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Bayesian method of SUSY parameter reconstruction - a case study - - PowerPoint PPT Presentation

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Bayesian method of SUSY parameter reconstruction - a case study Leszek Roszkowski U. of Sheffield, England and SINS, Warsaw, Poland with Roberto Ruiz de Austri and Roberto Trotta, arXiv:0907.0594 public tool: SuperBayes package, available from

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SLIDE 1

Bayesian method of SUSY parameter reconstruction - a case study

Leszek Roszkowski

  • U. of Sheffield, England and SINS, Warsaw, Poland

with Roberto Ruiz de Austri and Roberto Trotta, arXiv:0907.0594 public tool: SuperBayes package, available from www.superbayes.org

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.1

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SLIDE 2

Outline

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.2

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SLIDE 3

Outline

SUSY, Constrained MSSM (CMSSM) case study: ATLAS SU3 benchmark point

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.2

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SLIDE 4

Outline

SUSY, Constrained MSSM (CMSSM) case study: ATLAS SU3 benchmark point Bayesian parameter reconstruction for SU3

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.2

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SLIDE 5

Outline

SUSY, Constrained MSSM (CMSSM) case study: ATLAS SU3 benchmark point Bayesian parameter reconstruction for SU3 impact of additional info on Ωχh2 prior dependence, profile likelihood summary

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.2

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SLIDE 6

A conjecture

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.3

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SLIDE 7

A conjecture

SUSY cannot be experimentally ruled out

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.3

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SLIDE 8

A conjecture

SUSY cannot be experimentally ruled out it can only be discovered...

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.3

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SLIDE 9

A conjecture

SUSY cannot be experimentally ruled out it can only be discovered...

...or abandoned

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.3

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SLIDE 10

Parameter reconstruction

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.4

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SLIDE 11

Parameter reconstruction

...once positive measurements are made...

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.4

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SLIDE 12

Parameter reconstruction

...once positive measurements are made... task: reconstruct underlying SUSY parameters

model dependent program

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.4

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SLIDE 13

Constrained MSSM (CMSSM)

Kane, Kolda, LR, Wells (1993) ...“benchmark framework” for the LHC (...e.g., mSUGRA)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.5

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SLIDE 14

Constrained MSSM (CMSSM)

Kane, Kolda, LR, Wells (1993) ...“benchmark framework” for the LHC (...e.g., mSUGRA) At MGUT ≃ 2 × 1016 GeV: gauginos M1 = M2 = me

g = m1/2

scalars m2

e qi = m2 e li = m2 Hb = m2 Ht = m2

3–linear soft terms Ab = At = A0

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.5

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SLIDE 15

Constrained MSSM (CMSSM)

Kane, Kolda, LR, Wells (1993) ...“benchmark framework” for the LHC (...e.g., mSUGRA) At MGUT ≃ 2 × 1016 GeV: gauginos M1 = M2 = me

g = m1/2

scalars m2

e qi = m2 e li = m2 Hb = m2 Ht = m2

3–linear soft terms Ab = At = A0 radiative EWSB µ2 =

m2

Hb −m2 Ht tan2 β

tan2 β−1

− m2

Z

2

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.5

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SLIDE 16

Constrained MSSM (CMSSM)

Kane, Kolda, LR, Wells (1993) ...“benchmark framework” for the LHC (...e.g., mSUGRA) At MGUT ≃ 2 × 1016 GeV: gauginos M1 = M2 = me

g = m1/2

scalars m2

e qi = m2 e li = m2 Hb = m2 Ht = m2

3–linear soft terms Ab = At = A0 radiative EWSB µ2 =

m2

Hb −m2 Ht tan2 β

tan2 β−1

− m2

Z

2

five independent parameters:

m1/2, m0, A0, tan β, sgn(µ)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.5

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SLIDE 17

Constrained MSSM (CMSSM)

