Annual SFB and GrK Meeting Hamburger Sternwarte 4 th march 2009 B8: Global fits with Gfitter and Fittino Johannes Haller (Universität Hamburg)
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 data Study of systematic effects using SM standard candles (Z, W) Interpretation of the observables from LHC and other experiments using global fits Johannes Haller The electroweak fit with Gfitter 2
Basic principles of fits experimental measurements compared to theoretical predictions Often a χ 2 -like test statistics is minimized Checking the consistency of the model ( Probing the model) χ 2 /n dof, p-value (Prob(χ 2,n dof ) or better from MC toy) p-value : probability of wrongly rejecting the model ( Measurement of the model parameters (y mod ) In particle physics fits are particularly interesting since physics at much higher scales can be probed via loop corrections Need precise measurements Need accurate predictions Two fit packages developed in the new B8 project: Gfitter: Fittino: generic fit project (see later) χ fits of supersymmetric models (see later) = ( xi,exp xi,theo( ymod ) 2 2 ) i σ i 2 Johannes Haller The electroweak fit with Gfitter 3
The Gfitter project Gfitter: A Generic Fitter Project for HEP Model Testing Aim: provide a modular framework for involved fitting problems in the LHC era (and beyond). Software: code in C++ built upon ROOT functionality core 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 parameters G2HDM: 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 Johannes Haller The electroweak fit with Gfitter 4
Motivation of a global electroweak fit Huge amount of work done in the past Global electroweak fits routinely done by the LEP EW WG and others Why a new electroweak fit? Test Gfitter functionality with known fit Provide 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 luminosity SLD: electron-beam polarization Asymmetries and Cross-Sections Johannes Haller The electroweak fit with Gfitter 5
Radiative corrections Experimental precision tree level calculations not sufficient Tree-level: Higher-orders: M 2 M Z πα = 1+ 1 2 2 G F M Z 2 8 W M 2 M Z 8πα = 1+ 1 2 2 G FM Z 2 1 W ( Δr) Important consequence: All other SM parameters enter the calculations 2 In particular corrections are m and ln loop correction at order ~1%. t M H precision observables measured at LEP/SLC much better! can test the SM and constraint the unknown SM Parameters Johannes Haller The electroweak fit with Gfitter 6
Floating parameters of the SM Fit Naïve set of free parameters: relevant for the electroweak analysis: Coupling constants: electromagnetic (α), weak (G F ), strong (α S ) Boson masses: M γ, M Z, M W, M H Fermion masses: m f with f = e, μ, τ, ν e, ν μ, ν τ, u, c, t, d, s, b Simplification: massless neutrinos : m νe =m νμ =m ντ =0 Simplification from electroweak unification: Massless photon: M γ =0 Can express M W, as a function of M Z and the couplings α and G F Further simplification by fixing parameters with insignificant uncertainties compared to sensitivity of the fit G F precisely measured (Γ μ ) fixed to PDG value G F = leptonic and top contribution to running of α precisely known or small replace α by Δα had M 2 M Z πα = 1+ 1 2 2 G F M Z 2 8 W 1.16637(1) 10 5 GeV 2 Johannes Haller The electroweak fit with Gfitter 7
Floating parameters of the SM Fit Masses 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 PDG m exception: kept as floating fit parameters c ( m c ), m (m b b ) and m t but constrained to their experimental values (input measurements to the fit) List of remaining parameters in the SM Fit: Δα had (5) (M Z2 ), α S (M Z2 ), M Z, M H, m c, m b, m t Gfitter library: state-of- the art predictions of electroweak observables newly implemented as functions of these parameters in particular: M W and sin 2 θ eff (light fermions): full two-loop + leading beyondtwo-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 N 3 LO calculation of radiator functions for the hadronic width [P.A. Baikov et al., Phys. Rev. Lett. 101 (2008) 012022] included in Gfitter library α s Calculations and fit results thoroughly cross-checked against ZFitter (Fortran) package excellent agreement Johannes Haller The electroweak fit with Gfitter 8
