The ElectroWeak fit of Standard Model after the Discovery of the Higgs-like boson

Transcription

1 , on behalf of the Gfitter group (*) IVICFA Easter Workshop Valencia, th March EPJC 72, 2205 (2012), arxiv: after the Discovery of the Higgs-like boson weights / GeV weights - Bkg ATLAS Preliminary s=7 TeV, Ldt=4.8 fb Max (*) Baak M. Baak, (CERN) J. Haller, A. Höcker, Global R. Kogler, Fit of electroweak K. Mönig, M. SM Schott, and beyond J. Stelzer -1 s=8 TeV, Ldt=20.7 fb -1 Data S/B Weighted Sig+Bkg Fit (m =126.8 GeV) H Bkg (4th order polynomial) H [GeV] m m(γγ) [GeV] Events / 3.0 GeV 16 Data CMS preliminary * ZZ, Z Z+X ggh+tth (126 GeV) qqh+vh (126 GeV) -1 s = 7 TeV, L = 5.1 fb -1 s = 8 TeV, L = 19.6 fb (GeV) m m(4l) [GeV] 4l 1

2 Outline This presentation: Introduction to Gfitter Introduction to the electroweak fit of the Standard Model Inputs to the electroweak fit Fit results Future Prospects of ILC Conclusion & Outlook

3 The Gfitter Project Introduction A Generic Fitter Project for HEP Model Testing Gfitter = state-of-the-art HEP model testing tool for LHC era Gfitter software and features: Modular, object-oriented C++, relying on ROOT, XML, python, etc. Core package with data-handling, fitting, and statistics tools - Various fitting tools: Minuit (1/2), Genetic Algorithms, Simulated Annealing, etc. - Consistent treatment of statistical, systematic, theoretical uncertainties (Rfit prescription), correlations, and inter-parameter dependencies.» Theoretical uncertainties included in χ 2 with flat likelihood in allowed ranges - Full statistics analysis: goodness-of-fit, p-values, parameter scans, MC analyses. Independent plug-in physics libraries: SM, 2HDM, multiple BSM model,... Our publications and new results available at: 3

4 The global electroweak fit of the SM

5 Global EW fits: a long history Huge amount of pioneering work by many! Needed to understand importance of loop corrections - Observables (now) known at least at two-loop order, sometimes more. High-precision Standard Model (SM) predictions and measurements required - First from LEP/SLC, then Tevatron, now LHC. EW fits performed by many groups in past D. Bardinet al. (ZFITTER), G. Passarinoet al. (TOPAZ0), LEP EW WG (M. Grünewald, K. Mönig et al.), J. Erler (GAPP), Important results obtained!!" March 2008 Theory uncertainty!# (5) had = # # incl. low Q 2 data m Limit = 160 GeV (Global SM fits also used at lower energies [CKM-matrix], and many groups pursuing global beyond-sm fits.) 1 Excluded Preliminary m H!GeV" 5

6 The predictive power of the SM As the Z boson couples to all fermions, it is ideal to measure & study both the electroweak and strong interactions. Tree level relations for Z ff Unification connects the electromagnetic and weak couplings Cross Section [pb] s [GeV] The impact of radiative corrections Absorbed into EW form factors: ρ, κ, Δr Effective couplings at the Z-pole Quadraticly dependent on m t, logarithmic dependence on M H 6

7 Hunt for the Higgs Gfitter group, EPJC 72, 2003 (2012) LEP 95% CL Tevatron 95% CL Early Theory uncertainty Fit including theory errors Fit excluding theory errors M H [GeV] M H was last missing input parameter of the electroweak fit Indirect determination from EW fit (2012): M H = GeV (Direct Higgs limits of course also available in the EW fit.) 7

