, on behalf of the Gfitter group (*) Rencontres de Moriond QCD La Thuile, 9 th -15 th March 13 http://cern.ch/gfitter EPJC 7, 5 (1), arxiv:19.716 after the Discovery of the Higgs-like boson weights / GeV weights - Bkg 16 14 1 1 8 6 4 1 8 4-4 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 1 11 1 13 14 15 16 [GeV] m m(γγ) [GeV] Events / 3. GeV 16 Data 14 1 1 8 6 4 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 11 1 13 14 15 16 (GeV) m m(4l) [GeV] 4l 1
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]
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 = 96 +31-4 GeV (Direct exclusion limits also incorporated in EW fits.) Gfitter group, EPJC 7, 3 (1) 3
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 16 14 1 1 8 6 4 1 8 4-4 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 1 11 1 13 14 15 16 m [GeV] Events / 3. GeV 16 Data 14 1 1 8 6 4 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 11 1 13 14 15 16 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:114.1769] sin θ f eff Effective weak mixing angle [M. Awramik et al., JHEP 11, 48 (6), M. Awramik et al., Nucl.Phys.B813:174-187 (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
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] 8.385 ±.15 Γ W [GeV].85 ±.4 M Z [GeV] 91.1875 ±.1 Γ Z [GeV].495 ±.3 σ had [nb] 41.54 ±.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] 1.7.11 +.7 m b [GeV] 4..7 +.17 m t [GeV] 173.18 ±.94 α (5) had (M Z ) ( ) 757 ± 1 LHC Tevatron LHC SLC SLC LEP Tevatron 5
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 ±.4 94 +5 94 +5 M W [GeV] 8.385 ±.15 8.367 ±.7 8.38 ±.1 8.359 ±.11 Γ W [GeV].85 ±.4.91 ±.1.9 ±.1.91 ±.1 M Z [GeV] 91.1875 ±.1 yes 91.1878 ±.1 91.1874 ±.1 91.1983 ±.116 Γ Z [GeV].495 ±.3.4954 ±.14.4958 ±.15.4951 ±.17 σ had [nb] 41.54 ±.37 41.479 ±.14 41.478 ±.14 41.47 ±.15 Rl.767 ±.5.74 ±.17.743 ±.18.716 ±.6 A,l FB.171 ±.1.167 ±..1637 ±..164 ±. ( ) A l.1499 ±.18.1473.8 +.6.1477 ±.9.1468 ±.5 ( ) sin θeff l (Q FB).34 ±.1.3148.7 +.11.3143.1 +.1.315 ±.9 A c.67 ±.7.668.38 +.5.668.35 +.4.668 ±.31 A b.93 ±..93464.7 +.4.93468 ±.8.93463 ±.6 A,c FB.77 ±.35.739.5 +.3.74 ±.5.738 ±.4 A,b FB.99 ±.16.13.6 +.4.136 ±.7.134 ±.4 Rc.171 ±.3.173 ±.6.173 ±.6.173 ±.6 R b.169 ±.66.1474 ±.3.1475 ±.3.1473 ±.3 Right: fit incl M H, not the row m c [GeV] 1.7.11 +.7 yes 1.7.11 +.7 1.7.11 +.7 m b [GeV] 4..7 +.17 yes 4..7 +.17 4..7 +.17 m t [GeV] 173.18 ±.94 yes 173.5 ±.88 173.14 ±.93 175.8.4 +.7 α (5) had (M Z ) ( ) 757 ± 1 yes 755 ± 11 757 ± 11 716 43 +49 α S (MZ ) yes.1191 ±.8.119 ±.8.1191 ±.8 δ th M W [MeV] [ 4, 4] theo yes 4 4 δ th sin θ l eff ( ) [ 4.7, 4.7] theo yes 1.4 4.7 6
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) -3 - -1 1 3 (O - O meas ) / σ meas fit Plot inspired by Eberhardt et al. [arxiv:19.111] Feb 13-1. (-.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
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 = 94 +5 - GeV Consistent at 1.3σ with LHC measurement. 5 4.5 4 3.5 3.5 1.5 1.5 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. 6 7 8 9 1 11 1 13 14 A l (LEP) A l (SLD),b A FB M W Fit w/o M H LHC average 6 1 1 1 3 1 M H [GeV] M H fit below only includes the given observable G fitter SM Sep 1 +47 7-15 +56 6-19 +5 94 - [GeV] +48 19-66 +585 387-169 15.7 ±.4 8
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 1 9 8 7 6 5 4 3 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 ): 8.3 8.33 8.34 8.35 8.36 8.37 8.38 8.39 8.4 8.41 M W [GeV] 1 More precise estimate of M W than the direct measurements! Uncertainty on world average measurement: 15 MeV 9
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
Indirect determination of top mass 1 9 8 7 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 1 3 6 mt kin Tevatron average [arxiv:17.169] 5 m pole t obtained from Tevatron tt [arxiv:17.98] 4 3 1 1 16 165 17 175 18 185 19 [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 = 175.8 +.7 -.4 GeV (Tevatron average: 173. ±.9 GeV) 11
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 8.5 8.45 8.4 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 ± 1 8.35 8.3 8.5 M H =5 GeV M H =15.7 M H =3 GeV M H =6 GeV G fitter SM Sep 1 14 15 16 17 18 19 m t [GeV] Observed agreement demonstrates impressive consistency of the SM! 1
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 1 +.89 -.54 T 1 -.83 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
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 :.5 1 4 1 3 - With polarized beams, uncertainty on δa,f LR: 1 3 1 4, which translates to δsin θ l eff : 1.6 1 4 1.3 1 5 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: 1 4 5 1 5 14
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 = 94. +5.3-5. GeV Rfit scheme: M H = 9.3 +16.6-11.6 GeV 15
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
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: http://cern.ch/gfitter Results in this presentation: EPJC 7, 5 (1) 17
Backup A Generic Fitter Project for HEP Model Testing Backup 18
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
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)]
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
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
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:133.181 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 - 4 6 8 1 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:133.181 c V