Kane, Kolda, LR, Wells (1993) ...“benchmark framework” for the LHC (...e.g., mSUGRA) At MGUT ≃ 2 × 1016 GeV: gauginos M1 = M2 = me

g = m1/2

scalars m2

e qi = m2 e li = m2 Hb = m2 Ht = m2

3–linear soft terms Ab = At = A0 radiative EWSB µ2 =

m2

Hb −m2 Ht tan2 β

tan2 β−1

− m2

Z

2

five independent parameters:

m1/2, m0, A0, tan β, sgn(µ)

well developed machinery to compute masses and couplings

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.5

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SLIDE 18

Constrained MSSM (CMSSM)

Kane, Kolda, LR, Wells (1993) ...“benchmark framework” for the LHC (...e.g., mSUGRA) At MGUT ≃ 2 × 1016 GeV: gauginos M1 = M2 = me

g = m1/2

scalars m2

e qi = m2 e li = m2 Hb = m2 Ht = m2

3–linear soft terms Ab = At = A0 radiative EWSB µ2 =

m2

Hb −m2 Ht tan2 β

tan2 β−1

− m2

Z

2

five independent parameters:

m1/2, m0, A0, tan β, sgn(µ)

well developed machinery to compute masses and couplings neutralino χ mostly bino

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.5

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SLIDE 19

Constrained MSSM (CMSSM)

Kane, Kolda, LR, Wells (1993) ...“benchmark framework” for the LHC (...e.g., mSUGRA) At MGUT ≃ 2 × 1016 GeV: gauginos M1 = M2 = me

g = m1/2

scalars m2

e qi = m2 e li = m2 Hb = m2 Ht = m2

3–linear soft terms Ab = At = A0 radiative EWSB µ2 =

m2

Hb −m2 Ht tan2 β

tan2 β−1

− m2

Z

2

five independent parameters:

m1/2, m0, A0, tan β, sgn(µ)

well developed machinery to compute masses and couplings neutralino χ mostly bino some useful mass relations: bino: mχ ≃ 0.4m1/2 gluino e g: me

g ≃ 2.7m1/2

supersymmetric tau (stau) e τ1: me

τ1 ≃

q 0.15m2

1/2 + m2

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.5

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SLIDE 20

Case study: ATLAS SU3 Point

ATLAS SU3 benchmark point, arXiv:0901.0512

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.6

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SLIDE 21

Case study: ATLAS SU3 Point

ATLAS SU3 benchmark point, arXiv:0901.0512

Parameter SU3 benchmark value m0 100 GeV m1/2 300 GeV tan β 6.0 A0 −300 GeV Ωχh2 0.23319 ⇐ SUSY mass spectrum χ = χ0

1

117.9 GeV χ0

2

223.4 GeV f me

l

152.2 GeV me

q

652.4 GeV f me

l - lightest slepton mass

me

q

  • average light squark

mass

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.6

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SLIDE 22

Case study: ATLAS SU3 Point

ATLAS SU3 benchmark point, arXiv:0901.0512

Parameter SU3 benchmark value m0 100 GeV m1/2 300 GeV tan β 6.0 A0 −300 GeV Ωχh2 0.23319 ⇐ SUSY mass spectrum χ = χ0

1

117.9 GeV χ0

2

223.4 GeV f me

l

152.2 GeV me

q

652.4 GeV f me

l - lightest slepton mass

me

q

  • average light squark

mass study endpoint measurements dileptons + lepton+jets analysis of the decay chain e qL → χ0

2(→ e

l±l∓)q → χ0

1l+l−q

and the high-pT and large missing energy analysis of the decay chain e qR → χ0

1q

χ2 minimization

  • int. lum. 1 fb−1

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.6

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ATLAS SU3 measurements

Aad, et al., arXiv:0901.0512 1st errors: parabolic 2nd errors: jet energy scale The covariance matrix (ATLAS): mχ0

1

mχ0

2 − mχ0 1

f me

l − mχ0

1

me

q − mχ0

1

mχ0

1

3.72 × 103 53.40 1.92 × 103 10.75 × 102 mχ0

2 − mχ0 1

3.6 29.0 −1.3 f me

l − mχ0

1

1.12 × 103 4.65 me

q − mχ0

1

14.1

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.7

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SLIDE 24

SU3 parameter reconstruction by ATLAS

Aad, et al., arXiv:0901.0512

2D likelihood maps (int. lum. 1 fb−1) theory errors neglected neglect effect of SM parameters ranges around the true value found