8 The SM fit with Gfitter, including the Higgs Discovery of Higgs-like boson at LHC Cross section, branching ratios, spin, parity sofar compatible with SM Higgs boson. This talk: assume boson is SM Higgs. Use in EW fit: M H = ± 0.4 GeV - ATLAS: M H = ± 0.4 ± 0.4 GeV - CMS: M H = ± 0.4 ± 0.5 GeV [arxiv: , arxiv: ] Change in average between fully uncorrelated and fully correlated systematic uncertainties is minor: δm H : GeV weights / GeV weights - Bkg Events / 3.0 GeV Data ATLAS Preliminary s=7 TeV, Ldt=4.8 fb CMS preliminary * ZZ, Z Z+X ggh+tth (126 GeV) qqh+vh (126 GeV) -1 s=8 TeV, Ldt=20.7 fb -1 H -1 s = 7 TeV, L = 5.1 fb Data S/B Weighted Sig+Bkg Fit (m =126.8 GeV) H Bkg (4th order polynomial) [GeV] m -1 s = 8 TeV, L = 19.6 fb Unique situation: for first time SM is fully over-constrained Test its self-consistency! The focus of this talk (GeV) m 4l 8

9 Measurements at the Z-pole (1/2) Total cross-section Express in terms of partial decay width of initial and final width: with Full width: (Correlated set of measurements.) Corrected for QED radiation Set of input (width) parameters to EW fit: Z mass and width: M Z, Γ Z Hadronic pole cross section: Three leptonic ratios (lepton univ.): X-section [pb] Hadronic width ratios: s [GeV] 9

10 Measurements at the Z-pole (2/2) Definition of Asymmetry Distinguish vector and axial-vector couplings of the Z Directly related to Observables In case of no beam polarisation (LEP) use final state angular distribution to define forward/backward asymmetry Polarised beams (SLC), define left/right asymmetry Measurements: 10

11 2012 averages for M W and m top Latest Tevatron result from: arxiv: Tevatron result from: arxiv: Used here: m t = ± 0.94 GeV Moriond 13: m t = ± 0.87 GeV 11

12 The electromagnetic coupling The EW fit requires precise knowledge of α(m Z ) better than 1% level Enters various places: hadr. radiator functions, predictions of M W and sin 2 θ f eff Conventionally parametrized as (α(0) = fine structure constant) : Evolution with renormalization scale: Leptonic term known up to three loops (for q 2 m l ) Top quark contribution known up to 2 loops, small: -0.7x10-4 [M. Steinhauser, PLB 429, 158 (1998)] Hadronic contribution (from the 5 light quarks) is difficult to calculate, cannot be obtained from pqcd alone. Analysis of low-energy e + e - data (5) Usage of pqcd if lack of data Δα had ( M ) = ± 1.0 Z -4 ( ) 10 Similar analysis to evaluation of hadronic contribution to (g-2) µ [M. Davier et al., Eur. Phys. J. C71, 1515 (2011)] 12

13 Theoretical input In EW fit with Gfitter we use state-of-the-art calculations: MW Mass of the W boson [M. Awramik et al., Phys. Rev. D69, (2004)] sin 2 θ f eff Effective weak mixing angle [M. Awramik et al., JHEP 11, 048 (2006), M. Awramik et al., Nucl.Phys.B813: (2009)] - Full two-loop + leading beyond-two-loop form factor corrections Γhad QCD Adler functions at N 3 LO [P. A. Baikov et al., PRL108, (2012)] - N 3 LO prediction of the hadronic cross section Rb Partial width of Z bb [Freitas et al., JHEP08, 050 (2012)] New! full 2-loop calc. Two nuisance parameters in EW fit for theoretical uncertainties: δm W (4 MeV), δsin 2 θ l eff (4.7x10-5 ) Radiative corrections are important! E.g. consider tree-level EW unification relation: - This predicts: M W = ( ± 0.005) GeV - Experiment: M W = ( ± 0.015) GeV Without loop corrections: 27σ discrepancy! M W 2 tree-level = M 2 Z 2 % ( 8πα ' 1+ 1 * ' 2 G F M * & Z ) 13

14 Electroweak fit Experimental inputs Latest experimental inputs: Z-pole observables: from LEP / SLC [ADLO+SLD, Phys. Rept. 427, 257 (2006)] M W and Γ W from LEP/Tevatron [arxiv: ] m top : average from Tevatron [arxiv: ] m c, m b world averages (PDG) [PDG, J. Phys. G33,1 (2006)] Δα had (5) (M Z2 ) including α S dependency [Davier et al., EPJC 71, 1515 (2011)] M H from LHC [arxiv: , arxiv: ] 7+2 free fit parameters: M Z, M H, α S (M Z2 ), Δα had (5) (M Z2 ), m t, m c, m b 2 theory nuisance parameters - δm W (4 MeV), δsin 2 θ l eff (4.7x10-5 ) M H [GeV] ( ) ± 0.4 M W [GeV] ± Γ W [GeV] ± M Z [GeV] ± Γ Z [GeV] ± σ 0 had [nb] ± Rl ± A 0,l FB ± ( ) A l ± sin 2 θ l eff (Q FB) ± A c ± A b ± A 0,c FB ± A 0,b FB ± Rc ± R 0 b ± m c [GeV] m b [GeV] m t [GeV] ± 0.94 α (5) had (M Z 2 ) ( ) 2757 ± 10 2 LHC Tevatron LHC SLC SLC LEP Tevatron 14

