b8: global fits with gfitter and fittino - desy · b8: global fits with gfitter and fittino....

Annual SFB and GrK MeetingHamburger Sternwarte

4th march 2009

Johannes Haller(Universität Hamburg)

B8: Global fits with Gfitter and Fittino

Johannes Haller The electroweak fit with Gfitter 2

sub-project B8

New sub-project B8 approved in Oct 2008

“Interpretation of physics results from the LHC and other experiments”

Leaders: P. Bechtle (DESY), JH (UHH)

Topics:Extraction methods of observables usable in global fits from early LHC dataStudy of systematic effects using SM standard candles (Z, W)Interpretation of the observables from LHC and other experiments using global fits


Basic principles of fits

experimental measurements compared to theoretical predictions

Often a χ2-like test statistics is minimized

Checking the consistency of the model (“Probing” the model) χ2/ndof , p-value (Prob(χ2,ndof) or better from MC toy)

p-value : probability of wrongly rejecting the model (Measurement of the model parameters (ymod)

In particle physics fits are particularly interesting since physics at much higher scales can be probed via loop corrections

Need precise measurementsNeed accurate predictions

Two fit packages developed in the new B8 project: Gfitter: generic fit project (see later)Fittino: fits of supersymmetric models (see later)

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σχ


The Gfitter project

Gfitter: A Generic Fitter Project for HEP Model TestingAim: provide a modular framework for involved fitting problems in the LHC era (and beyond).

Software:code in C++ built upon ROOT functionalitycore package: tools for data handling, fitting, statistical analyses physics plug-in packages

GSM: Library for the Standard Model fit to the electroweak precision data (this talk)Goblique: BSM fits with oblique parametersG2HDM: Library for the 2HDM extension of the SM… more to come

Recent Paper:H. Flächer (CERN), M. Goebel (UHH/DESY), J. Haller (UHH), A. Höcker(CERN), K. Mönig (DESY), J. Stelzer (DESY),

“Revisiting the Global Electroweak Fit of the Standard Model and Beyond with Gfitter”, CERN-OPEN-2008-024, DESY-08-160, Nov 2008. 66pp, arXiv:0811.0009, accepted by Eur. Phys. Jour. C

http://arxiv.org/abs/0811.0009


Motivation of a global electroweak fit

Huge amount of work done in the pastGlobal electroweak fits routinely done by the LEP EW WG and others

Why a new electroweak fit?Test Gfitter functionality with known fitProvide SM fit in modern SW design for LHC era… and fresh ideas sometimes helpful

Most precise observables in the electroweak sector available from measurements at the Z-pole

LEP: high luminositySLD: electron-beam polarization

Asymmetries and Cross-Sections


Radiative corrections

Important consequence: All other SM parameters enter the calculationsIn particular corrections areloop correction at order ~1%.precision observables measured at LEP/SLC much better !

can test the SM and constraint the unknown SM Parameters

Ht Mm ln and 2 ∝∝

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⎠

⎞

⎜⎜

⎝

⎛−+⋅= 2

22 811

2 ZF

ZW MG

MM πα( )

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⎠

⎞

⎜⎜

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⎛ Δ−⋅−+⋅= 2

22 1811

2 ZF

ZW MG

rMM πα

Experimental precision tree level calculations not sufficient

Tree-level: Higher-orders:


Floating parameters of the SM Fit

Naïve set of free parameters: relevant for the electroweak analysis:Coupling constants: electromagnetic (α), weak (GF), strong (αS)Boson masses: Mγ, MZ, MW, MH

Fermion masses: mf with f = e, μ, τ, νe, νμ, ντ, u, c, t, d, s, b

Simplification: massless neutrinos : mνe=mνμ=mντ=0

Simplification from electroweak unification:Massless photon: Mγ=0Can express MW, as a function of MZand the couplings α and GF

Further simplification by fixing parameters with insignificant uncertainties compared to sensitivity of the fitGF precisely measured (Γμ) fixed to PDG valueleptonic and top contribution to running of α precisely known or small

replace α by Δαhad

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ZW MG

MM πα

25 GeV10)1(16637.1 −−⋅=FG


Floating parameters of the SM FitMasses of leptons and light quarks are small and/or sufficiently well known uncertainties are negligible in the fit

masses are fixed to world-averages from PDGexception: kept as floating fit parameters

but constrained to their experimental values (input measurements to the fit)tbbcc m)(mm, mm and )(