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.8

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SLIDE 25

Bayesian Analysis of the CMSSM

Apply to the CMSSM:

recent development, led by 2 groups

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.9

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SLIDE 26

Bayesian Analysis of the CMSSM

Apply to the CMSSM:

recent development, led by 2 groups

m = (θ, ψ) – model’s all relevant parameters

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.9

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SLIDE 27

Bayesian Analysis of the CMSSM

Apply to the CMSSM:

recent development, led by 2 groups

m = (θ, ψ) – model’s all relevant parameters CMSSM parameters θ = m1/2, m0, A0, tan β relevant SM param’s ψ = Mt, mb(mb)MS, αMS

s

, αem(MZ)MS

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.9

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SLIDE 28

Bayesian Analysis of the CMSSM

Apply to the CMSSM:

recent development, led by 2 groups

m = (θ, ψ) – model’s all relevant parameters CMSSM parameters θ = m1/2, m0, A0, tan β relevant SM param’s ψ = Mt, mb(mb)MS, αMS

s

, αem(MZ)MS ξ = (ξ1, ξ2, . . . , ξm): set of derived variables (observables): ξ(m)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.9

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SLIDE 29

Bayesian Analysis of the CMSSM

Apply to the CMSSM:

recent development, led by 2 groups

m = (θ, ψ) – model’s all relevant parameters CMSSM parameters θ = m1/2, m0, A0, tan β relevant SM param’s ψ = Mt, mb(mb)MS, αMS

s

, αem(MZ)MS ξ = (ξ1, ξ2, . . . , ξm): set of derived variables (observables): ξ(m) d: data (ΩCDMh2, b → sγ, mh, etc)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.9

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SLIDE 30

Bayesian Analysis of the CMSSM

Apply to the CMSSM:

recent development, led by 2 groups

m = (θ, ψ) – model’s all relevant parameters CMSSM parameters θ = m1/2, m0, A0, tan β relevant SM param’s ψ = Mt, mb(mb)MS, αMS

s

, αem(MZ)MS ξ = (ξ1, ξ2, . . . , ξm): set of derived variables (observables): ξ(m) d: data (ΩCDMh2, b → sγ, mh, etc) Bayes’ theorem: posterior pdf p(θ, ψ|d) = p(d|ξ)π(θ,ψ)

p(d)

posterior =

likelihood × prior normalization factor

p(d|ξ) = L: likelihood π(θ, ψ): prior pdf p(d): evidence (normalization factor)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.9

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SLIDE 31

Bayesian Analysis of the CMSSM

Apply to the CMSSM:

recent development, led by 2 groups

m = (θ, ψ) – model’s all relevant parameters CMSSM parameters θ = m1/2, m0, A0, tan β relevant SM param’s ψ = Mt, mb(mb)MS, αMS

s

, αem(MZ)MS ξ = (ξ1, ξ2, . . . , ξm): set of derived variables (observables): ξ(m) d: data (ΩCDMh2, b → sγ, mh, etc) Bayes’ theorem: posterior pdf p(θ, ψ|d) = p(d|ξ)π(θ,ψ)

p(d)

posterior =

likelihood × prior normalization factor

p(d|ξ) = L: likelihood π(θ, ψ): prior pdf p(d): evidence (normalization factor) usually marginalize over SM (nuisance) parameters ψ ⇒ p(θ|d)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.9

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SLIDE 32

The likelihood: 1-dim case

Take a single observable ξ(m) that has been measured

(e.g., MW )

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.10

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SLIDE 33

The likelihood: 1-dim case

Take a single observable ξ(m) that has been measured

(e.g., MW )

c – central value, σ – standard exptal error

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.10

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SLIDE 34

The likelihood: 1-dim case

Take a single observable ξ(m) that has been measured

(e.g., MW )

c – central value, σ – standard exptal error define χ2 = [ξ(m)−c]2

σ2

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.10

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SLIDE 35

The likelihood: 1-dim case

Take a single observable ξ(m) that has been measured

(e.g., MW )

c – central value, σ – standard exptal error define χ2 = [ξ(m)−c]2

σ2

assuming Gaussian distribution (d → (c, σ)): L = p(σ, c|ξ(m)) =

1 √ 2πσ exp

  • − χ2

2

  • GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.10
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SLIDE 36

