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Revisiting the Global Electroweak Fit of the Standard Model and Beyond

Revisiting the Global Electroweak Fit of the Standard Model and Beyond. Andreas H oecker (CERN) CAT Physics meeting, Dec 17, 2008. Gfitter Group : M. G ö bel, J. Haller, K. M ö nig, J. Stelzer (DESY) and H. Fl ä cher (CERN). Gfitter on the web: http://cern.ch/gfitter

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Revisiting the Global Electroweak Fit of the Standard Model and Beyond

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  1. Revisiting the Global Electroweak Fit of the Standard Model and Beyond Andreas Hoecker (CERN) CAT Physics meeting, Dec 17, 2008 Gfitter Group: M. Göbel, J. Haller, K. Mönig, J. Stelzer (DESY) and H. Flächer (CERN) Gfitter on the web: http://cern.ch/gfitter Paper reference for this talk: http://arxiv.org/abs/0811.0009, submitted to EPJ-C Gfitter code SVN repository: https://svnweb.cern.ch/world/wsvn/Gfitter/ A. Hoecker: Multivariate Analysis with TMVA

  2. From One Fit to the Other … The phenomenological exploitation of the experimental results in global fits … • should be done by collaboration of theoristsandexperimentalists • experimentalists learn theoretical background • theorists learn complex data treatment CKMfitter: http://ckmfitter.in2p3.fr See also M. Kobayashi’s Nobel lecture Gfitter: http://cern.ch/gfitter A. Hoecker: Multivariate Analysis with TMVA

  3. Why a new Global Electroweak (EW) Fit ? http://lepewwg.web.cern.ch/LEPEWWG/ • Global EW fits have been developed during the 90ies (LEP) amongst which is the ZFITTER Fortran EW library • Famous “Blue-band” plot provided by LEP Electroweak Working Group (LEPEWWG) • However, there are several problems: • Old programme structure, outdated programming language • Missing statistics library, toy tests, etc; inconsistent treatment of theory errors • Hard to maintain in line with experimental and theoretical progress • Unsatisfactory to rely on them during LHC area and ILC preparations • Difficult to add beyond SM scenarios, impossible to scan observables • This lead to development of Gfitter package A. Hoecker: Multivariate Analysis with TMVA

  4. Gfitter http://cern.ch/Gfitter • Outline: • The Gfitter project • The global electroweak fit – present and future • The Two-Higgs-Doublet-Model A. Hoecker: Multivariate Analysis with TMVA

  5. Abstract: The global fit of the Standard Model to electroweak precision data, routinely performed by the LEP electroweak working group and others, demonstrated impressively the predictive power of electroweak unification and quantum loop corrections. We have revisited this fit in view of (i) the development of the new generic fitting package Gfitter, (ii) the insertion of constraints from direct Higgs searches at LEP and the Tevatron, and (iii) a more thorough statistical interpretation of the results. Gfitter is a modular fitting toolkit, which features predictive theoretical models as independent plugins, and a statistical analysis of the fit results using toy Monte Carlo techniques. The state-of-the-art electroweak Standard Model is fully implemented, as well as generic extensions to it. This paper introduces the Gfitter project, and presents state-of-the-art results for the global electroweak fit in the Standard Model, and for a model with an extended Higgs sector (2HDM). Numerical and graphical results for fits with and without including the constraints from the direct Higgs searches at LEP and Tevatron are given. Perspectives for future colliders are analysed and discussed. Including the direct Higgs searches, we find MH = (116.4 +18.3 –1.3) GeV, and the 2sigma and 3sigma allowed regions [114,145] GeV and [[113,168] and [180,225]] GeV, respectively. For the strong coupling strength at fourth perturbative order we obtain S(MZ) = 0.1193 +0.0028 -0.0027(exp) ± 0.0001(theo). Finally, for the mass of the top quark, excluding the direct measurements, we find mtop= (178.2 +9.8 –4.2) GeV. In the 2HDM we exclude a charged-Higgs mass below 240 GeV at 95% confidence level. This limit increases towards larger tan(), where e.g., MH± < 780 GeV is excluded for tan() = 70. arXiv : 0811.0009 A. Hoecker: Multivariate Analysis with TMVA

  6. The Gfitter Project • Gfitter: A Generic Fitter Project for HEP Model Testing • Aim: provide a reliable and modular framework for involved HEP fitting problems in the LHC era (and beyond) • Software: • Modular object-oriented code in C++ based on ROOT functionality • Core package: • tools for data handling, fitting, statistical analysis • Physics: plug-in packages • GSM: Library for the Standard Model fit to the electroweak precision data (this talk) • G2HDM: Library for the 2HDM extension of the SM (this talk) • GSUSY: Library for Supersymmetry extensions of the SM (in preparation) A. Hoecker: Multivariate Analysis with TMVA

