Tools for Supersymmetric Phenomenology by Ben Allanach (University - - PowerPoint PPT Presentation

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Tools for Supersymmetric Phenomenology by Ben Allanach (University - - PowerPoint PPT Presentation

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Tools for Supersymmetric Phenomenology by Ben Allanach (University of Cambridge) Talk outline SPA project http://spa.desy.de/spa/ , http://www.ippp.dur.ac.uk/montecarlo/BSM/ Bestiary of public codes only: supposedly impartial

slide-1
SLIDE 1

Tools for Supersymmetric Phenomenology

by

Ben Allanach (University of Cambridge)

Talk outline

  • SPA project http://spa.desy.de/spa/,

http://www.ippp.dur.ac.uk/montecarlo/BSM/

  • Bestiary of public codes only: supposedly

impartial

  • Predictions for the LHC: partial

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.1/34

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SLIDE 2

MSSM Tools

Detector simulation Event generator Decays SUSY Spectrum calculator Theory BC Input observables: MZ, mt, Dark matter Indirect observables EW/flavour etc

SLHA: Skands et al, JHEP 0407 (2004) 036, SLHA2 on here (NMSSM, RPV, FV, CPV), arXiv:0801.0045

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.2/34

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SLIDE 3

Spectrum and decays

  • ISASUSY decouples particles at the mass

thresholds but misses some finite terms in the matching: re-sums log splittings.

  • SOFTSUSY, sPHENO, SUSPECT all catch the

finite terms but do the splittings to leading log in RPC-MSSM.

  • CPsuperH, FeynHiggs do Higgs mass

spectrum and decays with of CP violating MSSM

  • NMSPEC does the CNMSSM spectrum,

NMHDECAY gives the decays widths etc

  • PYTHIA, ISASUSY, sPHENO and SusyHIT do

decays of Higgs and SUSY particles in MSSM.

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.3/34

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SLIDE 4

Web Page

http://kraml.home.cern.ch/kraml/comparison/ BCA, S Kraml in hep-ph/0402295

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.4/34

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SLIDE 5

Matrix Element Generators

  • Feyn Arts/Feyn Calc
  • Additional hard jets cannot be modelled reliably

using the parton shower - you need to simulate the matrix element.

  • SMADGRAPH, compHEP, calcHEP, GRACE do

SUSY and more general models at tree level. 2 to 4 possible. BRIDGE can be used to remember spin information in the decays.

  • WHIZARD, SUSYGEN - polarisation included for

e+e−

  • PROSPINO does NLO-QCD sparticle

production ˜ q ˜ q

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.5/34

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SLIDE 6

Event Generation

  • Can pass matrix-element generated events to

event generators with the (original) Les Houches Accord

  • PYTHIA used extensively. Includes RPV.

phase-space decays. ISAJET too.

  • HERWIG maintains spin info down cascade
  • decays. RPV too.
  • SHERPA matches up ME with more standard

event generation.

  • Shift toward C++

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.6/34

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SLIDE 7

SUSY Prediction of Ωh2

  • Assume relic in thermal equilibrium with

neq ∝ (MT)3/2exp(−M/T).

  • Freeze-out with Tf ∼ Mf/25 once interaction

rate < expansion rate (teq critical)

  • microMEGAs uses calcHEP to automatically

calculate relevant Feynman diagrams for some given model Lagrangian: flexible. susyBSG

  • darkSUSY, ISATOOLS has MSSM

annihilation channels hard-coded. Much work on (in)-direct detection possibilities.

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.7/34

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SLIDE 8

Constraints on SUSY Models

CMSSM well-studied in literature: eg Ellis, Olive et al PLB565

(2003) 176; Roszkowski et al JHEP 0108 (2001) 024; Baltz, Gondolo, JHEP 0410 (2004) 052;...

100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800

mh = 114 GeV

m0 (GeV) m1/2 (GeV)

tan β = 10 , µ > 0 mχ± = 104 GeV

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.8/34

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SLIDE 9

b Observables

CMSSM: Ellis, Heinemeyer, Olive, Weber, Weiglein, arXiv:0706.0652

200 400 600 800 1000 1200 1400 1600 1800 2000

m1/2 [GeV]

2 4 6 8 10 12 14

χ

2 (today)

CMSSM, µ > 0, mt = 171.4 GeV tanβ = 50, A0 = 0 tanβ = 50, A0 = +m1/2 tanβ = 50, A0 = -m1/2 tanβ = 50, A0 = +2 m1/2 tanβ = 50, A0 = -2 m1/2 200 400 600 800 1000 1200 1400 1600 1800 2000

m1/2 [GeV]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

BR(Bu -> τ ντ): MSSM/SM

CMSSM, µ > 0, mt = 171.4 GeV tanβ = 50, A0 = 0 tanβ = 50, A0 = +m1/2 tanβ = 50, A0 = -m1/2 tanβ = 50, A0 = +2 m1/2 tanβ = 50, A0 = -2 m1/2

BR(Bu → τν), ∆MBs

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.9/34

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SLIDE 10

Fit Development

  • Typically done 2d scans with 2σ exclusion

regions, but in general we have α(MZ), αs(MZ), mt, mb, m0, M1/2, A0, tan β to vary

  • Effective 3d type scan done a which

parameterises a 2d surface of central Ωh2

  • 4d scan b used the impressive Markov Chain

Monte Carlo technique like in cosmology.

