The global electroweak fit at NNLO Prospects for LHC and ILC

Transcription

1 , on behalf of the Gfitter group (*) University of Birmingham / Warwick, UK January 14 th / 15 th, EPJC 74, 3046 (014), arxiv: The global electroweak fit at NNLO Prospects for LHC and ILC [GeV] % and 95% CL contours fit w/o M and m t measurements W fit w/o M, m and M measurements W t H direct M and m t measurements W world comb. ± 1σ = ± GeV m t world comb. ± 1σ m t = GeV σ = 0.76 GeV σ = theo GeV [GeV] % and 95% CL fit contour w/o M and sin (θ f ) measurements W eff Present SM fit Prospect for LHC Prospect for ILC/GigaZ Present measurement ILC precision LHC precision ± 1 σ sin (θ f ) ± 1 σ eff M H = 50 GeV M H = GeV M H = 300 GeV M H = 600 GeV G fitter SM Jul G fitter SM Jul m t [GeV] sin (θ l ) eff Max (*) Baak M. Baak, (CERN) J. Cuth, J. Haller, A. Global Höcker, Fit of R. electroweak Kogler, K. SM Mönig, and beyond M. Schott, J. Stelzer 1

2 Outline This presentation: Introduction to the Electroweak Fit Inputs to the electroweak fit - Full set of -loop calculations and theory uncertainties ü After the Higgs: predictions for key observables ü Modified Higgs couplings ü Prospects for LHC and ILC Conclusion & Outlook The ElectroWeak fit of Standard Model

3 The Gfitter Project Introduction A Generic Fitter Project for HEP Model Testing Gfitter = state-of-the-art HEP model testing tool Latest results always available at: (Most) results of this presentation: EPJC 74, 3046 (014) Gfitter software and features: Modular, object-oriented C++, relying on ROOT, XML, python, etc. Core package with data-handling, fitting, and statistics tools Independent plug-in physics libraries: SM, HDM, multiple BSM models,... The ElectroWeak fit of Standard Model 3

4 The global electroweak fit of the SM The ElectroWeak fit of Standard Model 4

5 Idea behind electroweak fits ü Observables receive quantum loop corrections from unseen virtual effects. ü If system is over-constrained, fit for unknown parameters or test the model s self-consistency. ü If precision is better than typical loop factor (α 1/137), test the model or try to obtain info on new physics in loops. For example, in the past EW fits were used to predict the Higgs mass. The ElectroWeak fit of Standard Model 5

6 Global EW fits: a long history Huge amount of pioneering work by many! Needed to understand importance of loop corrections - Important 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. Top mass predictions from loop effects available since ~1990. Official LEPEW fit since The EW fits have always been able to predict the top mass correctly! The ElectroWeak fit of Standard Model 6

7 Global EW fits: many fit codes EW fits performed by many groups in past and present. D. Bardinet al. (ZFITTER), G. Passarino et al. (TOPAZ0), LEPEW WG (M. Grünewald, et al.), J. Erler (GAP), Bayesian fit (M. Ciuchini et al.), etc Important results obtained! Several groups pursuing global beyond-sm fits, especially SUSY. Global SM fits also used at lower energies [CKM-matrix]. Fits of the different groups agree very well.!" March 008 m Limit = 160 GeV Theory uncertainty!# (5) had = # # incl. low Q data 3 1 Excluded Preliminary m H!GeV" Some differences in treatment of theory errors, which just start to matter. E.g. theoretical and experimental errors added linearly (= conservative) or quadratically. - In following: theoretical errors treated as Gaussian (quadratic addition.) The ElectroWeak fit of Standard Model 7

8 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 Prediction EWSB at tree-level: M Z cosθ W =1 Cross Section [pb] s [GeV] The impact of loop 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 The electroweak fit at NNLO Status and Prospects 8

9 The SM fit with Gfitter, including the Higgs Discovery of Higgs-like boson at LHC Cross section, production rate time 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 = ± 0.37 ± 0.18 GeV CMS: M H = ± 0.7 ± 0.14 GeV [arxiv: , CMS-PAS-HIG ] Change in average between fully uncorrelated and fully correlated systematic uncertainties is minor: δm H : GeV EW fit unaffected at this level of precision - ln L CMS Preliminary H γγ + H ZZ µ, µ (ggh,tth), ZZ γγ µ (VBF,VH) γγ fb (8 TeV) fb (7 TeV) Combined H γγ tagged H ZZ tagged m H (GeV) The electroweak fit at NNLO Status and Prospects 9

