Extraction of SUSY Parameters from Collider Data

SUSY 2008 Seoul06/17/2008

Dirk ZerwasLAL Orsay

• Introduction• Measurements• Reconstruction of fundamental Parameters• Summary

Supersymmetry

3 neutral Higgs bosons: h, A, H1 charged Higgs boson: H±

and supersymmetric particles

spin-0 spin-1/2 spin-1

squarks:

qR, qL

q

gluino: g g

sleptonen:

ℓR, ℓL

ℓ

h,H,A neutralino χi=1-4

Z, γ

H± charginos: χ±

i=1-2 W±

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Many different models:• MSSM (low scale many parameters)• mSUGRA (high scale few parameters)• DSS (SUSY with heavy scalars)• GMSB• AMB• NMSSM

R-parity• production of SUSY particles in pairs• (Cascade-) decays to the lightest SUSY particle • LSP stable, neutral and weakly interacting: neutralino (χ1)• experimental signature: missing ET

• fermion boson • has “no” problems with radiative corrections (quadrat. div.)• has a light Higgs Boson (<150GeV)• interesting pheno at the TeV scale

A typical (optimistic) point

gluinos and squarks (not too heavy)

light sleptons

heavy and light gauginos

Higgs boson mass at the LEP limit

τ1 lighter than the lightest χ± :• χ± BR 100% τν• χ2 BR 90% ττ • cascade:qL χ2 q ℓR ℓ q ℓ ℓ qχ1

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“Physics Interplay of the LHC and ILC” G. Weiglein et al

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SPS1a SPS1a’ SU3 LM1

M0 (GeV) 100 70 100 60

m1/2 (GeV) 250 250 300 250

tanβ 10 10 6 10

A0 (GeV) -100 -300 -300 0

Edges at the LHC

hard jets with leptonsinvariant mass:• jet-lepton• lepton-lepton-jet• lepton-lepton

less statistics: 1-10fb-1

Improvements over past studies:• full simulation and reconstruction • realistic detector description (with additional distorsions)• early Data: 0.5-10fb-1

SUSY08: Paul de Jong, Peter Wienemann, talks by CMS

LHC and ILC measurements

SPS1a

Linear collider• e+e- collisions• up to 1TeV

LHC: lepton energy scale 0.1%LHC: jet energy scale 1%luminosity 100fb-1

1

for the following continue with SPS1a as example

LHC:• from edges/thresholds to masses: toy/fit

ILC:• direct measurements/threshold scans

• mass spectra and decays: SOFTSUSY, SUSPECT, FeynHiggs, ISASUSY,SPHENO, SDecay, SUSY-HIT, HDECAY, NMSSMtools,…• NLO cross sections from Prospino2.0,…• dark matter: micrOMEGAS, DarkSUSY, IsaRED,…

Beenakker et al

Search for parameter point, determine errors including treatement of error correlations:Pioneers: G. Blair, W. Porod and P.M. Zerwas (Eur.Phys.J.C27:263-281,2003) /Allanach et al. hep-ph/0403133 FITTINO: P. Bechtle, K. Desch, P. Wienemann with W. Porod (Eur.Phys.J.C46:533-544,2006)SFITTER: R. Lafaye, T. Plehn, M. Rauch, D. Z. (Eur.Phys.J.C54:617-644,2008)GFITTER: M. Goebel, J. Haller, A. Hoecker, K. Moenig, J. Stelzer (EW fit)EW fits plus dark matter: Buchmueller et al, Phys.Lett.B657:87-94,2007 Super-Bayes: R.R. de Austri, R. Trotta, (MCMC, collider observables and dark matter…)CMSSM fits and weather forcasts: B. Allanach, K. Cranmer, C. Lester, A. Weber…

Determination of Supersymmetric Parameters

from edges, masses (etc) to fundamental parameters:e.g.: mSUGRAm(Smuon) = f(m0, m1/2, tanβ)m(Chargino) = f(m1/2, tanβ,…)correlations exp and theoreticaltreatment of theory errors! global ansatz necessary

See Allanach arXiv:0805.2088[hep-ph] for complete list

Information Extraction from Standard Measurements alone

Buchmueller et al:electroweak plus dark matter, bsγ, bμμCMSSM χ2 slightly better than SMmh=110+8

-10±3GeV

Allanach et al:Predict SUSY cross sections at LHC: ~fb μ and B (high scale parameters)Bayesian measure: same order of magnitude for all parameters (no scale imposed nor unification)slightly higher cross sections in non-Bayesian approach (Profile Likelihood ~maximum instead of measure)

SUSY08: Sven Heinemeyer

Lagrangian@GUT scale: mSUGRA

SPS1a Start

m0 100 1TeV

m1/2 250 1TeV

tanβ 10 50

A0 -100 0GeV

First question:• do we find the right point?

mSUGRA advantage: few parameters, testing ground for studies of principles disadvantage: starts at GUT scale and adds RGE extrapolation, not the most general lagrangian

Sign(μ) fixed

~300 toy experiments: convergence OK with MINUIT alone for LHC (largest errors)!

brute force method GRID:disadvantage: NP advantage: computer industry (OECD?)