  • Combine likelihoods from all of the different

measurements.

aEllis et al, arXiv:0706.0652 bBaltz, Gondolo, JHEP 0410 (2004) 052

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.10/34

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SLIDE 11

Markov-Chain Monte Carlo

Metropolis-Hastings Markov chain sampling consists

  • f list of parameter points x(t) and associated

posterior probabilities p(t). x(t), p(t) x(t+1), p(t+1) r

p(r) r σ

P =min(p(t+1)/p(t), 1) Final density of x points ∝ p. Required number of points relatively insensitive to number of dimensions.

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.11/34

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SLIDE 12

Implementation

Input parameters are: m0, A0, M1/2, tan β,

  • mt = 171.4 ± 2.9, mb(mb) = 4.24 ± 0.11 GeV,
  • αs(MZ)MS = 0.1176 ± 0.002,

α−1(MZ)MS = 127.918 ± 0.018 For the likelihood, we also use

  • ΩDMh2 = 0.104+0.0073

−0.0128 micrOMEGAs

  • δ(g − 2)µ/2 = (22 ± 10) × 10−10 Stöckinger et al
  • BR[b → sγ] = (3.55 ± 0.38) × 10−4 susyBSG
  • sin2 θl

w(eff) = 0.23153 ± 0.000175

  • MW = 80.392 ± 0.031 GeV W Hollik, A Weber et al

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.12/34

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SLIDE 13

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M1/2 (TeV) m0 (TeV) P/P(max) 0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 3.5 4 0.2 0.4 0.6 0.8 1 M1/2 (TeV) m0 (TeV) P/P(max) 0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 3.5 4

0.2 0.4 0.6 0.8 1 1.2

  • 6
  • 4
  • 2

2 4 6 L/L(max) log10σ/fb strong weak gaugino slepton

Killer Inference for Susy METeorology

BCA, Cranmer, Weber, Lester, arXiv:0705.0487

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M1/2 (TeV) m0 (TeV) (L/Lmax) 0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 3.5 4

Frequentist

http://users.hepforge.org/˜allanach/benchmarks/kismet.html

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.13/34

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SLIDE 14

0.2 0.4 0.6 0.8 1 1.2

  • 6
  • 4
  • 2

2 4 6 L/L(max) log10σ/fb strong weak gaugino slepton

Killer Inference for Susy METeorology

BCA, Cranmer, Weber, Lester, arXiv:0705.0487

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M1/2 (TeV) m0 (TeV) (L/Lmax) 0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 3.5 4

Bayesian 1 Bayesian 2 Frequentist

http://users.hepforge.org/˜allanach/benchmarks/kismet.html

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.13/34

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SLIDE 15

Higgs Meteorology

BCA, Cranmer, Lester, Weber arXiv:0705:0487

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 110 115 120 125 130 135 P mh/GeV w=1 w=2 profile

90 100 110 120 130 140 0.5 1 1.5 2 2.5 3 3.5 4

excluded LEP inaccessible Theoretically

90 100 110 120 130 140 0.5 1 1.5 2 2.5 3 3.5 4

Buchmuller et al, arXiv:0707:3447

Figure 0: Including (LHS) or not including (RHS) the LEP2 direct Higgs mass constraints on the CMSSM.

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.14/34

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SLIDE 16

Other literature

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

mχ (TeV) Log[σp

SI (pb)]

CDMS−II EDELWEISS−I ZEPLIN−I

CMSSM, µ > 0

Roszkowski, Ruiz & Trotta (2007)

0.2 0.4 0.6 0.8 1 −11 −10 −9 −8 −7 −6 −5 −4

  • R. R. de Austri, R. Trotta and L. Roszkowski,

arXiv:0705.2012, including some NNLO b → sγ

  • pieces. susyBayes

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.15/34

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SLIDE 17

Fitting to SUSY Breaking Model

200 300 400 500 600 360 380 400 420 440 460 480 Spheno Isajet Softsusy Suspect

m1/2 [GeV] m0 [GeV]

200 300 400 500 600 1.6 1.8 2. 2.2 2.4 Softsusy Spheno Suspect Isajet

tan β m0 [GeV]

