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

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1 , on behalf of the Gfitter group (*) Rencontres de Moriond QCD La Thuile, 9 th -15 th March 13 EPJC 7, 5 (1), 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=.7 fb -1 Data S/B Weighted Sig+Bkg Fit (m =16.8 GeV) H Bkg (4th order polynomial) H [GeV] m m(γγ) [GeV] Events / 3. GeV 16 Data CMS preliminary * ZZ, Z Z+X ggh+tth (16 GeV) qqh+vh (16 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 Reminder: the predictive power of the SM Tree level relations for Z ff Unification connects the electromagnetic and weak couplings E.g. M W can be expressed as function of M Z and G F Cross Section [pb] 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 s [GeV]

3 Global EW fits: a long tradition EW fits: a long tradition Huge amount of pioneering work by many! Precision measurements crucial, first from LEP/SLC, then Tevatron and now LHC. Precise understanding of loop corrections essential. - Observables known at least at two-loop order, sometimes more. Hunt for the Higgs M H last missing input parameter Indirect determination from EW fit (1): M H = GeV (Direct exclusion limits also incorporated in EW fits.) Gfitter group, EPJC 7, 3 (1) 3

4 The SM fit with Gfitter, including the Higgs Discovery of Higgs-like boson by LHC Cross section and branching ratios sofar ~compatible with SM Higgs boson This talk: assume boson is SM Higgs. Use in EW fit: M H = 15.7 ±.4 GeV Change between fully uncorrelated and fully correlated systematic uncertainties is minor: δm H :.4.5 GeV weights / GeV weights - Bkg ATLAS Preliminary -1 s=7 TeV, Ldt=4.8 fb -1 s=8 TeV, Ldt=.7 fb Data S/B Weighted Sig+Bkg Fit (m =16.8 GeV) H Bkg (4th order polynomial) H m [GeV] Events / 3. GeV 16 Data CMS preliminary * ZZ, Z Z+X ggh+tth (16 GeV) qqh+vh (16 GeV) -1 s = 7 TeV, L = 5.1 fb -1 s = 8 TeV, L = 19.6 fb m 4l (GeV) For first time SM is fully over-constrained test its self-consistency! 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, 536 (4)] ΓZ, ΓW Partial and total widths of the Z and W [Cho et. al, arxiv: ] sin θ f eff Effective weak mixing angle [M. Awramik et al., JHEP 11, 48 (6), M. Awramik et al., Nucl.Phys.B813: (9)] Γhad QCD Adler functions at N3LO [P. A. Baikov et al., PRL18, 3 (1)] Rb Partial width of Z bb [Freitas et al., JHEP8, 5 (1)] New! full -loop calc. 4

5 Electroweak fit Experimental inputs Latest experimental inputs: Z-pole observables: from LEP / SLC [ADLO+SLD, Phys. Rept. 47, 57 (6)] M W and Γ W from LEP/Tevatron [arxiv:14.169] m top : average from Tevatron [arxiv:17.169] m c, m b world averages [PDG, J. Phys. G33,1 (6)] Δα had (5) (M Z ) including α S dependency [Davier et al., EPJC 71, 1515 (11)] M H from LHC [arxiv:17.714, arxiv:17.735] 7 free fit parameters: M Z, M H, α S (M Z ), Δα had (5) (M Z ), m t, m c, m b Two nuisance parameters for theoretical uncertainties: δm W (4 MeV), δsin θ l eff (4.7x1-5 ) M H [GeV] ( ) 15.7 ±.4 M W [GeV] ±.15 Γ W [GeV].85 ±.4 M Z [GeV] ±.1 Γ Z [GeV].495 ±.3 σ had [nb] ±.37 Rl.767 ±.5 A,l FB.171 ±.1 ( ) A l.1499 ±.18 sin θ l eff (Q FB).34 ±.1 A c.67 ±.7 A b.93 ±. A,c FB.77 ±.35 A,b FB.99 ±.16 Rc.171 ±.3 R b.169 ±.66 m c [GeV] m b [GeV] m t [GeV] ±.94 α (5) had (M Z ) ( ) 757 ± 1 LHC Tevatron LHC SLC SLC LEP Tevatron 5