  7. Gfitter code on the web: https://svnweb.cern.ch/trac/Gfitter/browser Check out Gfitter: svn co svn+ssh://<your_afs_account>@svn.cern.ch/reps/Gfitter Gfitter drwxr-xr-x 3 zp 6.0K Dec 15 21:19 src/ drwxr-xr-x 3 zp 4.0K Dec 15 21:19 gsm/ drwxr-xr-x 3 zp 2.0K Dec 15 21:19 g2hdm/ drwxr-xr-x 3 zp 2.0K Dec 15 21:20 goblique/ drwxr-xr-x 3 zp 2.0K Dec 15 21:20 glh/ drwxr-xr-x 3 zp 2.0K Dec 15 21:20 gsusy/ drwxr-xr-x 3 zp 2.0K Dec 15 21:19 gckm/ drwxr-xr-x 3 zp 2.0K Dec 15 21:19 gtest/ drwxr-xr-x 3 zp 2.0K Dec 15 21:19 test/ drwxr-xr-x 6 zp 2.0K Dec 15 21:19 macros/ drwxr-xr-x 3 zp 2.0K Dec 15 21:19 scripts/ drwxr-xr-x 5 zp 2.0K Dec 15 21:19 apps/ drwxr-xr-x 6 zp 2.0K Dec 15 21:20 doc/ -rwxr-xr-x 1 zp 979 Dec 15 21:20 setup.sh -rwxr-xr-x 1 zp 1.2K Dec 15 21:20 setup.csh -rw-r--r-- 1 zp 822 Dec 15 21:20 README.svn -rw-r--r-- 1 zp 1.3K Dec 15 21:20 README -rw-r--r-- 1 zp 1.7K Dec 15 21:20 LICENSE A. Hoecker: Multivariate Analysis with TMVA

  8. The Gfitter Project • Gfitter features: • Consistent treatment of statistical, systematic and theoretical errors, correlations, and inter-parameter dependencies • theoretical uncertainties: Rfit prescription: [CKMfitter Group: EPJ C21, 225 (2002)] theory uncertainties included in 2 with uniform likelihood within allowed ranges • Fitting: • several minimization algorithms available (GA, SA via TMVA), default: TMinuit • Caching of computation results between fit steps • recalculatedonly the theory predictions that depend on modified parameters • substantial speed improvement • Advanced statistical analysis: • e.g. observable scans, contours, MC toy analyses, goodness-of-fit p-value, … • dynamic rescaling in case of parameter interdependencies A. Hoecker: Multivariate Analysis with TMVA

  9. T h e G l o b a l E W F i t Since the neutral weak vector boson, Z0, couples to all fermion and anti-fermion pairs, it is an ideal particle for measuring and studying the electroweak and strong interactions. A. Hoecker: Multivariate Analysis with TMVA

  10. H H Theoretical Prediction • First theoretical library implemented in Gfitter framework: SM predictions of electroweak precision observables • State-of-the art calculations, in particular: • MWand sin2feff : 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.] • Radiator functions: N3LO prediction of the massless QCD cross section • [P.A. Baikov et al., Phys. Rev. Lett. 101 (2008) 012022] Logarithmic Higgs dependence enters through virtual corrections, e.g. : A. Hoecker: Multivariate Analysis with TMVA

  11. Theoretical Prediction • First theoretical library implemented in Gfitter framework: SM predictions of electroweak precision observables • State-of-the art calculations, in particular: • MWand sin2feff : 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.] • Radiator functions: N3LO prediction of the massless QCD cross section • [P.A. Baikov et al., Phys. Rev. Lett. 101 (2008) 012022] • Wherever possible, calculations cross-checked against ZFITTER  excellent agreement • Free fit parameters are : • MZ, MH, mt, had(MZ), s(MZ), mc, mb • Scale parameters for theoretical uncertainties on MW ((MW)= 4–6 MeV), sin2leff ((sin2leff) = 4.7·10–5), and the electroweak form factors fZ, fZ A. Hoecker: Multivariate Analysis with TMVA