List of remaining parameters in the SM Fit:Δαhad

(5)(MZ2), αS(MZ

2), MZ, MH, mc, mb, mt

Gfitter library: state-of- the art predictions of electroweak observables newly implemented as functions of these parameters

in particular: MW and sin2θeff (light fermions): full two-loop + leading beyond-two-loop corrections [M. Awramik et al., Phys. Rev D69, 053006 (2004 and ref.][M. Awramik et al., JHEP 11, 048 (2006) and refs.], recent 2-loop calculation for b-quarks not yet included, instead full one-loop + leading 2-loop calculation

recent N3LO calculation of radiator functions for the hadronic width [P.A. Baikov

et al., Phys. Rev. Lett. 101 (2008) 012022] included in Gfitter library αs

Calculations and fit results thoroughly cross-checked against ZFitter(Fortran) package → excellent agreement


Summary of observables

Usage of latest experimental results:Z-pole observables: LEP/SLD results [ADLO+SLD, Phys. Rept. 427, 257 (2006)]

Total cross-sections sensitive to total coupling strength of Z to fermions: MZ, ΓZ, σhad

0, Rl0, Rc

0, Rb0

Asymmetries sensitive to the ratio of the Z vector- to axial-vector couplings (ie sin2qeff): AFB

0,l, AFB0,b, AFB

0,c, Al, Ac, Ab,, sin2θl

eff (QFB)

MW and ΓW: latest world average[ADLO+TeVatron,arXiv:0811.4682]

mc, mb: world averages [PDG, J. Phys. G33,1 (2006)]

mt: latest Tevatron average [CDF+D0, arXiv:0808.1089]

Δαhad(5)(MZ

2): [K. Hagiwara et al., Phys. Lett. B649, 173 (2007)]

Fits are performed in two versions:Standard fit: all data except results from direct Higgs searchesComplete fit: all data including results from direct Higgs searches at LEP and Tevatron


Standard fit (i.e. w/o Higgs searches)

Standard fit converges at global minimum of χ2

min=16.4 with ndof=13p-value: Prob(16.4,13)=0.23No single pull exceeds 3σ

Pulls of some floating parameters (mb, mc, MZ, Δαhad, (mt))) are very small

Parameters could have been fixed without significant impact on goodness-of-fit

measurement fit result


Standard fit (i.e. w/o Higgs searches)

Scan of Δχ2=χ2-χ2min as function of MH from standard fit:

GeV 80 3023

+−=HMcentral value ±1σ:

2σ interval: [39, 155] GeV3σ interval: [26, 209] GeVTheory errors directly included in χ2 of fit! (flat likelihood in allowed ranges)Including errors → smaller ndof → smaller χ2

min

For comparison


Results published using likelihood ratios

Difference of data to SM expectation (s+b) translated into contribution to χ2

Insertion of the direct Higgs searches

Information on MH also from direct Higgs searches (LEP/Tevatron)

LEPTevatron, 2.4fb-1(appr.) Tevatron, 3fb-1

bbs LLQ /+=Qln2−

data

exp. for “s+b”

exp. for “b”


central value ±1σ:

2σ interval: [114, 145] GeV3σ interval: [[113, 168] and

[180,225]] GeV

Results of complete fit (i.e. with Higgs searches)

The complete fit converges at a global minimum of χ2

min=18.0 for ndof=14 p-value=0.21

Scan of Δχ2 as function of MH:

Note: “hypothesis-only” test (like the –2lnQ curves delivered by the collab.)Procedure tests only the MH under consideration It neglects that a given SM signal hypothesis entails background hypotheses

I.e. if SM Higgs is found at a certain MH other values of MH are excludedeffect expected to be small today, but relevant once the Higgs is discovered.

GeV 4.116 3.183.1

+−=HM


Gfitter allows 1-dim, 2-dim scans and contour plotsFit (i.e. excluding the Higgs searches and the respective measurements)Fit + Higgs searchesFit + Higgs searches + direct measurements best knowledge of SM

Indirect fit results agree with experimental values SM consistencyHiggs searches significantly reduce the allowed parameter space.

for comparison:




Other examples: MH vs. variables with strongest correlation with MH

Fit (i.e. excluding the respective measurements and Higgs searches)Fit + respective measurementsFit + respective measurements + Higgs searches

The structures reflect presence of local minima in (Δχ2 vs. MH)-plotToday’s precision in Δαhad and mt sufficient for this fit


Probability of falsely rejecting the SM is sufficient no significant requirement for BSM physics

Deeper statistical analysis

evaluation of p-value of global SM fit using MC toy experiments

For each toy complete fit is performed

02.001.022.0value −±=−p

Derivation of p-values for standard fit as function of MH

Curve gives the probability of wrongly rejecting the SM hypothesis assuming a certain value for MH.


