Extraction of Parameters from Collider Data?

NPF 2009 Heidelberg02/26/2009

Klaus Desch and Dirk ZerwasUni Bonn and LAL Orsay

• Introduction• Finding the right parameter set• getting the errors right• other applications• Open questions

• Definition 1: mSUGRA=toy (Klaus left to hide from Tilman)• Definition 2: MSSM=oset 4711

• 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 treatment 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)Master Code: Buchmueller et al, Phys.Lett.B657:87-94,2007 (my name is Vader, Dirk Vader)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.: mSUGRA (from Klaus to Tilman with love)m(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

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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~ ~

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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

Forced to talk about SPS1a(‘) by genetic pre-disposition (quote from Mihoko)

SUSY already discovered?

Global mSugra fit to measured things… (to compare with Buchmüller ea – consistent)

dominated by g-2 and h2DM - but encouraging…

From LE fit: predicted mass spectra

no (g-2) no h2DM

Prediction driven by g-2 and Ωh2

LHC measurements

SPS1a

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

1

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

NPF: Shoji, Dan

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?

Sign(μ) fixed

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

brute force method GRID:disadvantage: NP advantage: computer industry

Hypothesis: SUSY particles discovered and non-discrete quantum numbers to be measured

brute force method MINUIT:disadvantage: starting point

Model discrimination

What are fits to mSugra are good for after all?

- rule out the most simple assumptions (degenerate masses…)- discriminate between different „digital“ assumptions, e.g.

sgn

=

-1

sgn = +1

with 1 fb-1: correct model (sgn =+)preferred with 96% probability

misinterpreation of edgereplace

with 1 fb-1: correct modelpreferred with 77% probability

Lagrangian@GUT scale: mSUGRA

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)

Simulated annealing

Ranked list of minima:

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

Fittino: error determination from Toy Fits

Parameter fits: 2 distribution as reliable „quality control“ for derived uncertainties - simulated annealing find global minimum - Toy MC map out spread of parameters when observables vary within their expt. errors

MC Toy fits:

mSUGRA: Theory Errors and Standard Model 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%

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)

MSSM18

Tilman doesn‘t like mSugra – so could we fit (much) more general models?

LHC: 300 fb-1

But remember: this maybe possible in the „best of all worlds“ (=SPS1a-like point)Much less will be possible if e.g. no dilepton edge is visible

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

The Higgs sectorMeasurements

Theory Errors

Experimental Errors

Applying same techniques:Likelihood map with reduction of dimensions either Bayesian of Profile Likelihood (more appropriate here in absence of true secondary minima)

Thanks Gavin

SFitter+Michael Duehrssen

Profile likelihood 30fb-1 theory errors

ZH/WH absent

ZH/WH full sensitivity

ZH/WH half sensitivity

Questions for discussion• Several methods to scan n-dimensional parameter space. Enough?• Agree on error treatment (esp theory errors)?• extension from SUSY model A to SUSY model B easy• Higgs sector study ok • other non-susy models? • How to communicate (spectrum/observables) without re-inventing the wheel?• Do these models Z’, UED etc need n-dimensional scan tools?• Is it a particularity of SUSY that a measurement depends on N parameters?• Is the theoretical precision sufficient everywhere? • Inclusion of exclusion?• observed rates: clearly, how to predict N (SUSY pars) for fits? how to implement in fits?• interfacing to theory codes: SLHA quite good – problems if > 1 code is used in a fit (e.g. separate RGE running in SPheno + mastercode)• fast (parametrized) rate calculator – any ideas?• stability of Markov chain MCs (dependence on start values, alg. parameters, statistics,…)

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

backup: LE input

backup: MSSM18 fitted model parameters

backup: LHC inputs

note: - all inputs based on +- recent ATLAS/CMS simulation - of course „correct“ interpretation of the edges is assumed / wrong assignment has to be tested separately