  12. Experimental Input • Usage of latest experimental results: • Z-pole observables: LEP/SLD results • [ADLO+SLD, Phys. Rept. 427, 257 (2006)] • MW and W: LEP + Tevatron • [ADLO, hep-ex/0612034] [CDF, Phys Rev. D77, 112001 (2008)] [CDF, Phys. Rev. Lett. 100, 071801 (2008)] [CDF+D0, Phys. Rev. D 70, 092008 (2004)] • mc, mb: world averages [PDG, J. Phys. G33,1 (2006)] • mt: latest Tevatron average [arXivx:0808.1089 [hep-ex]] • had(MZ): [K. Hagiwara et al., Phys. Lett. B649, 173 (2007)] + Gfitter rescaling mechanism to account for s dependency • Direct Higgs searches at LEP and Tevatron • [ADLO: Phys. Lett. B565, 61 (2003)][CDF+D0: arXiv:0804.3423, CDF+D0: arXiv:0808.0534] • All SM fits performed in two versions: • Standard Fit: all data except for direct Higgs searches • Complete Fit: all data including direct Higgs searches A. Hoecker: Multivariate Analysis with TMVA

  13. Experimental Input A. Hoecker: Multivariate Analysis with TMVA

  14. Input from Direct Higgs Searches Since LEP, experiments use vexatious statistical means for the interpretation direct Higgs searches … (won’t go into the details here !) • In Gfitter: usage of CLS+B(non-optimal, but best we can do with given experimental information) • Describes probability of upwards fluctuations of the test statistics • (LLR: –2lnQ, where Q = LS+B / LB) • Transform one-sided CLS+B into a two-sided CLS+B • Contribution to 2 estimator obtained via inverse error function: More info in backup High-mass update, replaces results from left plot A. Hoecker: Multivariate Analysis with TMVA

  15. Input from Direct Higgs Searches • Contribution to 2 function from direct Higgs searches: A. Hoecker: Multivariate Analysis with TMVA

  16. Experimental Input and Fit Results A. Hoecker: Multivariate Analysis with TMVA

  17. Experimental Input and Fit Results A. Hoecker: Multivariate Analysis with TMVA

  18. Fit Results Pulls of completefit • Goodness of fit: • Standard fit: 2min =16.4 → Prob(2min,13) = 0.23 • Complete fit: 2min=18.0 → Prob(2min,14) = 0.21 • (see later for toy-based GoF evaluation) • Pull values for Complete Fit:(right figure) • No individual pull exceeds 3 • FB(b) asymmetry largest contributor to 2min • Small contributions from MZ, had(MZ), mc, mb indicate that their input accuracies exceed fit requirements A. Hoecker: Multivariate Analysis with TMVA

  19. Goodness of Fit from Toy MC Analysis • From toy analysis: p-value for wrongly rejecting the SM = 0.22 ± 0.01–0.02 (theo) CompleteFit Total of 10,000 toy experiments A. Hoecker: Multivariate Analysis with TMVA

  20. Higgs Mass Constraint StandardFit • MH from Standard Fit: • Central value ±1: • 2 interval: [39, 155] GeV • 3 interval: [26, 209] GeV Green band due to Rfit treatment of theory errors, fixed errors lead to larger 2min CompleteFit • MH from Complete Fit(incl. direct Higgs searches): • Central value ±1: • 2 interval: [114, 145] GeV • 3 interval: [113, 168] and [180, 225] GeV A. Hoecker: Multivariate Analysis with TMVA

  21. Higgs Mass Constraint Known tension between A0,bFB and Alep(SLD) and MW: • Toy analysis gives for “probability to observe a 2 = 8.0 when removing the least compatible input”: 1.4% (2.5) Right: central value for MH when excluding indicated observable from fit Below (complementary): fits include only the given observable A. Hoecker: Multivariate Analysis with TMVA

  22. Higgs Mass Constraint • Gaussian behavior? Toy scan of Higgs mass to “measure” confidence level curve StandardFit A. Hoecker: Multivariate Analysis with TMVA

  23. Top-Quark Mass • Quadratic dependence of EW fit on mtop • Standard fit: • Complete fit: • Tevatron average: (172.4 ± 1.2) GeV for comparison A. Hoecker: Multivariate Analysis with TMVA

  24. Next-to-next-to-next-to-LO Determination of s • s(MZ) from Complete Fit: • s(MZ) = 0.1193 ± 0.0028 ± 0.0001 • First error experimental • Second error theoretical (!) • [ incl. variation of renorm. scale from MZ/2 to 2MZ and massless terms of order/beyond aS5(MZ) and massive terms of order/beyond aS4(MZ) ] • Excellent agreement with recent N3LO result from hadronic  decays [M. Davier et al., arXiv:0803.0979] • s(MZ) = 0.1212 ± 0.0005exp • ± 0.0008theo • ± 0.0005evol Left: 4-loop RGE evolution of s() and measurements A. Hoecker: Multivariate Analysis with TMVA