15 Electroweak Fit SM Fit Results From the Gfitter Group, EPJC 72, 2205 (2012) Left: full fit incl. M H Middle: fit not incl. M H Parameter Input value Free Fit result Fit result Fit result incl. M H in fit incl. M H not incl. M H but not exp. input in row M H [GeV] ( ) ± 0.4 yes ± M W [GeV] ± ± ± ± Γ W [GeV] ± ± ± ± M Z [GeV] ± yes ± ± ± Γ Z [GeV] ± ± ± ± σ 0 had [nb] ± ± ± ± Rl ± ± ± ± A 0,l FB ± ± ± ± ( ) A l ± ± ± ( ) sin 2 θeff l (Q FB) ± ± A c ± ± A b ± ± ± A 0,c FB ± ± ± A 0,b FB ± ± ± Rc ± ± ± ± R 0 b ± ± ± ± Right: fit incl M H, not the row m c [GeV] yes m b [GeV] yes m t [GeV] ± 0.94 yes ± ± α (5) had (M Z 2 ) ( ) 2757 ± 10 yes 2755 ± ± α S (MZ 2 ) yes ± ± ± δ th M W [MeV] [ 4, 4] theo yes 4 4 δ th sin 2 θ l eff ( ) [ 4.7, 4.7] theo yes

16 Electroweak Fit SM Fit Results sin 2 lept Θ eff (Q ) FB 0,c A FB 0,b A FB A c (5) Δα had A b 0 Rc 0 Rb m c m b m t 2 (M ) Z H M W Γ W M Z Γ Z 0 σ had 0 Rlep 0,l A FB A l (LEP) A l (SLD) with M H measurement w/o M H measurement M G fitter SM 0.0 (-1.5) (O - O meas ) / σ meas fit Plot inspired by Eberhardt et al. [arxiv: ] Feb (-0.3) 0.2 (0.2) 0.2 (0.0) 0.1 (0.3) -1.7 (-1.7) -1.1(-1.0) -0.8 (-0.7) 0.2 (0.4) -1.9 (-1.7) -0.7 (-0.8) 0.9 (1.0) 2.5 (2.7) 0.0 (0.0) 0.6 (0.6) 0.0 (0.0) -2.4 (-2.3) 0.0 (0.0) 0.0 (0.0) 0.4 (0.0) -0.1 (0.0) No individual value exceeds 3σ Small pulls for M H, M Z, Δα had (5) (M Z2 ), m c, m b indicate that input accuracies exceed fit requirements Largest deviations in b-sector: A 0,b FB and R0 b with 2.5σ and -2.4σ à largest contribution to χ 2 R 0 b using one-loop calculation -0.8σ R 0 b has only little dependence on M H Most affected when including M H : M W prediction: Shift in predicted M W value of 13 MeV. 16

17 Goodness of Fit Toy analysis: p-value for wrongly rejecting the SM = (theo) p-value is equivalent to 1.8σ. Evaluated with 20k pseudo experiments follows χ 2 with 14 d.o.f. For comparison: χ 2 min = 21.8 à Prob(χ2 min, 14) = 8 % Large value of χ 2 min not due to inclusion of M H measurement. Without M H measurement: χ 2 min = 20.3 à Prob(χ2 min, 13) = 9% 17