The likelihood: 1-dim case

Take a single observable ξ(m) that has been measured

(e.g., MW )

c – central value, σ – standard exptal error define χ2 = [ξ(m)−c]2

σ2

assuming Gaussian distribution (d → (c, σ)): L = p(σ, c|ξ(m)) =

1 √ 2πσ exp

  • − χ2

2

  • when include theoretical error estimate τ (assumed Gaussian):

σ → s = √σ2 + τ 2

TH error “smears out” the EXPTAL range

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.10

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SLIDE 37

The likelihood: 1-dim case

Take a single observable ξ(m) that has been measured

(e.g., MW )

c – central value, σ – standard exptal error define χ2 = [ξ(m)−c]2

σ2

assuming Gaussian distribution (d → (c, σ)): L = p(σ, c|ξ(m)) =

1 √ 2πσ exp

  • − χ2

2

  • when include theoretical error estimate τ (assumed Gaussian):

σ → s = √σ2 + τ 2

TH error “smears out” the EXPTAL range

for several uncorrelated observables (assumed Gaussian): L = exp

  • −

i χ2

i

2

  • GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.10
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SLIDE 38

Probability maps of the CMSSM

Bayesian posterior pdf

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.11

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SLIDE 39

Probability maps of the CMSSM

Bayesian posterior pdf

arXiv:0705.2012

m1/2 (TeV) m0 (TeV)

CMSSM µ>0

Roszkowski, Ruiz & Trotta (2007)

0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 3.5 4

Relative probability density

0.2 0.4 0.6 0.8 1

MCMC scan (4 CMSSM + 4 SM param’s) Bayesian analysis relative probability density fn (pdf) flat priors 68% total prob. – inner contours 95% total prob. – outer contours 2-dim pdf p(m0, m1/2|d) favored: m0 ≫ m1/2 (FP region)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.11

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SLIDE 40

Probability maps of the CMSSM

Bayesian posterior pdf

arXiv:0705.2012

m1/2 (TeV) m0 (TeV)

CMSSM µ>0

Roszkowski, Ruiz & Trotta (2007)

0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 3.5 4

Relative probability density

0.2 0.4 0.6 0.8 1

MCMC scan (4 CMSSM + 4 SM param’s) Bayesian analysis relative probability density fn (pdf) flat priors 68% total prob. – inner contours 95% total prob. – outer contours 2-dim pdf p(m0, m1/2|d) favored: m0 ≫ m1/2 (FP region) similar study by Allanach+Lester(+Weber) see also, Ellis et al (EHOW, χ2 approach, no MCMC, fixed SM parameters)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.11

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SLIDE 41

Probability maps of the CMSSM

Bayesian posterior pdf

arXiv:0705.2012

m1/2 (TeV) m0 (TeV)

CMSSM µ>0

Roszkowski, Ruiz & Trotta (2007)

0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 3.5 4

Relative probability density

0.2 0.4 0.6 0.8 1

MCMC scan (4 CMSSM + 4 SM param’s) Bayesian analysis relative probability density fn (pdf) flat priors 68% total prob. – inner contours 95% total prob. – outer contours 2-dim pdf p(m0, m1/2|d) favored: m0 ≫ m1/2 (FP region) unlike others (except for A+L), we vary also SM parameters

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.11

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SLIDE 42

Reconstruction of m1/2, m0 with SB

ATLAS SU3 benchmark point

Bayesian analysis, use Gaussian approx. with publicly available info

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.12

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SLIDE 43

Reconstruction of m1/2, m0 with SB

ATLAS SU3 benchmark point

Bayesian analysis, use Gaussian approx. with publicly available info

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

280 300 320 50 100 150 200 250 300

ATLAS analysis θ = {mχ0

1, mχ0 2−mχ0 1, f

me

l−mχ0

1, me

q −mχ0

1}

−2 ln LATLAS = χ2

ATLAS

= (θ − θML)tC−1(θ − θML) red diamond: SU3 point green cross in circle: best-fit value big dot: posterior mean dark blue: 68% total prob. region light blue: 95% total prob. region