  25. P r o s p e c t s f o r t h e S M F i t A. Hoecker: Multivariate Analysis with TMVA

  26. Prospects for LHC, ILC and ILC with Giga-Z • Assumed experimental improvements for prospective study: • LHC: MW, mtop • ILC: MW, mtop • Giga-Z: MW, mtop, sin2leff, Rlep • ISR-based (BABAR) and BESIII cross-section measurements should improve had(MZ) A. Hoecker: Multivariate Analysis with TMVA

  27. Prospects for LHC, ILC and ILC with Giga-Z • Prospective study: results on MH, including (solid) and excluding (dotted) theoretical errors StandardFit A. Hoecker: Multivariate Analysis with TMVA

  28. T w o – H i g g s – D o u b l e t M o d e l A. Hoecker: Multivariate Analysis with TMVA

  29. Two-Higgs-Doublet Model • Extend SM by adding another scalar Higgs doublet (2HDM): • Type-II 2HDM: one doublet couples to up-type, one doublet couples to down-type quarks • 6 free parameters: MH± , MA0, MH0, Mh, tan = v2 /v1,  (governing h–H0 mixing) • So far: only looked at processes sensitive to charged Higgs: MH±, tan : • Hadronic Z width ratio: R0b • Leptonic meson decays: B → Xs, B →  / , K →  /  →  • Semileptonic B decay: B → D A. Hoecker: Multivariate Analysis with TMVA

  30. Two-Higgs-Doublet Model Slight tension between BABAR+Belle result: BR(B → ) = (1.73 ± 0.35) 10–4 and CKM fit (sin2): (0.83 +0.27–0.10) 10–4 A. Hoecker: Multivariate Analysis with TMVA

  31. Two-Higgs-Doublet Model • Combined: exclude at 95% CL MH± < 240 GeV everywhere, and MH± < 780 GeV at tan = 70 A. Hoecker: Multivariate Analysis with TMVA

  32. Wh a t ’ s N e x t ? • Gfitter is growing: • Max Baak and Matthias Schott (CERN), Doerthe Ludwig (DESY, PhD thesis) • Programming of “oblique” parameters (S, T, U) • For SM fit and Little Higgs corrections (possibly also Technicolor) • Maintain SM package in line with experimental progress • Maintain and extend 2HDM package • Include more rare decays, such as K →  • Long-term goal: mSUGRA and MSSM • Start with wrappers around existing code (FeynHiggs (Higgs, B, K, g–2, …), microMEGA, Pope, …) • Maintain and improve Gfitter core package A. Hoecker: Multivariate Analysis with TMVA

  33. B a c k u p Statistical inclusion of direct Higgs searches A. Hoecker: Multivariate Analysis with TMVA

  34. Insertion of the Direct Higgs Searches LEP and Tevatron analyses based on –2lnQ, where Q = LS+B / LB Experimental data available: [ADLO: Phys. Lett. B565, 61 (2003)] [CDF+D0, 2.4fb-1): arXiv:0804.3423] [CDF+D0, 3fb-1: arXiv:0808.0534] data exp. for “b” exp. for “s+b” • For insertion in fit: • Aim of the fit is to measure the deviation from the SM (“s+b”), not a discovery of the Higgs (ie. deviation from Null hypothesis) • Interpret the -2lnQ results as measurements for a given MH • Derive log-likelihood estimator quantifying deviation of the data from the expectation of our hypothesis (ie. the presence of a SM Higgs with a given mass  “s+b”) A. Hoecker: Multivariate Analysis with TMVA

  35. Insertion of the Direct Higgs Searches The collaborations quantify the level of agreement of the data with the “s+b” hypothesis by CLs+b using toy MC experiments • For insertion in fit: • Only the tail of large values is integrated (corresponds to “too few Higgs-like events” in simple counting experiment) • In the SM fit, we are interested in any kind of deviation from the “s+b” hypothesis (including the case of “too many Higgs-like events”) • Transform 1-sided in 2-sided CL (conservative, but needed for SM fit): • for: CLs+b 0.5 : CLs+b[2-sided] = 2 CLs+b • for: CLs+b > 0.5 : CLs+b[2-sided] = 2 (1 – CLs+b) Then transform into a contribution to c2 assuming symmetric PDF via: A. Hoecker: Multivariate Analysis with TMVA

  36. Insertion of the Direct Higgs Searches Resulting contribution added to the 2 during the fit Approximation needed for low MH of Tevatron as CLs+b not available [arXiv:0804.3423] • We estimate CLs+b from measured -2lnQ, and expectation for “s+b” and error for “b” • Approximation tested in region where CLs+b available  apply fudge factor of 0.77 • Of course: replace approximated CLs+b by experimental value once made available A. Hoecker: Multivariate Analysis with TMVA

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