Global Fits to MSSM Models by Ben Allanach (University of - PowerPoint PPT Presentation

Global Fits to MSSM Models by Ben Allanach (University of Cambridge) Talk outline a • LHC SUSY Searches • SUSY fits to Indirect Data • Effect of Searches Please ask questions while I’m talking a BCA, arXiv:1102.3149 ; BCA, Khoo, Lester, Williams, arXiv:1103.0969 Global Fits to MSSM Models B.C. Allanach – p. 1

Supersymmetric Copies H Global Fits to MSSM Models B.C. Allanach – p. 2

Supersymmetric Copies ˜ H × 2 H × 2 Global Fits to MSSM Models B.C. Allanach – p. 2

Electroweak Breaking Both Higgs get vacuum expectation values: � H 0 � v 1 � H + � 0 � � � � 1 2 → → H − H 0 0 v 2 2 1 and to get M W correct, match with v SM = 246 GeV: v SM tan β = v 2 v 2 v 1 v 1 β 2 t R + h b ¯ L = h t ¯ t L H 0 b L H 0 τ L H 0 1 b R + h τ ¯ 1 τ R ⇒ m t = h t v SM cos β = h b,τ v SM m b,τ √ 2 , √ . sin β 2 Global Fits to MSSM Models B.C. Allanach – p. 3

CMS α T Search CMS: jets and missing energy arXiv:1101.1628 L = 35 pb − 1 . H T = � N jet i =1 | p j i T | > 350 GeV . � | p j i � | p j i (1) ∆ H T ≡ T | − T | . j i ∈ A j i ∈ B One then calculates α T = H T − ∆ H T (2) > 0 . 55 � / 2 H 2 2 T − H T � ( � N jet x ) 2 + ( � N jet i =1 p j i i =1 p j i y ) 2 . where H / T = Global Fits to MSSM Models B.C. Allanach – p. 4

Results Global Fits to MSSM Models B.C. Allanach – p. 5

ATLAS 0-lepton, jets and / p T m eff = � p ( j ) T + p / T , 2 ( p T ( i ) , / � − 2 p T ( i ) · / m ( i ) � p T ( i ) � � � � ( i ) � ( i ) ) ≡ 2 ( i ) � / q T q T q T T ( i ) is the transverse momentum of particle where / q T ( i ) . For each event, it is a lower bound on m ( NLSP ) . � � �� m (1) T , m (2) (1) , p T (2) , / M T 2 ( p T p T ) ≡ min � max q T = / / T p T Global Fits to MSSM Models B.C. Allanach – p. 6

Candidate Event: High E T ( j ) Global Fits to MSSM Models B.C. Allanach – p. 7

MSSM Exclusion: Simplified Model 2000 squark mass [GeV] ATLAS int -1 L = 35 pb , s =7 TeV 0 lepton combined exclusion 0 lepton combined exclusion 1750 Observed 95% CL limit Median expected limit 1500 ± σ Expected limit 1 ~ LEP 2 q FNAL MSUGRA/CMSSM, Run I 1250 D0 MSUGRA/CMSSM, Run II CDF MSUGRA/CMSSM, Run II 1000 σ = 0.1 pb SUSY 750 σ = 1 pb SUSY 500 σ = 10 pb SUSY 250 0 0 250 500 750 1000 1250 1500 1750 2000 ∼ gluino mass [GeV] χ 0 Squark-gluino-neutralino model (massless ) 1 Global Fits to MSSM Models B.C. Allanach – p. 7

SUSY Dark Matter astro-ph/0608407 χ 0 p 1 σ p ′ χ 0 1 Global Fits to MSSM Models B.C. Allanach – p. 8