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: M Z, Γ Z, σ had0, R l0, R c0, R b 0 Asymmetries sensitive to the ratio of the Z vector- to axial-vector couplings (ie sin 2 q eff ): A FB 0,l, A FB 0,b, A FB 0,c, A l, A c, A b,, sin 2 θ l eff (Q FB ) M W and Γ W : latest world average [ADLO+TeVatron,arXiv:0811.4682] m c, m b : world averages [PDG, J. Phys. G33,1 (2006)] m t : latest Tevatron average [CDF+D0, arxiv:0808.1089] Δα had (5) (M Z2 ): [K. Hagiwara et al., Phys. Lett. B649, 173 (2007)] Fits are performed in two versions: Standard fit: all data except results from direct Higgs searches Complete fit: all data including results from direct Higgs searches at LEP and Tevatron Johannes Haller The electroweak fit with Gfitter 9
Standard fit (i.e. w/o Higgs searches) measurement fit result Standard fit converges at global minimum of χ 2 min=16.4 with n dof =13 p-value: Prob(16.4,13)=0.23 No single pull exceeds 3σ Pulls of some floating parameters (m b, m c, M Z, Δα had, (m t) )) are very small Parameters could have been fixed without significant impact on goodness-of-fit Johannes Haller The electroweak fit with Gfitter 10
Standard fit (i.e. w/o Higgs searches) Scan of Δχ 2 =χ 2 -χ 2 min as function of M H from standard fit: For comparison central value ±1σ: M H = + 80 30 23 GeV 2σ interval: [39, 155] GeV 3σ interval: [26, 209] GeV Theory errors directly included in χ 2 of fit! (flat likelihood in allowed ranges) Including errors smaller n dof smaller χ 2 min Johannes Haller The electroweak fit with Gfitter 11
Insertion of the direct Higgs searches Information on M H also from direct Higgs searches (LEP/Tevatron) data exp. for b exp. for s+b Results published using likelihood ratios 2lnQ Q = L s / L + b b Difference of data to SM expectation (s+b) translated into contribution to χ 2 LEP Tevatron, 2.4fb -1 (appr.) Tevatron, 3fb -1 Johannes Haller The electroweak fit with Gfitter 12
Results of complete fit (i.e. with Higgs searches) The complete fit converges at a global minimum of χ 2 min=18.0 for n dof =14 p-value=0.21 Scan of Δχ 2 as function of M H : central value ±1σ: M H = 116.4 + 18.3 1.3 GeV 2σ interval: [114, 145] GeV 3σ interval: [[113, 168] and [180,225]] GeV Note: hypothesis-only test (like the 2lnQ curves delivered by the collab.) Procedure tests only the M H under consideration It neglects that a given SM signal hypothesis entails background hypotheses I.e. if SM Higgs is found at a certain M H other values of M H are excluded effect expected to be small today, but relevant once the Higgs is discovered. Johannes Haller The electroweak fit with Gfitter 13
Results of complete fit (i.e. with Higgs searches) Gfitter allows 1-dim, 2-dim scans and contour plots Fit (i.e. excluding the Higgs searches and the respective measurements) Fit + Higgs searches Fit + Higgs searches + direct measurements best knowledge of SM for comparison: Indirect fit results agree with experimental values SM consistency Higgs searches significantly reduce the allowed parameter space. Johannes Haller The electroweak fit with Gfitter 14
Results of complete fit (i.e. with Higgs searches) Other examples: M H vs. variables with strongest correlation with M H Fit (i.e. excluding the respective measurements and Higgs searches) Fit + respective measurements Fit + respective measurements + Higgs searches The structures reflect presence of local minima in (Δχ 2 vs. M H )-plot Today s precision in Δα had and m t sufficient for this fit Johannes Haller The electroweak fit with Gfitter 15