6 Electroweak Fit SM Fit Results From the Gfitter Group, EPJC 7, 5 (1) 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] ( ) 15.7 ±.4 yes 15.7 ± M W [GeV] ± ± ± ±.11 Γ W [GeV].85 ±.4.91 ±.1.9 ±.1.91 ±.1 M Z [GeV] ±.1 yes ± ± ±.116 Γ Z [GeV].495 ± ± ± ±.17 σ had [nb] ± ± ± ±.15 Rl.767 ±.5.74 ± ± ±.6 A,l FB.171 ± ± ±..164 ±. ( ) A l.1499 ± ± ±.5 ( ) sin θeff l (Q FB).34 ± ±.9 A c.67 ± ±.31 A b.93 ± ± ±.6 A,c FB.77 ± ± ±.4 A,b FB.99 ± ± ±.4 Rc.171 ± ± ± ±.6 R b.169 ± ± ± ±.3 Right: fit incl M H, not the row m c [GeV] yes m b [GeV] yes m t [GeV] ±.94 yes ± ± α (5) had (M Z ) ( ) 757 ± 1 yes 755 ± ± α S (MZ ) yes.1191 ± ± ±.8 δ th M W [MeV] [ 4, 4] theo yes 4 4 δ th sin θ l eff ( ) [ 4.7, 4.7] theo yes

7 Electroweak Fit SM Fit Results sin lept Θ eff (Q ) FB,c A FB,b A FB A c (5) Δα had A b Rc Rb m c m b m t (M ) Z H M W Γ W M Z Γ Z σ had Rlep,l A FB A l (LEP) A l (SLD) with M H measurement w/o M H measurement M G fitter SM. (-1.5) (O - O meas ) / σ meas fit Plot inspired by Eberhardt et al. [arxiv:19.111] Feb (-.3). (.). (.).1 (.3) -1.7 (-1.7) -1.1(-1.) -.8 (-.7). (.4) -1.9 (-1.7) -.7 (-.8).9 (1.).5 (.7). (.).6 (.6). (.) -.4 (-.3). (.). (.).4 (.) -.1 (.) Pull values of full fit (with M H ) No individual value exceeds 3σ Small pulls for M H, M Z, Δα (5) had (M Z ), m c, m b indicate that input accuracies exceed fit requirements Largest deviations in b-sector: A,b FB and R b with.5σ and -.4σ à largest contribution to χ R b using one-loop calculation -.8σ - R b has only little dependence on M H Goodness of fit p-value: χ min = 1.8 à Prob(χ min, 14) = 8 % From pseudo experiments: 7±1% - Large value of χ min not due to inclusion of M H measurement. - Without M H measurement: χ min =.3 à Prob(χ min, 13) = 9% 7

8 Higgs results of the EW fit Scan of Δχ 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:17.714] CMS measurement [arxiv:17.735] G fitter SM Sep 1 1 Bottom plot: impact of other most sensitive Higgs observables Determination of M H removing all sensitive observables except the given one. Known tension (.5σ) between A l (SLD), A,b FB, and M W clearly visible A l (LEP) A l (SLD),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] ±.4 8

9 Indirect determination of W mass Scan of Δχ 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:14.4] G fitter SM Sep 1 3 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 9

10 Indirect effective weak mixing angle Right: scan of Δχ profile versus sin 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 θ l eff Fit result for indirect determination of sin θ l eff : More precise than direct determination (from LEP/SLD)! Uncertainty on LEP/SLD average: 1.7x1-4 1

11 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 ATLAS measurement [arxiv:13:5755] CMS measurement [arxiv:19:319] G fitter SM Sep mt kin Tevatron average [arxiv:17.169] 5 m pole t obtained from Tevatron tt [arxiv:17.98] [GeV] Shown: scan of Δχ 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 Indirect result: m t = GeV (Tevatron average: 173. ±.9 GeV) 11