SUSY Prediction of Ω h 2 • Assume relic in thermal equilibrium with n eq ∝ ( MT ) 3 / 2 exp ( − M/T ) . • Freeze-out with T f ∼ M f / 25 once interaction rate < expansion rate ( t eq critical) • microMEGAs uses calcHEP to automatically calculate relevant Feynman diagrams for some given model Lagrangian: flexible . • darkSUSY , IsaRED has MSSM annihilation channels hard-coded. • Both darkSUSY and micrOMEGAs calculate (in-)direct predictions. Global Fits to MSSM Models B.C. Allanach – p. 9

WMAP+BAO+Ia Fits Global Fits to MSSM Models B.C. Allanach – p. 10

WMAP+BAO+Ia Fits Ω DM h 2 = 0 . 1143 ± 0 . 0034 Power law Λ CDM fit Global Fits to MSSM Models B.C. Allanach – p. 10

Universality Reduces number of SUSY breaking parameters from 100 to 3: • tan β ≡ v 2 /v 1 • m 0 , the common scalar mass (flavour). • M 1 / 2 , the common gaugino mass (GUT/string). • A 0 , the common trilinear coupling (flavour). These conditions should be imposed at M X ∼ O (10 16 − 18 ) GeV and receive radiative corrections ∝ 1 / (16 π 2 ) ln( M X /M Z ) . Also, Higgs potential parameter sgn( µ )= ± 1. Global Fits to MSSM Models B.C. Allanach – p. 11

Implementation We use • 95 % C.L. direct search constraints • Ω DM h 2 = 0 . 1143 ± 0 . 02 Boudjema et al • δ ( g − 2) µ / 2 = (29 . 5 ± 8 . 8) × 10 − 10 Stöckinger et al • B − physics observables including BR [ b → sγ ] E γ > 1 . 6 GeV = (3 . 52 ± 0 . 38) × 10 − 4 • Electroweak data W Hollik, A Weber et al ( p i − e i ) 2 � � χ 2 2 ln L = − i + c = + c σ 2 i i i Global Fits to MSSM Models B.C. Allanach – p. 12

Additional observables � 2 � 100 GeV δ ( g − 2) µ ∼ 13 × 10 − 10 tan β 2 M SUSY χ ± γ µ ˜ γ i χ 0 µ µ µ µ ν ˜ 1 BR [ b → sγ ] ∝ tan β ( M W /M SUSY ) 2 χ ± γ γ H ± i ˜ t i b s b t s Global Fits to MSSM Models B.C. Allanach – p. 13

mSUGRA Global Fits There are 3 methodologies of doing these type of global fits: • Markov Chain Monte Carlo: BCA et al ; Ruiz de Austri et al : primary interpretation is Bayesian . • MultiNest: Ruiz de Austri et al : Bayesian interpretation only. • Minimising χ 2 /Profile likelihood: Buchmueller et al . Impressive array of electroweak observables. Moving to a hybrid approach. Frequentist interpretation only. Global Fits to MSSM Models B.C. Allanach – p. 14

Application of Bayes’ L ≡ p ( d | m, H ) is pdf of reproducing data d assuming pMSSM hypothesis H and model parameters m p ( m | d, H ) = p ( d | m, H ) p ( m, H ) p ( d, H ) p ( m | d, H ) is called the posterior pdf. We will compare p ( m, H ) = c with a different prior. � p ( m 0 , M 1 / 2 | d, H ) = do p ( m 0 , M 1 / 2 , o | d, H ) Called marginalisation . Global Fits to MSSM Models B.C. Allanach – p. 15

Log Fits B.C. Allanach, Feb 2011 B.C. Allanach, Feb 2011 0.4 1 1 60 0.35 0.8 50 0.8 0.3 40 m 0 (TeV) 0.6 0.6 0.25 tan β 30 0.2 0.4 0.4 20 0.15 0.2 0.2 0.1 10 0.05 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 m 1/2 (TeV) m 1/2 /TeV Choose priors on SM parameters set from data. Priors on SUSY parameters up to 4 TeV: flat in tan β , A 0 , ln( m 0 ) , ln( m 1 / 2 ) . Global Fits to MSSM Models B.C. Allanach – p. 16