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.12

slide-44
SLIDE 44

Reconstruction of m1/2, m0 with SB

ATLAS SU3 benchmark point

Bayesian analysis, use Gaussian approx. with publicly available info

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

280 300 320 50 100 150 200 250 300

ATLAS analysis Nested Sampling (NS) scan 50 GeV ≤ m1/2, m0 ≤ 500 GeV, µ > 0 −2 TeV ≤ A0 ≤ 2 TeV, 2 ≤ tan β ≤ 62 follow ATLAS input NO exptal constraints applied (b → sγ, Ωχh2, etc) similar for flat prior and profile likelihood (akin to χ2) determination of m0 a bit poorer than ATLAS

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.12

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SLIDE 45

Reconstruction of A0, tan β with SB

ATLAS SU3 benchmark point

Bayesian analysis, use Gaussian approx. with publicly available info

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.13

slide-46
SLIDE 46

Reconstruction of A0, tan β with SB

ATLAS SU3 benchmark point

Bayesian analysis, use Gaussian approx. with publicly available info

A0 (TeV) tan β

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

−2 2 10 20 30 40 50 60

ATLAS analysis θ = {mχ0

1, mχ0 2−mχ0 1, f

me

l−mχ0

1, me

q −mχ0

1}

−2 ln LATLAS = χ2

ATLAS

= (θ − θML)tC−1(θ − θML) red diamond: SU3 point green cross in circle: best-fit value big dot: posterior mean dark blue: 68% total prob. region light blue: 95% total prob. region

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.13

slide-47
SLIDE 47

Reconstruction of A0, tan β with SB

ATLAS SU3 benchmark point

Bayesian analysis, use Gaussian approx. with publicly available info

A0 (TeV) tan β

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

−2 2 10 20 30 40 50 60

ATLAS analysis NS scan 50 GeV ≤ m1/2, m0 ≤ 500 GeV, µ > 0 −2 TeV ≤ A0 ≤ 2 TeV, 2 ≤ tan β ≤ 62 follow ATLAS input fix SM (nuisance) parameters NO exptal constraints applied (b → sγ, Ωχh2, etc) similar result for flat prior and profile likelihood (akin to χ2) cannot resolve sign of A0

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.13

slide-48
SLIDE 48

1dim posterior pdfs

ATLAS SU3 benchmark point

m0 (GeV) Probability

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

100 200 300 0.2 0.4 0.6 0.8 1 A0 (TeV) Probability

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

−2 2 0.2 0.4 0.6 0.8 1 m1/2 (GeV) Probability

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

280 300 320 0.2 0.4 0.6 0.8 1 tan β Probability

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

20 40 60 0.2 0.4 0.6 0.8 1

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.14

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SLIDE 49

SU3: CMSSM vs MSSM

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.15

slide-50
SLIDE 50

SU3: CMSSM vs MSSM

mχ

1 0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Green: CMSSM prior Red: ATLAS likelihood Blue: Posterior true value

CMSSM, µ>0 ATLAS SU3 point

mχ0

2 − mχ0 1(GeV )

50 100 150 200 50 100 150 200

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.15

slide-51
SLIDE 51

SU3: CMSSM vs MSSM

mχ

1 0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Green: CMSSM prior Red: ATLAS likelihood Blue: Posterior true value

CMSSM, µ>0 ATLAS SU3 point

mχ0

2 − mχ0 1(GeV )

50 100 150 200 50 100 150 200 mχ

1 0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Green: CMSSM prior Red: ATLAS likelihood Blue: Posterior true value

CMSSM, µ>0 ATLAS SU3 point

m˜

q − mχ0

1(GeV)

100 200 300 200 300 400 500 600 700 800

green points: allowed by CMSSM red ellipses: ATLAS likelihood blue ellipses: posterior constraints theory advantage: ⇒ using posterior allows much better determination of mχ0

1

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.15

slide-52
SLIDE 52

Add info about Ωχh2

take WMAP error on Ωχh2: 0.0062

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.16

slide-53
SLIDE 53

Add info about Ωχh2

take WMAP error on Ωχh2: 0.0062

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS only Blue: ATLAS+WMAP true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