18 Higgs results of the EW fit Scan of Δχ 2 profile versus M H Grey band: fit w/o M H measurement Blue line: full SM fit, with M H meas. Fit w/o M H measurement gives: M H = GeV Consistent at 1.3σ with LHC measurement SM fit SM fit w/o M measurement H ATLAS measurement [arxiv: ] CMS measurement [arxiv: ] G fitter SM Sep Bottom plot: impact of other most sensitive Higgs observables Determination of M H removing all sensitive observables except the given one. Known tension (2.5σ) between A l (SLD), A 0,b FB, and M W clearly visible A l (LEP) A l (SLD) 0,b A FB M W Fit w/o M H LHC average M H [GeV] M H fit below only includes the given observable G fitter SM Sep [GeV] ±

19 Prediction for α s (M Z ) from Z hadrons Scan of Δχ 2 versus α s Also shown: SM fit with minimal inputs: M Z, G F, Δα (5) had (M Z ), α s (M Z ), M H, and fermion masses Determination of α s at N 3 LO. Most sensitive through total hadronic cross-section σ 0 had and partial leptonic width R 0 l Theory uncertainty at per-mille level (obtained by scale variation of Γ had ). In good agreement with value from τ decays, also at N 3 LO. (Improvements in precision only expected with ILC/GigaZ. See later.) 19

20 Indirect determination of W mass Scan of Δχ 2 profile versus M W Also shown: SM fit with minimal inputs: M Z, G F, Δα had (5) (M Z ), α s (M Z ), M H, and fermion masses Good consistency between total fit and SM w/ minimal inputs SM fit w/o M W measurement SM fit w/o M and M measurements W H SM fit with minimal input M W world average [arxiv: ] G fitter SM Sep M H measurement allows for precise constraint on M W 1 Agreement at 1.4σ Fit result for indirect determination of M W (full fit w/o M W ): M W [GeV] 1 More precise estimate of M W than the direct measurements! Uncertainty on world average measurement: 15 MeV 20

21 Indirect effective weak mixing angle Right: scan of Δχ 2 profile versus sin 2 θ l eff All sensitive measurements removed from the SM fit. Also shown: SM fit with minimal inputs M H measurement allows for very precise constraint on sin 2 θ l eff Fit result for indirect determination of sin 2 θ l eff : More precise than direct determination (from LEP/SLD)! Uncertainty on LEP/SLD average: 1.6x

22 Indirect determination of top mass SM fit w/o m t measurement SM fit w/o m t and M H measurements mt kin mt kin mt kin m pole t ATLAS measurement [arxiv:1203:5755] CMS measurement [arxiv:1209:2319] Tevatron average [arxiv: ] obtained from Tevatron tt [arxiv: ] G fitter SM Sep [GeV] Shown: scan of Δχ 2 profile versus m t (without m t measurement) m t M H measurement allows for significant better constraint of m t Indirect determination consistent with direct measurements - Remember: fully obtained from loop corrections! Indirect result: m t = GeV (Tevatron w.a.: ± 0.9 GeV) 22

23 State of the SM: W versus top mass Scan of M W vs m t, with the direct measurements excluded from the fit. Results from Higgs measurement significantly reduces allowed indirect parameter space corners the SM! [GeV] M W M W 68% and 95% CL fit contours w/o M W and m t measurements 68% and 95% CL fit contours w/o M W, m and M H measurements world average ± 1 t mkin t Tevatron average ± M H =50 GeV M H =125.7 M H =300 GeV M H =600 GeV G fitter SM Sep m t [GeV] Observed agreement demonstrates impressive consistency of the SM! 23

24 Constraints on Oblique Corrections Oblique corrections from New Physics described through STU parametrization [Peskin and Takeuchi, Phys. Rev. D46, 1 (1991)] At low energies, BSM physics appears dominantly through vacuum polarization corrections Aka, oblique corrections Oblique corrections reabsorbed into electroweak form factors Δρ, Δκ, Δr parameters, appearing in: M W2, sin 2 θ eff, G F, α, etc. Electroweak fit sensitive to BSM physics through oblique corrections Similar to sensitivity to Higgs loop corrections. X X O meas = O SM,REF (m H,m t ) + c S S + c T T +c U U S : New Physics contributions to neutral currents T : Difference between neutral and charged current processes sensitive to weak isospin violation U : (+S) New Physics contributions to charged currents. U only sensitive to W mass and width, usually very small in NP models (often: U=0) Also implemented: correction to Zà bb coupling, extended parameters (VWX) [Burgess et al., Phys. Lett. B326, 276 (1994)] [Burgess et al., Phys. Rev. D49, 6115 (1994)] 24

