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

Mar 25, 2023 332 likes •562 views

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 fr Experimentelle Kernphysik KIT Universitt des Landes

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KIT – Universität des Landes Baden-Württemberg und nationales Forschungszentrum in der Helmholtz-Gemeinschaft

Institut für Experimentelle Kernphysik

www.kit.edu

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
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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

allowed at 95% CL allowed at 95% CL

Problem: different groups get different excluded regions χ2 -based method

MCMC sampling Genetic Algorithms Multinest

Possible reasons: by strong correlations some regions may be missed different error treatments

Outline

Trotta et al. arXiv: 0809.3792v2 Buchmueller et al. arXiv: 0907.5568v1 Feroz et al. arXiv: 0807.4512 Akrami et al. arXiv: 0910.3950

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

allowed at 95% CL allowed at 95% CL LHC excluded

Problem: different groups get different excluded regions χ2 -based method

MCMC sampling Genetic Algorithms Multinest

Possible reasons: by strong correlations some regions may be missed different error treatments

Outline

Trotta et al. arXiv: 0809.3792v2 Buchmueller et al. arXiv: 0907.5568v1 Feroz et al. arXiv: 0807.4512 Akrami et al. arXiv: 0910.3950

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Start with Relic Density Constraint

2 / 1

2 m m mA ∝ ∝ ⇒

χ 4 2

tan

A

m β σν ∝

Problem: for excluded first diagram too small. Last diagram also small → can get correct relic density by mA s-channel annihilation

q

m~

mA can be tuned with tanβ for any m1/2 → tanβ ≈ 50 (see next slide)

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

tanβ ≈ 50

Co-annihilation

Relic Density Constraint – Dependence on tanβ

2 2 2 1 2

m m mA + =

arXiv:1008.2150

(Tree Level)

b

h ∝

( ) ( )

( )

2 2 1 2 2 2 2 2 1 2 2 2 1 2 3 2 2 2 2 1 2 1 2 1

2 8 . . ,

2

− +

+ − ′ + + + − + = H H g H H g g c h H H m H m H m H H Vtree

t

h ∝

running < 0 → if ht and hb similar → small mA for tanβ= mt/mb ≈ 50 Fit of Ωh2 determines mA and tanβ m1 running m2 running

mA∝m1/2

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

tanβ ≈ 50

(CMS PAS HIG-11-009) Atlas similar

For tanβ ≈ 50 mA > 440 GeV

What about Higgs mA limit?

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

CMSSM – electroweak and other Constraints

  • Higgs Mass mh

mh > 114.4 GeV

  • Myon g-2
  • b→sγ

BRexp(b→sγ) = (3.55 ± 0.24)·10-4

  • Bs→μμ

BRexp(Bs→μμ) < 1.1·10-8

  • B→τν

BRexp(B→τν) = (1.68 ± 0.31)·10-4

  • Finding consistent points by minimizing a χ2-function
  • Minimization by Minuit

Problem: 3 of 4 free CMSSM parameters are HIGHLY correlated

( )

10 exp

10 4 . 12 2 . 30

−

⋅ ± = − = ∆

theo

a a a

µ µ µ

2 exp exp mod 2

        − = σ χ χ χ

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Examples for high correlation

χ2 for Bs → μμ and Ωh2 co-annihilation region

mA exchange

focus point region Origin of correlation: Both strongly dependent on tanβ Bs → μμ Ωh2

For given m0 only very specific values of tanβ For given tanβ only very specific values of A0

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Origin of correlation

Upper Limit for Bs → μμ

(LHCb, CMS)

  • exp. Value Ωh2

Upper limit for tanβ for upper limit on Bs → μμ Best tanβ for Ωh2 A0=0

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Origin of correlation

Upper Limit for Bs → μμ

  • exp. Value Ωh2

A0=1580 GeV Best tanβ for Bs → μμ and Ωh2 simultaneously Common tanβ can

  • nly be found for

specific A0 value

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Reason for strong A0 dependence of Bs → μμ

Becomes small, if can be achieved by adjusting At, till mixing term ~ (At – μ/tanβ) becomes small. Important only for light SUSY masses (see blue region)

arXiv:hep-ph/0203069v2

2 1

~ ~ t t ≈

Stop mass difference

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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 σtheo ~ σexp (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.

2 exp 2 2

σ σ σ + =

+ theo exp

~ σ σ σ +

+ theo

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

95% CL (quad. Add.) 95% CL (lin. Add.) mainly important for g-2, where theory and exp. 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 → not necessarily Gaussian error distribution

allowed

Difference between linear and quadratic error addition

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

g-2 + b→sγ all constraints mh

95% CL exclusion from cosmology/EW

Allowed parameter space (95% CL contour) in the m0-m1/2 plane including all constraints

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

95% C.L. (∆χ 2=5.99) exclusion contours allowed

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Cosmo/EW

95% C.L. (∆χ 2=5.99) exclusion contours allowed

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Cosmo/EW LHC direct Searches

(CMS-SUS-11-003) (Atlas similar)

95% C.L. (∆χ 2=5.99) exclusion contours allowed

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Cosmo/EW LHC direct Searches

(CMS-SUS-11-003) (Atlas similar)

LHC Higgs combined with cosmology (p. 6)

95% C.L. (∆χ 2=5.99) exclusion contours allowed

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Conny Beskidt, IEKP Susy2011, FNAL, Aug. 2011

Including Direct Dark Matter Search

Problem: χN 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!

; 02 . ; 026 . ; 02 . = = =

p s p d p u

f f f ; 02 . ; 036 . ; 014 . = = =

p s p d n u

f f f ; 26 . ; 033 . ; 023 . = = =

p s p d p u

f f f ; 26 . ; 042 . ; 018 . = = =

p s p d n u

f f f

minimum maximum

arXiv:0806.4744v3 arXiv:1006.4811v2 arXiv:0803.2360v2 preliminary m a x i m u m minimum Red=95% C.L. excluded by combined LHC/COSMO/EW

allowed

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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 tanβ (≈50) outside co- annihilation regions Tension at large tanβ from Bs→µµ can be removed by large A0 No sign for SUSY yet, but lots of parameter space still allowed

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Effect of LHC limit on allowed region

If added to χ2 → not much changed (in contrast to case when we would have added errors quad. → large shifts in allowed region by adding LHC to SHALLOW χ2

(since minimum χ2 is increasing)

arXiv:1106.2529