280 300 320 50 100 150 200 250 300

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.16

slide-54
SLIDE 54

Add info about Ωχh2

take WMAP error on Ωχh2: 0.0062

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS only Blue: ATLAS+WMAP true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

280 300 320 50 100 150 200 250 300 A0 (TeV) tanβ

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS alone Blue: ATLAS+WMAP true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

−2 2 10 20 30 40 50 60

similar result for flat prior and profile likelihood

determination of m1/2, m0 spot on! tan β resolved reasonably well determination of A0 remains poor still cannot resolve sign of A0

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.16

slide-55
SLIDE 55

Add info about Ωχh2 from Planck

assume Planck-like error on Ωχh2 of ∼ < 0.0016 (WMAP error/5)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.17

slide-56
SLIDE 56

Add info about Ωχh2 from Planck

assume Planck-like error on Ωχh2 of ∼ < 0.0016 (WMAP error/5)

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS only Blue: ATLAS+Planck true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

280 300 320 50 100 150 200 250 300

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.17

slide-57
SLIDE 57

Add info about Ωχh2 from Planck

assume Planck-like error on Ωχh2 of ∼ < 0.0016 (WMAP error/5)

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS only Blue: ATLAS+Planck true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

280 300 320 50 100 150 200 250 300 A0 (TeV) tanβ

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS alone Blue: ATLAS+Planck true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

−2 2 10 20 30 40 50 60

similar result for flat prior and profile likelihood

determination of m1/2, m0 spot on! tan β resolved reasonably well determination of A0 remains poor still cannot resolve sign of A0

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.17

slide-58
SLIDE 58

Profile likelihood

different statistical measure, independent of priors

Regions of high posterior probability do not always give the best fits

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.18

slide-59
SLIDE 59

Profile likelihood

different statistical measure, independent of priors

Regions of high posterior probability do not always give the best fits Take two regions: a ‘spike’ - tiny region with excellent fit to data and a large region with somewhat worse fit to data

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.18

slide-60
SLIDE 60

Profile likelihood

different statistical measure, independent of priors

Regions of high posterior probability do not always give the best fits Take two regions: a ‘spike’ - tiny region with excellent fit to data and a large region with somewhat worse fit to data Bayesian statistics: pdf would peak at large region (‘volume’ effect)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.18

slide-61
SLIDE 61

Profile likelihood

different statistical measure, independent of priors

Regions of high posterior probability do not always give the best fits Take two regions: a ‘spike’ - tiny region with excellent fit to data and a large region with somewhat worse fit to data Bayesian statistics: pdf would peak at large region (‘volume’ effect) define profile likelihood for, e.g., parameter m1

L(m1) ≡ maxm2,...,mN L(d|m)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.18

slide-62
SLIDE 62

Profile likelihood

different statistical measure, independent of priors

Regions of high posterior probability do not always give the best fits Take two regions: a ‘spike’ - tiny region with excellent fit to data and a large region with somewhat worse fit to data Bayesian statistics: pdf would peak at large region (‘volume’ effect) define profile likelihood for, e.g., parameter m1

L(m1) ≡ maxm2,...,mN L(d|m)

PL maximizes the likelihood along marginalized dimensions marginal posterior integrates them out

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.18

slide-63
SLIDE 63

Profile likelihood

different statistical measure, independent of priors

Regions of high posterior probability do not always give the best fits Take two regions: a ‘spike’ - tiny region with excellent fit to data and a large region with somewhat worse fit to data Bayesian statistics: pdf would peak at large region (‘volume’ effect) define profile likelihood for, e.g., parameter m1

L(m1) ≡ maxm2,...,mN L(d|m)

PL maximizes the likelihood along marginalized dimensions marginal posterior integrates them out any tension between Bayesian pdf and profile likelihood indicates that data is not constraining enough

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.18

slide-64
SLIDE 64

Profile likelihood

different statistical measure, independent of priors

Regions of high posterior probability do not always give the best fits Take two regions: a ‘spike’ - tiny region with excellent fit to data and a large region with somewhat worse fit to data Bayesian statistics: pdf would peak at large region (‘volume’ effect) define profile likelihood for, e.g., parameter m1