Prospects of the fit with future colliders

Future colliders (LHC/ILC) can increase precision of electroweak observables

Improvement of the predictive power of the fitHiggs discovery testing goodness-of-fit sensitivity to new physics

Expected improvement from LHC:δMW: 25 MeV 15 MeVδmt: 1.2 GeV 1.0 GeV

Expected improvement from ILC:From threshold scan δmt=50 MeV, translates to 100-200 MeV on the MS-mass

Expected improvement from GigaZ:From WW threshold scan: δMW=6 MeVFrom ALR: δsin2θl

eff : 17·10-5 1.3·10-5

δRl0: 2.5·10-2 0.4·10-2

improved determination of Δαhad

(5)(MZ2) will be needed

needs improvement in hadroniccross section data around cc res. [Jegerlehner, hep-ph/0105283]: expected uncertainty of 7·10-5

(today 22·10-5) if relative cross-section precision below J/Ψ 1%Experiments with better acceptances and control of systematics needed Promising: ISR analyses at B and Φ factories; new data from BESIII


Prospects of the fit with future colliders

Summary of expected improvements

Δχ2 profileAssume MH=120 GeV by adjusting central values of observablesTheoretical errors

broad plateauLarge improvement with GigaZ option

With mH measured at LHC with ~1% MW prediction with 13 MeV confront with experiment, check p-value


… and many more results

Deeper statistical analysis of the fitOblique parameters (littlest Higgs model)2HDM extension of the SM… ww.cern.ch/gfitter


Fits of supersymmetric models using Fittino

People: P. Bechtle (DESY), K. Desch, M. Uhlenbrock, P. Wienemann (U Bonn)

SUSY predictions from SoftSUSY and Mastercode (combination ofSoftSUSY, FeynHiggs, SuperIso, MicrOMEGAs, DarkSUSYimplementation)

mSUGRA, GMSB, MSSM18

Experimental observables used:SM precision observables (see before)Low-energy observables: (g-2)μ, BR(b sγ), BR(Bs Xsll), BR(B τν), Δ(MBs), BR(K ln)Cosmology: density of cold dark matter ΩCDMh2

Future measurements: LHC + ILC


mSUGRA fit results

Using SM + LE observablesFloating parameters:

SM parameters mSUGRA parameters

Fixing |μ|=+Fit converges at χ2=20.2 with ndof=21 Prob()=51%Fixing SM parameters makes no difference (MHpredicted in SUSY)


GMSB fit results

Using SM + LE observablesFloating parameters:

SM parameters GMSB parameters

Fixing |μ|=+, N5=1Fit converges at χ2=19.4 with ndof=56 Prob()=56%Fixing SM parameters makes no difference (MHpredicted in SUSY)


mSUGRA fits with LE observables

Fit results can also be translated in “predictions” of SUSY masses

Example: mSUGRA

In M0-M1/2 plane:1σ allowed region including all observables2σ allowed region incl. SM+ B-physics (e.g. b sγ)2σ allowed region incl. SM+ B-physics + (g-2)μ

To be compared with LHC discovery potential


Input from LHCLHC:

no direct mass measurementsInformation from edges in invariant mass distributions

Test scenario: mSUGRA SPS1aM0=100, M1/2=250, A0=-100, tanβ=10, |μ|=+

using expected measurements from ATLAS CSC + CMS TDRLE observables shifted to expected values

Already with 10 fb-1 LHC can constraint mSUGRA parameters… if mSUGRA really realized in nature ! (check p-value)


SUSY fits and the need for the ILC

However, what happens in more realistic SUSY scenarios ?Higher number of degree of freedom E.g. MSSM with 18 free parameters (still assumes CP conservation, no flavour mixing between sectors, first and second generation same RGE running)

LHC data not sufficient to constraint modelPrecision from ILC very helpful

LE + LHC (300fb-1): LE + LHC +ILC:


Summary

New SFB project B8 “Interpretation of physics results from the LHC and other experiments”Started in Oct 2008Interesting results obtained already

Fittino:Fits of supersymmetric modelsObservables from low energy + LHC + ILC

Gfitter:Global SM fitOblique parameters (littlest Higgs Model)2HDM fit…

b8: global fits with gfitter and fittino - desy · b8: global fits with gfitter and fittino....

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