Killer Inference for Susy METeorology BCA, Cranmer, Weber, Lester, arXiv:0705.0487 BCA, Cranmer, Weber, Lester, arXiv:0705.0487 http://users.hepforge.org/ ˜ allanach/benchmarks/kismet.html P/P(max) P/P(max) 4 4 1 1 0.9 3.5 3.5 flat tan β 0.8 0.8 3 3 0.7 m 0 (TeV) 2.5 m 0 (TeV) 2.5 0.6 0.6 2 2 0.5 1.5 1.5 0.4 0.4 flat µ, B 1 1 0.3 0.5 0.5 0.2 0.2 0 0 0.1 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0 M 1/2 (TeV) M 1/2 (TeV) 100 fb -1 300 fb -1 L = 1 fb -1 10 fb -1 2000 m 0 ( GeV) CMS tan β = 35 1800 1600 ~ ~ g g ( 2 0 ( 3 0 ~ 0 0 ) 0 0 ) g ( 1 0 1400 0 0 ) ~ ~ g ( g ( 1 5 0 2 5 0 1200 0 ) 0 ) b → s γ limit 1000 800 q ~ (2500) q ~ (2000) 600 ~ (1500) q q ~ (1000) 400 M h limit 200 Charged LSP 0 0 375 750 1125 1500 Global Fits to MSSM Models B.C. Allanach – p. 17 m 1/2 (GeV)

Killer Inference for Susy METeorology BCA, Cranmer, Weber, Lester, arXiv:0705.0487 Bayesian 1 Bayesian 2 100 fb -1 300 fb -1 L = 1 fb -1 10 fb -1 2000 m 0 ( GeV) CMS tan β = 35 1800 1600 ~ ~ g g ( 2 0 ( 3 0 ~ 0 0 ) 0 0 ) g ( 1 0 1400 0 0 ) ~ ~ g ( g ( 1 5 0 2 5 0 1200 0 ) 0 ) b → s γ limit 1000 800 q ~ (2500) q ~ (2000) 600 ~ (1500) q q ~ (1000) 400 M h limit 200 Charged LSP 0 0 375 750 1125 1500 Global Fits to MSSM Models B.C. Allanach – p. 18 m 1/2 (GeV)

Collider SUSY Dark Matter Production Strong sparticle production and decay to dark matter particles. q q q q p p 7 TeV 7 TeV q,g q,g Interaction ~ ~ q q q q χ 0 χ 0 1 1 Any (light enough) dark matter candidate that couples to hadrons can be produced at the LHC Global Fits to MSSM Models B.C. Allanach – p. 19

Validation of CMS Analysis Used SOFTSUSY3.1.7 , Herwig++-2.4.2 and fastjet-2.4.2 to simulate 10000 signal events α T distributions with H T > 350 GeV: α T distributions for SUSY point LM0 m 0 = 200 , m 1 / 2 = 160 , A 0 = − 400 , tan β = 10 by my simulation (solid) and CMS’ (dashed). Global Fits to MSSM Models B.C. Allanach – p. 20

CMS Validation II tan β = 3 tan β = 30 ∆ χ 2 approx tan β , A 0 independent ⇒ interpolate it across m 0 and m 1 / 2 , then re-weight fit with ∆ χ 2 . Global Fits to MSSM Models B.C. Allanach – p. 21

CMS Weighted Fits B.C. Allanach, Feb 2011 B.C. Allanach, Feb 2011 0.4 1 0.4 1 0.35 0.35 0.8 0.8 0.3 0.3 m 0 (TeV) m 0 (TeV) 0.6 0.6 0.25 0.25 0.2 0.2 0.4 0.4 0.15 0.15 0.2 0.2 0.1 0.1 0.05 0 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 m 1/2 (TeV) m 1/2 (TeV) Global Fits to MSSM Models B.C. Allanach – p. 22