10 The SM fit with Gfitter, including the Higgs Unique situation: For first time SM is fully over-constrained. And for first time electroweak observables can be unambiguously predicted at loop level. Powerful predictions of key observables now possible, much better than w/o M H. Can now test for: Self-consistency of SM. Possible contributions from BSM models. Part of focus of this talk The ElectroWeak fit of Standard Model 10

11 Measurements at the Z-pole (1/) Total cross-section of e - e + Z ff Expressed 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] The ElectroWeak fit of Standard Model 11

12 Measurements at the Z-pole (/) 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: The ElectroWeak fit of Standard Model 1

13 Latest averages for and m top Latest Tevatron result from: arxiv: Top mass WA (March 014): arxiv: ± 0.76 GeV/c Tevatron (Jul 14): arxiv: ± 0.64 GeV/c The ElectroWeak fit of Standard Model 13

14 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 and sin θ f eff Conventionally parametrized as (α(0) = fine structure constant) : Evolution with renormalization scale: The ElectroWeak fit of Standard Model 14

15 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 and sin θ f eff Conventionally parametrized as (α(0) = fine structure constant) : Evolution with renormalization scale: Leptonic term known up to four loops (for q m l ) Top quark contribution known up to loops, small: -0.7x10-4 [C.Sturm, arxiv: ] [M. Steinhauser, PLB 49, 158 (1998)] The ElectroWeak fit of Standard Model 15

16 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 and sin θ f eff Conventionally parametrized as (α(0) = fine structure constant) : Evolution with renormalization scale: Hadronic contribution (from the 5 light quarks) completely dominates overall uncertainty on α(m Z ). Difficult to calculate, cannot be obtained from pqcd alone. Analysis of low-energy e + e - data Usage of pqcd if lack of data Δ (5) α had M Z -4 ( 74.9 ± 1.0) 10 ( ) = Similar analysis to evaluation of hadronic contribution to (g-) µ [M. Davier et al., Eur. Phys. J. C71, 1515 (011)] The ElectroWeak fit of Standard Model 16

17 Theoretical inputs at NNLO Radiative corrections are important! E.g. consider tree-level EW unification relation: - This predicts: = ( ± 0.005) GeV - Experiment: = ( ± 0.015) GeV Without loop corrections: shift of 400 MeV, 7σ discrepancy! tree-level = M Z % ( 8πα ' 1+ 1 * ' G F M * & Z ) The ElectroWeak fit of Standard Model 17

18 Theoretical inputs at NNLO Radiative corrections are important! E.g. consider tree-level EW unification relation: - This predicts: = ( ± 0.005) GeV - Experiment: = ( ± 0.015) GeV Without loop corrections: shift of 400 MeV, 7σ discrepancy! tree-level = M Z % ( 8πα ' 1+ 1 * ' G F M * & Z ) 1. Experimental precision (<1%), better than typical loop factor (α 1/137) Requires radiative corrections at -loop level.. Before Higgs discovery: uncertainty on M H largest uncertainty in EW fit. After: inclusion of all relevant theoretical uncertainties. (Part of focus of this talk ) The electroweak fit at NNLO Status and Prospects 18

19 Theoretical inputs at NNLO Radiative corrections are important! E.g. consider tree-level EW unification relation: - This predicts: = ( ± 0.005) GeV - Experiment: = ( ± 0.015) GeV Without loop corrections: shift of 400 MeV, 7σ discrepancy! tree-level = M Z % ( 8πα ' 1+ 1 * ' G F M * & Z ) In EW fit with Gfitter we use state-of-the-art calculations: sin θ f eff Effective weak mixing angle [M. Awramik et al., JHEP 11, 048 (006), M. Awramik et al., Nucl.Phys.B813: (009)] - Full two-loop + leading beyond-two-loop form factor corrections MW Mass of the W boson [M. Awramik et al., arxiv: v] - Full two-loop + leading beyond-two-loop + 4-loop QCD correction [Kuhn et al., hep-hp/ ,060501,06063] Γhad QCD Adler functions at N 3 LO [P. A. Baikov et al., PRL108, 003 (01)] - N 3 LO prediction of the hadronic cross section Γi Partial Z decay widths [A. Freitas, JHEP04, 070 (014)] New: all EWPOs (*) now described at -loop level or better! New! New! full fermionic -loop calc. The ElectroWeak fit of Standard Model 19

20 Theory uncertainties from unknown H.O. terms Most important observables: Theory uncertainties accounted for in EW fit (w/ Gauss constraints): Old setup: two nuisance pars for theoretical uncertainties: δ (4 MeV), δsin θ l eff (4.7x10-5 ) Newly included in EW fit setup: Full fermionic -loop corrections of partial Z decay widths (A. Freitas) 6 corresponding nuisance parameters. (δγ Z = 0.5 MeV) Γhad QCD Adler functions at N 3 LO nuisance parameters. Top quark mass: conversion from measurement to pole to MS-bar mass Agnostic value used here: δ theo m t = 0.5 GeV. (more later) New in EW fit The electroweak fit at NNLO Status and Prospects