  • Experimenters pick a SUSY breaking point
  • They derive observables and errors after detector

simulation

  • We fit

this “data” with our codes

BCA, S Kraml, W Porod, JHEP 0303 (2003) 016

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.16/34

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SLIDE 18

Fits to future collider data

100 200 300 400 500 600 700 800 9001000 100 200 300 400 500 600 700 800 900 1000

Mass (GeV)

1

χ

∼

Mass (GeV)

L

e

~

100 200 300 400 500 600 700 800 9001000 100 200 300 400 500 600 700 800 900 1000

Mass (GeV)

1

χ

∼

Mass (GeV)

L

e

~

115 120 125 130 135 140 145 220 225 230 235 240 245 250 255 260 265 270

Mass (GeV)

1

χ ∼ Mass (GeV)

L

e ~

Lester, Parker, White, JHEP 0601 (2006) 080

σ(P T)

  • Assume edge measurements from some SUSY

point: what constraints exist on the phenomenological MSSM?

  • SFITTER/FITTINO

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.17/34

slide-19
SLIDE 19

Summary

  • There is now a bewildering multitude of codes for

calculating SUSY related observables.

  • There has been some organisation and

consolidation between them, notably in the form

  • f Les Houches Accords.
  • SUSY fitting in the multi-dimensional régime,
  • currently. Could easily still be in this situation

after early LHC data.

  • Markov Chain Monte Carlos are a very useful

tool for exploring such a régime.

  • Current dependence on priors should not be a

surprise: probably only eliminated after ILC data.

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.18/34

slide-20
SLIDE 20

Supplementary Material

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.19/34

slide-21
SLIDE 21

Likelihood and Posterior

Q: What’s the chance of observing someone to be pregnant, given that they are female? Likelihood p(pregnant | female, human) = 0.01 Posterior p(female | pregnant, human) = 1.00

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.20/34

slide-22
SLIDE 22

Sanity Check

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mh (GeV) mχ1

0 (TeV)

L/L(max) 80 90 100 110 120 130 140 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mA (TeV) mχ1

0 (TeV)

L/L(max) 0.5 1 1.5 2 2.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 mτ (TeV) mχ1

0 (TeV)

L/L(max) 0.5 1 1.5 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.01 0.02 0.03 0.04 0.05 0.06 0.5 1 1.5 2 2.5 3 3.5 4 L per bin m (TeV) RH slepton gluino LH squark light stop Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.21/34

slide-23
SLIDE 23

Electroweak Observables

80.3 80.35 80.4 80.45 80.5 80.55 80.6 0.5 1 1.5 2 2.5 3 3.5 4 MW (GeV) m0=M1/2 (TeV) SOFTSUSY 2-loop SM expt 1 sigma 0.231 0.2312 0.2314 0.2316 0.2318 0.232 0.5 1 1.5 2 2.5 3 3.5 4 sin2 θw

l (eff)

m0=M1/2 (TeV) SOFTSUSY 2-loop SM exp 1 sigma

They prefer light SUSY . Be careful of 1-loop ap- prox.

Ellis et al, hep-ph/0411216; hep-ph/0602220.

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.22/34

slide-24
SLIDE 24

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 110 115 120 125 130 135 P mh/GeV w=1 w=2 profile 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.5 1 1.5 2 2.5 3 P mA (TeV) w=1 w=2 profile 0.05 0.1 0.15 0.2 0.25 0.3 0 0.5 1 1.5 2 2.5 3 3.5 4 P mqL (TeV) w=1 w=2 profile 0.05 0.1 0.15 0.2 0.25 0.5 1 1.5 2 2.5 3 P mg (TeV) w=1 w=2 profile 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.2 0.4 0.6 0.8 1 P mχ1

0 (TeV)

w=1 w=2 profile 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.5 1 1.5 2 P mχ1

+/- (TeV)

w=1 w=2 profile 0.02 0.04 0.06 0.08 0.1 1 2 3 4 5 P meR (TeV) w=1 w=2 profile 0.01 0.02 0.03 0.04 0.05 1000 2000 3000 4000 mτ-mχ1

0 (GeV)

w=1 w=2 profile

0.02 0.04 0.06 0.08 0.1 5 10 15 20

(a) (b) (c) (d) (e) (f) (g) (h)

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.23/34

slide-25
SLIDE 25

Caveats

  • Implicitly assumed that LSP constitutes all of

dark matter

  • Assumed radiation domination in post-inflation
  • era. No clear evidence between freeze-out+BBN

that this is the case (teq changes).

  • Examples of non-standard cosmology that would

change the prediction:

  • Extra degrees of freedom
  • Low reheating temperature
  • Extra dimensional models
  • Anisotropic cosmologies
  • Non-thermal production of neutralinos (late

decays?)