Deeper statistical analysis evaluation of p-value of global SM fit using MC toy experiments For each toy complete fit is performed Derivation of p-values for standard fit as function of M H p value = 0.22 ± 0.01 0.02 Probability of falsely rejecting the SM is sufficient no significant requirement for BSM physics Curve gives the probability of wrongly rejecting the SM hypothesis assuming a certain value for M H. Johannes Haller The electroweak fit with Gfitter 16
Prospects of the fit with future colliders Future colliders (LHC/ILC) can increase precision of electroweak observables Improvement of the predictive power of the fit Higgs discovery testing goodness-of-fit sensitivity to new physics Expected improvement from LHC: δm W : 25 MeV 15 MeV δm t : 1.2 GeV 1.0 GeV Expected improvement from ILC: From threshold scan δm t =50 MeV, translates to 100-200 MeV on the MSmass Expected improvement from GigaZ: From WW threshold scan: δm W =6 MeV From A LR : δsin 2 θ l eff : 17 10-5 1.3 10-5 δr l0 : 2.5 10-2 0.4 10-2 improved determination of Δα had (5) (M Z2 ) will be needed needs improvement in hadronic cross section data around cc res. [Jegerlehner, hep-ph/0105283]: expected uncertainty of 7 10-5 (today 22 10-5 ) if relative crosssection 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 Johannes Haller The electroweak fit with Gfitter 17
Prospects of the fit with future colliders Summary of expected improvements Δχ 2 profile Assume M H =120 GeV by adjusting central values of observables Theoretical errors broad plateau Large improvement with GigaZ option With m H measured at LHC with ~1% M W prediction with 13 MeV confront with experiment, check p-value Johannes Haller The electroweak fit with Gfitter 18
and many more results Deeper statistical analysis of the fit Oblique parameters (littlest Higgs model) 2HDM extension of the SM ww.cern.ch/gfitter Johannes Haller The electroweak fit with Gfitter 19
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 of SoftSUSY, FeynHiggs, SuperIso, MicrOMEGAs, DarkSUSY implementation) msugra, GMSB, MSSM18 Experimental observables used: SM precision observables (see before) Low-energy observables: (g-2) μ, BR(b sγ), BR(B s X s ll), BR(B τν), Δ(M Bs ), BR(K ln) Cosmology: density of cold dark matter Ω CDM h 2 Future measurements: LHC + ILC Johannes Haller The electroweak fit with Gfitter 20
msugra fit results Using SM + LE observables Floating parameters: SM parameters msugra parameters Fixing μ =+ Fit converges at χ 2 =20.2 with n dof =21 Prob()=51% Fixing SM parameters makes no difference (M H predicted in SUSY) Johannes Haller The electroweak fit with Gfitter 21
GMSB fit results Using SM + LE observables Floating parameters: SM parameters GMSB parameters Fixing μ =+, N 5 =1 Fit converges at χ 2 =19.4 with n dof =56 Prob()=56% Fixing SM parameters makes no difference (M H predicted in SUSY) Johannes Haller The electroweak fit with Gfitter 22
msugra fits with LE observables Fit results can also be translated in predictions of SUSY masses Example: msugra In M 0 -M 1/2 plane: 1σ allowed region including all observables 2σ 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 Johannes Haller The electroweak fit with Gfitter 23
LHC: no direct mass measurements Information from edges in invariant mass distributions Test scenario: msugra SPS1a M 0 =100, M 1/2 =250, A 0 =-100, tanβ=10, μ =+ using expected measurements from ATLAS CSC + CMS TDR LE observables shifted to expected values Already with 10 fb -1 LHC can constraint msugra parameters if msugra really realized in nature! (check p-value) Input from LHC Johannes Haller The electroweak fit with Gfitter 24
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 model Precision from ILC very helpful LE + LHC (300fb -1 ): LE + LHC +ILC: Johannes Haller The electroweak fit with Gfitter 25
Summary New SFB project B8 Interpretation of physics results from the LHC and other experiments Started in Oct 2008 Interesting results obtained already Gfitter: Global SM fit Oblique parameters (littlest Higgs Model) 2HDM fit Fittino: Fits of supersymmetric models Observables from low energy + LHC + ILC Johannes Haller The electroweak fit with Gfitter 26