12 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 =5 GeV M H =15.7 M H =3 GeV M H =6 GeV G fitter SM Sep m t [GeV] Observed agreement demonstrates impressive consistency of the SM! 1

13 Constraints on S, T, U Electroweak fit sensitive to BSM physics through vacuum polarization corrections (also absorbed in ρ, κ, Δr). Described with STU parametrization [Peskin and Takeuchi, Phys. Rev. D46, 1 (1991)] SM: M H = 15.7 GeV, m t = 173. GeV This defines (S,T,U) = (,,) S, T depend logarithmically on M H Fit result: S T U S =.3 ±.1 T =.5 ±.1 U =.3 ±.1 S T U 1 Stronger constraints from fit with U= No indication for new physics. Can now use this constrain 4 th gen, Ex-Dim, T-C, Higgs couplings, etc. 13

14 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 :.9.1 GeV Z pole measurements - High statistics: 1 9 Z decays: δr lep : With polarized beams, uncertainty on δa,f LR: , which translates to δsin θ l eff : Low-energy data results For Δαhad: - more precise e + e - cross section results for low energy ( s < 1.8 GeV) and around cc resonance (KLOE-II, BaBar-ISR, BES-III), improved αs, improvements in theory: Δαhad:

15 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 Rfit scheme: M H = GeV 15

16 Prospects for ILC with Giga Z Assuming also 5% 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 16

17 Conclusion and Today s Prospects 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 (8 11 MeV), sin θ l eff (.3x1-5 1.x1-5 ), m t (6..5 GeV) Improved accuracies set benchmark for new direct measurements! δm W (indirect) = 11 MeV Large contributions to δm W (and δsin θ l eff) from top and unknown higher-order EW corrections δδαhad δαs δmz 5% 4% 1% 43% δmtop δm W (direct) = 15 MeV δtheo 38% Latest results always available at: Results in this presentation: EPJC 7, 5 (1) 17

18 Backup A Generic Fitter Project for HEP Model Testing Backup 18

19 Goodness of Fit Toy analysis with k pseudo experiments p-value = probability of getting χ min, toy larger than χ min from data i.e probability of incorrectly rejecting the SM as false =.7 ±.1 (theo) 19

20 A Gfitter package for 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 parameters Δρ, Δκ, Δr parameters, appearing in: M W, sin θ eff, G F, α, etc Electroweak fit sensitive to BSM physics through oblique corrections In direct competition with 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=) Also implemented: correction to Zà bb coupling, extended parameters (VWX) [Burgess et al., Phys. Lett. B36, 76 (1994)] [Burgess et al., Phys. Rev. D49, 6115 (1994)]

21 New R b calculation [A. Freitas et al., JHEP 18, 5 (1)] The branching ratio R b : partial decay width of Z bb to Z qq Freitas et al: full -loop calculation of Z bb Contribution of same terms as in the calculation of sin θ bb eff cross-check of two results found good agreement Two-loop corrections comparable to experimental uncertainty (6.6x1 4 ) 1-loop EW and QCD correction to FSR -loop EW correction -loop EW and +3-loop QCD correction to FSR 1+-loop QCD correction to gauge boson self-energies 1

22 α s (M Z ) from Z hadrons Determination of α s at N3LO. Most sensitive through total hadronic cross-section σ had and partial leptonic width R l Theory uncertainty obtained by scale variation, at per-mille level. Good agreement with value from t decays, also at N3LO. Improvements in precision only expected with ILC/GigaZ

23 Higgs couplings in the EW fit In latest ATLAS H γγ,.3σ deviation seen from SM µ ( 1.) 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 = M W Tree-level relation: c =1+α T W M Z 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 1 data combined ATLAS Preliminary Data 1, s = 8 TeV Ldt =.7 fb H -1 = 16.8 GeV m H Signal strength Reminder: T =.5 ±.1 (Gfitter) EW-fit Falkowski et al: c V 1.8 ±.7 Blue dashed: c V from µ s, black: comb. w/ EW Falkowski et al, arxiv: c V