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.24/34

slide-26
SLIDE 26

Collider SUSY Dark Matter Production

Strong sparticle production and decay to dark matter particles.

q q q,g χ0

1

χ0

1

p Interaction q q

7 TeV 7 TeV

q,g q q ~ ~ q q p

Q: Can we measure enough to predict σ?

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.25/34

slide-27
SLIDE 27

Collider SUSY Dark Matter Production

Strong sparticle production and decay to dark matter particles.

q q q,g χ0

1

χ0

1

p Interaction q q

7 TeV 7 TeV

q,g q q ~ ~ q q p

Any dark matter candidate that couples to hadrons can be produced at the LHC

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.25/34

slide-28
SLIDE 28

Collider Check

Need corroboration with direct detection. If we can pin particle physics down, a comparison between the predicted relic density and that observed is a test of the cosmological assumptions used in the prediction. Thus, if it doesn’t fit, you change the cosmology until it does.

BCA, G. Belanger, F. Boudjema, A. Pukhov, JHEP 0412 (2004) 020.; M. Nojiri, D. Tovey, JHEP 0603 (2006) 063

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.26/34

slide-29
SLIDE 29

Predicting Ωh2

Not much left that’s allowed but edge measurements allow reasonable Ωh2 error for 300 fb−1.

20 40 60 0.05 0.1 0.15 0.2

59.34 / 54 Constant 38.39 Mean 0.1046 Sigma 0.1966E-01

Ωh2 Experiments/bin

Q: What about other bits of parameter space?

M Nojiri, G Polesello, D Tovey, JHEP 0603 (2006) 063, hep-ph/0512204.

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.27/34

slide-30
SLIDE 30

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M1/2 (TeV) m0 (TeV) L/L(max) 0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 tan β m0 (TeV) L/L(max) 10 20 30 40 50 60 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 tan β m1/2 (TeV) L/L(max) 10 20 30 40 50 60 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 tan β A0 (TeV) L/L(max) 10 20 30 40 50 60

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.28/34

slide-31
SLIDE 31

Volume Effects

Can’t rely on a good χ2 in non-Gaussian situation ρ x

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.29/34

slide-32
SLIDE 32

Comparison

  • LHS: allowing non thermal-χ0

1 contribution

  • RHS: only χ0

1 dark matter

  • (flat priors)

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.30/34

slide-33
SLIDE 33

Comparison

200 400 600 800 1000

m1/2 [GeV]

  • 3000
  • 2500
  • 2000
  • 1500
  • 1000
  • 500

500 1000 1500 2000 2500 3000

A0 [GeV]

CMSSM, µ > 0, tanβ = 10 ∆χ

2, 90% CL

∆χ

2, 68% CL

best fit

0.2 0.4 0.6 0.8 1 M1/2 (TeV) A0 (TeV) P/P(max) 0.2 0.4 0.6 0.8 1

  • 3
  • 2
  • 1

1 2 3

J Ellis et al

  • Fix tan β = 10 and all SM inputs
  • Restrict m0, M1/2 < 1 TeV.
  • Same fits!

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.31/34

slide-34
SLIDE 34

Priors

We have assumed a flat prior in tan β, implies a measure: p(m0|data) =

  • dM1/2 dA0 d tan β ds

p(m0, M1/2, A0, tan β, s|data). µB = sin 2β 2 ( ¯ m2

H1 + ¯

m2

H2 + 2µ2),

µ2 = ¯ m2

H1 − ¯

m2

H2 tan2 β

tan2 β − 1 − M 2

Z

2 . Change variables:

  • dµdB →
  • dMZd tan β|J|

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.32/34

slide-35
SLIDE 35

EWSB prior

p(all data|m0, M1/2, A0, µ, B, s) ≈ p(data|m0, M1/2, A0, µ, B, s) × p(MZ|m0, M1/2, A0, µ, B, s). ≈ p(data|m0, M1/2, A0, µ, B, s) × δ(MZ − M cen

Z )

Change variables

  • dµdBδ(MZ − M cen

Z ) →

  • d tan β|J|:

J = B µ tan β tan2 β + 1 tan2 β − 1

Tools for Supersymmetric Phenomenology: YETI 2008 B.C. Allanach – p.33/34

slide-36
SLIDE 36

Same order prior

We wish to encode the idea that “SUSY breaking terms should be of the same order of magnitude” p(m0|MS) = 1 √ 2πw2m0 exp

  • − 1

2w2 log2( m0 MS )

  • ,

p(A0|MS) = 1 √ 2πe2wMS exp

  • − 1

2e2w A2 M 2

S

  • ,

We don’t know SUSY breaking scale MS: p(m0, M1/2, A0, µ, B) = ∞ dMS p(m0, M1/2, A0, µ, B|MS) p(MS)

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