L(m1) ≡ maxm2,...,mN L(d|m)

PL maximizes the likelihood along marginalized dimensions marginal posterior integrates them out any tension between Bayesian pdf and profile likelihood indicates that data is not constraining enough need to do both to see if that is the case

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.18

slide-65
SLIDE 65

Posterior pdf vs. profile likelihood

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.19

slide-66
SLIDE 66

Posterior pdf vs. profile likelihood

ATLAS data only

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS, posterior pdf Beige: ATLAS, profile likelihood true value

280 300 320 50 100 150 200 250 300 A0 (TeV) tanβ

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS, posterior pdf Beige: ATLAS, profile likelihood true value

−2 2 10 20 30 40 50 60

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.19

slide-67
SLIDE 67

Posterior pdf vs. profile likelihood

ATLAS data only

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS, posterior pdf Beige: ATLAS, profile likelihood true value

280 300 320 50 100 150 200 250 300 A0 (TeV) tanβ

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS, posterior pdf Beige: ATLAS, profile likelihood true value

−2 2 10 20 30 40 50 60

add Ωχh2+ Planck-like error

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS+Planck, posterior pdf Beige: ATLAS+Planck, profile likelihood true value

280 300 320 50 100 150 200 250 300 A0 (TeV) tanβ

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS+Planck, posterior pdf Beige: ATLAS+Planck, profile likelihood true value

−2 2 10 20 30 40 50 60

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.19

slide-68
SLIDE 68

Posterior pdf vs. profile likelihood

ATLAS data only

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS, posterior pdf Beige: ATLAS, profile likelihood true value

280 300 320 50 100 150 200 250 300 A0 (TeV) tanβ

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS, posterior pdf Beige: ATLAS, profile likelihood true value

−2 2 10 20 30 40 50 60

add Ωχh2+ Planck-like error

m1/2 (GeV) m0 (GeV)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS+Planck, posterior pdf Beige: ATLAS+Planck, profile likelihood true value

280 300 320 50 100 150 200 250 300 A0 (TeV) tanβ

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS+Planck, posterior pdf Beige: ATLAS+Planck, profile likelihood true value

−2 2 10 20 30 40 50 60

⇒ good agreement

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.19

slide-69
SLIDE 69

Determination of Ωχh2

ATLAS SU3 point

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.20

slide-70
SLIDE 70

Determination of Ωχh2

ATLAS SU3 point

Ωχh2 Probability

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

0.1 0.2 0.3 0.4 0.2 0.4 0.6 0.8 1

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.20

slide-71
SLIDE 71

Determination of Ωχh2

ATLAS SU3 point

Ωχh2 Probability

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

0.1 0.2 0.3 0.4 0.2 0.4 0.6 0.8 1

use only ATLAS data similar result for log prior and pro- file likelihood red diamond: SU3 point green cross in circle: best-fit value dark blue dot: posterior mean

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.20

slide-72
SLIDE 72

Determination of Ωχh2

ATLAS SU3 point

Ωχh2 Probability

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours best fit mean true value

0.1 0.2 0.3 0.4 0.2 0.4 0.6 0.8 1

use only ATLAS data similar result for log prior and pro- file likelihood red diamond: SU3 point green cross in circle: best-fit value dark blue dot: posterior mean

⇒ Ωχh2 = 0.253 ± 0.034

relative accuracy of ∼ 10%

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.20

slide-73
SLIDE 73

Determination of σSI

p

assume Planck-like error: reduce WMAP error on Ωχh2 by ∼ 5 (∼ < 0.0016)

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.21

slide-74
SLIDE 74

Determination of σSI

p

assume Planck-like error: reduce WMAP error on Ωχh2 by ∼ 5 (∼ < 0.0016)

mχ (GeV) log(σp

SI) (pb)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS only Blue: ATLAS+WMAP true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

110 115 120 125 −9.5 −9 −8.5 −8 −7.5 −7 −6.5

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.21

slide-75
SLIDE 75

Determination of σSI

p

assume Planck-like error: reduce WMAP error on Ωχh2 by ∼ 5 (∼ < 0.0016)

mχ (GeV) log(σp

SI) (pb)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS only Blue: ATLAS+WMAP true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

