 0 dependence of B s → μμ Becomes small, if can be achieved by adjusting A t, till mixing term ~ (A t – μ/tanβ) becomes small. Important only for light SUSY masses (see blue region) arXiv:hep-ph/0203069v2 Stop mass difference

33. 33 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Combination of B s → μμ and Ωh 2 Tension at large tan  from B s   can be removed by large A 0 Tension can’t be removed by varying A 0  because A 0 < 3m 0, A 0 not high enough to get small BR Tension still there although A 0 large enough to get small BR

34. 34 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Why there‘s still a tension for large m 0 ? Small Stau mass contribute to Ωh 2 B s →μμ needs large A 0 for large tanβ Ωh 2 too high for large A 0 m A high → small cross section B s →μμ smaller than SM value, even at large tanβ m 0 =1000 m 1/2 =250 SM value

35. 35 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 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 2 Gaussians Convolution of Gaussian + “flat top Gaussian” (expected if theory errors indicate a range) Adding errors linearly more conservative approach for theory errors.

36. 36 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 SUSY particles can be produced in pp collisions at the LHC Combination of the different cross sections of Direct searches for SUSY particles 95% CL exclusion by CMS + Atlas (Jets+MET) CMS PAS SUS-11- 003 arXiv:1109.6572 Contribution to σ tot =0,1pb Parametrization of with σ eff 2 that Δχ 2 = χ 2 – χ 2 min = 5,99

37. 37 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Direct search for dark matter (DDMS) Assume Neutralino is LSP and therefore perfect WIMP candidate Direct detection of WIMPs through elastic scattering on heavy nuclei Coherent scattering: σ ~ N 2 and effective coupling on proton/neutron f p /f n Effective coupling includes couplings of WIMPs on quarks f q n /f q p 90% CL → Δχ 2 = 4,21 (arXiv:1005.0380)

38. 38 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Including DDMS constraint into χ 2 Uncertainties Local DM density (0,3/1,3 GeV/cm³) Effective coupling (especially s-quark) because of different calculations lattice πNπN conservative

39. 39 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Excluded parameter space by XENON100 Scattering cross section is proportional to the product of gaugino und higgsino component → Increase of the cross section if higgsino component is increasing Higgsino component increases for high values of m 0 → DDMS is sensitive for high m 0 in contrast to the direct searches at the LHC

40. 40 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Comparison to other groups Strong correlation between A 0 and tanβ Buchmueller et al. arXiv: 1110.3568 If one include the exclusion limit of the LHC, the difference between the 95% CL contour of the quadratic and linear addition of the errors vanishes.

41. 41 Conny Beskidt, IEKP GK Workshop, Bad Liebenzell, 10.10.2012 Exclusion because of Ωh 2 for large values of m 1/2 Excluded region for large values of m 1/2 and small m 0 because of the relic density For this combination of m 0 and m 1/2 one needs a high value of tanβ for the correct relic density For such high values of tanβ the Neutralino is not the LSP anymore Χ 2 contribution of Ωh 2 m 0 =500 GeV m 1/2 =1300 GeV LSP

42. Contributors to CF and CV