Hypothesis: SUSY particles discovered and discrete quantum numbers (spin) measured

brute force method MINUIT:disadvantage: starting point

Lagrangian@GUT scale: mSUGRA

SFitter:Markov Chains (efficient sampling in high dimensions, linear in number of parameters)

Full dimensional exclusive likelihood map with the possibility of different types of projections:• marginalisation (Bayes) introduces a measure• profile likelihood (Frequentist approach)

• Fittino:Simulated annealing

Ranked list of minima:

• secondary minima exist (LHC)• discarded by χ2 alone• interplay with top mass (parameter!)

mSUGRA: Errors RFit Scheme: Höcker, Lacker, Laplace, Lediberder

• use edges not masses (improvement: 10x)!• e-scale correlations at LHC 25-50% impact on error• remember the standard model (top quark mass 1GeV at LHC) 10%.

• No information within theory errors: flat distribution

Higgs sleptons squarks,gluinos neutralinos, charginos

3GeV 1% 3% 1%

mSUGRA: Errors LHC and ILC

SPA project: precision of the theoretical calculations Eur.Phys.J.C46:43-60,2006

• ILC improves by 3-4x on LHC

• LHC+ILC better than any machine alone

• theory errors impact the expected precision at all machines also at LHC

Fittino:• the beginning 1 fb-1

• 1 year low lumi 10 fb-1• 3 years nominal 300 fb-1

and then the ILC:

SFitter

The LHC neutralino enigma

Exchanging χ3 and χ4 leads to a secondary minimum• M0 and M1/2 ok, but tanβ and A0 more than 2-3σ from nominal values• so in principle need ILC to see which neutralino are present….• the predicted mass of χ4 is about 400GeV• the predicted branching ratios would lead us to expect more χ4 than χ3 in the measurement channel in disagrement with the observation• general rule: beware of the “hidden” measurements……

SPS1a LHCmasses ΔLHCmasses LHCedges ΔLHCedges

m0 100 99.6 4 100.3 2.6

m1/2 250 250.1 1.7 248.8 2.1

tanβ 10 8.1 0.8 7.7 0.73

A0 -100 -196 30 -186 39

top 175 175 1 175.5 0.75

χ2/p.d.f 0 - 0.2/16 - 2/11

χ1 97.2 4.8

χ2 180.8 4.7

χ3 -- --

χ4 381.9 5.1

The uniqueness problem: • LHC measures the neutralino index in SPS1a?• permute: χ4 with χ3

MSSM

19 parameters at the EW scaleno unification of the 1st and 2nd generation

• 3 neutralino masses at LHC• M1, M2, μ• 8 fold ambiguity in Gaugino-Higgsino subspace at the LHC!

mix techniques:• markov flat full Parameter space• MINUIT in 5 best points• Markov flat gaugino-higgsino space• MINUIT on 15 best points• BW pdf on remaining parameters• MINUIT on 5 best solutions (all parameters)

LHC+ILC:• all parameters determined• several parameters improved

MSSMRunning up to the GUT scale:G. Blair, W. Porod and P.M. Zerwas (Eur.Phys.J.C27:263-281,2003)P. Bechtle, K. Desch, P. Wienemann with W. Porod (Eur.Phys.J.C46:533-544,2006)

SPS1a (SPA1):dashed bands: today’s theory errors included unification measured from low energy (TeV) data from LHC+ILCremember: all results valid within a well defined model/hypothesis

A difficult example: SUSY with heavy scalars

N. Bernal, A. Djouadi, P. Slavich JHEP 0707:016,2007 E. Turlay et al. (Proceedings BSM-SUSY les Houches 2007)

DSS parameters:• MS: decoupling scale, scalar masses• m1/2: gaugino mass parameter• μ: Higgs mass parameter• At: trilinear coupling at MS• tanβ: mixing angle between Higgs at MS

Phenomenology:• scalar Mass scale 104 to 16 GeV• scalars are at MS

• fermions O(TeV)• SM Higgs h

• effective theory below MS• at MS matching with complete theory and standard RGE

Parameter determination at LHC possible

Arkani-Hamed & Dimopoulos 2004Giudice, Romanino 2004

ATLAS/CMS talks: Paul de Jong, Tapas Sarangi, Daniel Teyssier

Connection Colliders-Cosmology

Measurement of the fluctuations of the cosmic microwave backgroundWMAP• ΩCDMh2=0.127±0.01 (astro-ph/0603449)Planck• ΩCDMh2 ~ 2%

• SUSY breaking parameters (determined)• spectrum and couplings (deduced)• darkSUSY, isaRed or micrOMEGAsΩCDMh2=nLSP*mLSP (relic density)

MSUGRA SPS1a (central value irrelevant)• LHC : Ωh2 = 0.19060.0033• LHC+ILC: Ωh2 = 0.19100.0003• % precision at LHC, permil LHC+ILC• theory errors!

NASA/WMAP science team

Temperature range: ±200μK

E. Baltz,M.Battaglia, M.Peskin, T.Wizansky: Phys.Rev.D74:103521,2006 Nojiri et al/Dutta et al

Comparable precision of CMB and Collider data possible

SPS1a’

Summary• LHC alone could provide a wealth of measurements for SUSY• LHC+ILC is the dream team• will collider dark matter property predictions be comparable to WMAP/Planck?• LHC is starting now, is SUSY just around the corner?

Thank you: Klaus Desch, Remi Lafaye, Tilman Plehn, Michael Rauch, Laurent Serin, Mathias Uhlenbrock, Peter Wienemann

• Hope to start testing grand unification soon!

SFitter+Suspect

MSSM

LHC:• can assign errors on badly measured parameters

LHC+ILC:• all parameters determined• several parameters improved