25 Fit results for S, T, U S,T,U obtained from fit to the EW observables SM: M H = 126 GeV, m t = 173 GeV This defines (S,T,U) = (0,0,0) SM: S, T depend logarithmically on M H Fit result: S = 0.03 ± 0.10 T = 0.05 ± 0.12 U = 0.03 ± 0.10 S T U S T U 1 Stronger constraints from fit with U=0. Also available for Zà bb correction. No indication for new physics. Can now use this to constrain 4 th gen, Ex-Dim, T-C, Higgs couplings, etc. 25

26 ILC Prospects for the Standard Model fit 26

27 Prospects for ILC with Giga Z Future Linear Collider could improve precision of EW observables tremendously. WW threshold, to obtain MW - from threshold scan: δmw : 15 6 MeV ttbar threshold, to obtain mt - obtain mt indirectly from production cross section: δmt : GeV Z pole measurements - High statistics: 10 9 Z decays: δr 0 lep : With polarized beams, uncertainty on δa 0,f LR: , which translates to δsin 2 θ l eff : Low-energy data results to improve Δαhad: ISR-based (BABAR) and KLOE-II, BESIII e + e - cross-section measurements, in particular around cc resonance plus: improved αs, improvements in theory: Δαhad:

28 Prospects for ILC with Giga Z M H avg Logarithmic dependency on M H cannot compete with direct M H meas. Indirect prediction M H dominated by theory uncertainties. No theory uncertainty: M H = GeV R-fit scheme: M H = GeV 28

29 Prospects for ILC with Giga Z Assuming also 50% of today s theoretical uncertainties Implies three-loop EW calculations! Huge reduction of uncertainty on indirect determinations current precision prospects for direct ILC measurements Also strong constraints on S, T, U 29

30 Summary Including M H measurement, for first time SM is fully over-constrained! M H consistent at 1.3σ with indirect prediction from EW fit. p-value of global electroweak fit of SM: 7% (pseudo-experiments) Would be great to revisit Z bb, both theoretically and experimentally Knowledge of M H dramatically improves SM prediction of key observables M W (28 11 MeV), sin 2 θ l eff (2.3x x10-5 ), m t ( GeV) Improved accuracies set benchmark for new direct measurements! 30

31 Outlook Paradigm shift for EW fit: from Higgs mass prediction to consistency tests of the Standard Model: δδαhad δαs δm W (indirect) = δmz = 11 MeV Large contributions to δm W (and δsin 2 θ l eff) from top and unknown higher-order EW corrections. δm W (direct) = 15 MeV δtheo 10% 38% 5% 4% 43% δmtop What s next for Gfitter: combine Higgs couplings in the EW fit. To be continued Latest results always available at: Results of this presentation: EPJC 72, 2205 (2012) 31

32 Backup A Generic Fitter Project for HEP Model Testing Backup 32

33 New R 0 b calculation [A. Freitas et al., JHEP 1208, 050 (2012)] The branching ratio R 0 b : partial decay width of Z bb to Z qq Freitas et al: full 2-loop calculation of Z bb Contribution of same terms as in the calculation of sin 2 θ bb eff cross-check of two results found good agreement Two-loop corrections comparable to experimental uncertainty (6.6x10 4 ) 1-loop EW and QCD correction to FSR 2-loop EW correction 2-loop EW and 2+3-loop QCD correction to FSR 1+2-loop QCD correction to gauge boson self-energies 33

34 Higgs couplings in the EW fit In latest ATLAS H γγ, 2.3σ deviation seen from SM µ ( 1.0) Interpret.: H VV couplings scaled with c V From: Falkowski et al, arxiv: Modified Higgs couplings can be constrained by EW fit through extended STU formalism. Result of c V driven by limit on T parameter. ρ 0 = M 2 W Tree-level relation: c =1+α T W M Z0 Unconv. central low p Tt Unconv. central high p Tt Unconv. rest low p Tt Unconv. rest high p Tt Conv. central low p Tt Conv. central high p Tt Conv. rest low p Tt Conv. rest high p Tt Conv. transition Loose high-mass two-jet Tight high-mass two-jet Low-mass two-jet miss significance E T One-lepton 2012 data combined ATLAS Preliminary Data 2012, s = 8 TeV Ldt = 20.7 fb H -1 = GeV m H Signal strength Reminder: T = 0.05 ± 0.12 (Gfitter) EW-fit Falkowski et al: c V 1.08 ± 0.07 Blue dashed: c V from µ s, black: comb. w/ EW Falkowski et al, arxiv: c V 34