110 115 120 125 −9.5 −9 −8.5 −8 −7.5 −7 −6.5 mχ (GeV) log(σp

SI) (pb)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS only Blue: ATLAS+Planck true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

110 115 120 125 −9.5 −9 −8.5 −8 −7.5 −7 −6.5

similar result for flat prior and profile likelihood

determination of σSI

p much improved by adding WMAP error on Ωχh2

Planck: limited impact

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.21

slide-76
SLIDE 76

Determination of σSI

p

assume Planck-like error: reduce WMAP error on Ωχh2 by ∼ 5 (∼ < 0.0016)

mχ (GeV) log(σp

SI) (pb)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS only Blue: ATLAS+WMAP true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

110 115 120 125 −9.5 −9 −8.5 −8 −7.5 −7 −6.5 mχ (GeV) log(σp

SI) (pb)

Roszkowski, Ruiz de Austri & Trotta (2009)

68%, 95% contours Black: ATLAS only Blue: ATLAS+Planck true value

Posterior pdf Log priors CMSSM, µ>0 ATLAS SU3 point

110 115 120 125 −9.5 −9 −8.5 −8 −7.5 −7 −6.5

similar result for flat prior and profile likelihood

determination of σSI

p much improved by adding WMAP error on Ωχh2

Planck: limited impact

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.21

slide-77
SLIDE 77

Summary

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.22

slide-78
SLIDE 78

Summary

MCMC + Bayesian statistics: powerful tool for LHC/Planck era to properly analyze multi-dim. “new physics” models like SUSY tool: SuperBayes package, available from www.superbayes.org

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.22

slide-79
SLIDE 79

Summary

MCMC + Bayesian statistics: powerful tool for LHC/Planck era to properly analyze multi-dim. “new physics” models like SUSY tool: SuperBayes package, available from www.superbayes.org Constrained MSSM – currently underconstrained

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.22

slide-80
SLIDE 80

Summary

MCMC + Bayesian statistics: powerful tool for LHC/Planck era to properly analyze multi-dim. “new physics” models like SUSY tool: SuperBayes package, available from www.superbayes.org Constrained MSSM – currently underconstrained

CMSSM SU3 benchmark point with 1 fb−1

Bayesian reconstruction of CMSSM parameters with simple Gaussian approximation and public info (except covariance matrix) comparable to that claimed in ATLAS analysis almost no prior dependence left

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.22

slide-81
SLIDE 81

Summary

MCMC + Bayesian statistics: powerful tool for LHC/Planck era to properly analyze multi-dim. “new physics” models like SUSY tool: SuperBayes package, available from www.superbayes.org Constrained MSSM – currently underconstrained

CMSSM SU3 benchmark point with 1 fb−1

Bayesian reconstruction of CMSSM parameters with simple Gaussian approximation and public info (except covariance matrix) comparable to that claimed in ATLAS analysis almost no prior dependence left theory extras: adding WMAP or Planck error on Ωχh2: determination of m1/2, m0 excellent (for SU3) tan β resolved reasonably well still cannot resolve A0, not even its sign DM: σSI

p

improved by a factor of ∼ 2 Planck error on Ωχh2: limited further impact

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.22

slide-82
SLIDE 82

Summary

MCMC + Bayesian statistics: powerful tool for LHC/Planck era to properly analyze multi-dim. “new physics” models like SUSY tool: SuperBayes package, available from www.superbayes.org Constrained MSSM – currently underconstrained

CMSSM SU3 benchmark point with 1 fb−1

Bayesian reconstruction of CMSSM parameters with simple Gaussian approximation and public info (except covariance matrix) comparable to that claimed in ATLAS analysis almost no prior dependence left theory extras: adding WMAP or Planck error on Ωχh2: determination of m1/2, m0 excellent (for SU3) tan β resolved reasonably well still cannot resolve A0, not even its sign DM: σSI

p

improved by a factor of ∼ 2 Planck error on Ωχh2: limited further impact

⇒ SUSY parameter reconstruction with open-access data (+ convariance matrix) seems doable

GGI mini-workshop on LHC and dark matter, 10 June 2010 – p.22