35 Radiator Functions Partial widths are defined inclusively: contain both QCD and QED contributions. Corrections expressed as so-called radiator functions R A,f and R V,f High sensitivity to the strong coupling α s Recently, full four-loop calculation of QCD Adler function became available (N 3 LO) Much-reduced scale dependence! Theoretical uncertainty of 0.1 MeV, compared with experimental uncertainty of 2.0 MeV. [D. Bardin, G. Passarino, The Standard Model in the Making, Clarendon Press (1999)] O(αs 3 ) O(αs 4 ) O(αs) O(αs 2 ) [P. Baikov et al., Phys. Rev. Lett. 108, (2012)] [P. Baikov et al Phys. Rev. Lett. 104, (2010)] 35

36 Calculation of M W Full EW one- and two-loop calculation of fermionic and bosonic contributions. One- and two-loop QCD corrections and leading terms of higher order corrections. Results for Δr include terms of order O(α), O(αα s ), O(αα s2 ), O(α 2 ferm ), O(α 2 bos ), O(α2 α s m t4 ), O(α 3 m t6 ) Uncertainty estimate: Missing terms of order O(α 2 α s ): about 3 MeV (from O(α 2 α s m t4 )) Electroweak three-loop correction O(α 3 ): < 2 MeV Three-loop QCD corrections O(αα s3 ): < 2 MeV Total: δm W 4 MeV [M Awramik et al., Phys. Rev. D69, (2004)] [M Awramik et al., Phys. Rev. Lett. 89, (2002)] [A Freitas et al., Phys. Lett. B495, 338 (2000)] 36

37 Calculation of sin 2 (θ l eff ) Effective mixing angle: [M Awramik et al, Phys. Rev. Lett. 93, (2004)] [M Awramik et al., JHEP 11, 048 (2006)] Two-loop EW and QCD correction to Δκ known, leading terms of higher order QCD corrections. Fermionic two-loop correction about 10 3, whereas bosonic one Uncertainty estimate obtained with different methods, geometric progression, leading to total: δsin 2 (θ l eff ) = 4.7x

38 Input correlations of the EW fit Input correlation coefficients between Z pole measurements 38

39 Top mass dependence on Event Kinematics Difficult to define a pole mass for heavy, unstable and colored particle. The top mass extracted in hadron collisions is not well defined below a precision of O(Γ t ) ~ 1 GeV Single top decays before hadronizing. To have colorless final states, additional quarks needed. - Non-perturb. color-reconnection effects in fragmentation. - Ambiguities in top mass definition Result: m t exp m t pole, and event-dependent. With additional theo. uncertainty of 0.5 GeV on m t : M H = GeV, M W = ±0.013 GeV, sin2 θ l eff = ± Only small deterioration in precision.

40 Extended STU results Several extended STU parametrizations available Here: STU + δε b, latter parameter describing Z bb vertex SM: M H = GeV, m t = GeV This defines (S,T,U) = (0,0,0) S, T depend logarithmically on M H Fit result: S = 0.00 ± 0.10 T = 0.00 ± 0.12 U = 0.06 ± 0.10 S T U δε b S T Δε b = (2.4 ± 1.4) x 10-3 U δε b 1 (Stronger constraints from fit with U=0.) 40

41 Prospects for LHC, ILC and ILC with Giga-Z Assumed experimental improvements for prospective study: LHC: M W, m top ILC: M W, m top Giga-Z: M W, m top, sin 2 θ l eff, R lep ISR-based (BABAR) and BESIII, KLOE-II cross-section measurements, should improve Δα had (M Z ) Input from: [ATLAS, Physics TDR (1999)] [CMS, Physics TDR (2006)] [A. Djouadi et al., arxiv: ][i. Borjanovic, EPJ C39S2, 63 (2005)] [S. Haywood et al., hep-ph/ ] [R. Hawkings, K. Mönig, EPJ direct C1, 8 (1999)] [A. H. Hoang et al., EPJ direct C2, 1 (2000)] [M. Winter, LC-PHSM ] 41