21 Electroweak Fit Experimental inputs Latest experimental inputs: Z-pole observables: from LEP / SLC [ADLO+SLD, Phys. Rept. 47, 57 (006)] and Γ W from LEP/Tevatron [arxiv: , arxiv: ] m top latest avg from Tevatron+LHC [arxiv: ] m c, m b world averages (PDG) [PDG, J. Phys. G33,1 (006)] Δα had (5) (M Z ) including α S dependency [Davier et al., EPJC 71, 1515 (011)] M H from LHC [arxiv: , CMS-PAS-HIG ] 7 (+10) free fit parameters: M H, M Z, α S (M Z ), Δα had (5) (M Z ), m t, m c, m b 10 theory nuisance parameters - e.g. δ (4 MeV), δsin θ l eff (4.7x10-5 ) The electroweak fit at NNLO Status and Prospects LHC Tevatron LEP SLC SLC LEP Tevatron + LHC 1

22 Electroweak Fit SM Fit Results From the Gfitter group: /gfitter Left: full fit result Middle: fit excluding the row Right: not incl. theory errors Parameter Input value Free w/o exp. input w/o exp. input Fit Result in fit in line in line, no theo. unc M H [GeV] ( ) ± 0.4 yes ± [GeV] ± ± ± ± Γ W [GeV].085 ± ± ± ± M Z [GeV] ± yes ± ± ± Γ Z [GeV].495 ± ± ± ± σ 0 had [nb] ± ± ± ± Rl ± ± ± ± 0.06 A 0,l FB ± ± ± ± ( ) A l ± ± ± ± sin θ l eff (Q FB) 0.34 ± ± ± ± A c ± ± ± ± A b 0.93 ± ± ± ± A 0,c FB ± ± ± ± A 0,b FB ± ± ± ± Rc ± ± ± Rb ± ± ± ± m c [GeV] yes m b [GeV] yes m t [GeV] ± 0.76 yes ± 0.85 ( ) ( ) ±.3 α (5) had (M Z )( ) 757 ± 10 yes 756 ± ± 44 7 ± 4 α s (MZ ) yes ± ± ± The ElectroWeak fit of Standard Model

23 Electroweak Fit SM Fit Results Results drawn as pull values: deviations to the indirect determinations, divided by total error. Total error: error of direct measurement plus error from indirect determination. Black: direct measurement (data) Orange: full fit Light-blue: fit excluding input from the row The prediction (light blue) is often more precise than the measurement! The ElectroWeak fit of Standard Model 3

24 Electroweak Fit SM Fit Results Results drawn as pull values: deviations to the indirect determinations, divided by total error. Total error: error of direct measurement plus error from indirect determination. Black: direct measurement (data) Orange: full fit Light-blue: fit excluding input from the row The prediction (light blue) is often more precise than the measurement! The ElectroWeak fit of Standard Model 4

25 Electroweak Fit SM Fit Results No individual value exceeds 3σ Largest deviations in b-sector: A 0,b FB with.5σ à largest contribution to χ Small pulls for M H, M Z, Δα had (5) (M Z ), m c, m b indicate that input accuracies exceed fit requirements Small changes from switching between 1 and -loop calc. for partial Z widths and small correction. χ min (complete setup) = 17.8 χ min (1-loop Z width) = 18.0 χ min (no correction) = 17.4 χ min (no extra theory errors) = 18. The ElectroWeak fit of Standard Model 5

26 Goodness of Fit Number of toy experiments distribution for n dof =14 χ = min,data Toy analysis: p-value for wrongly rejecting the SM = 1 ± (theo) % p-value is equivalent to 0.8σ Evaluated with 0k pseudo experiments follows χ with 14 d.o.f. χ Toy analysis incl. theo. errors Toy analysis excl. theo. errors p-value incl. theo. errors p-value excl. theo. errors p-value = ± p-value = 0.10 ± For comparison: χ min = 17.8 à Prob(χ min, 14) = 1 % Large value of χ min not due to inclusion of M H measurement. Without M H measurement: χ min = 16.3 à Prob(χ min, 13) = 3% 6 χ min SM ) data p-value for ( The ElectroWeak fit of Standard Model

27 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 measurements. χ measurement SM fit with M H measurement SM fit w/o M H ATLAS measurement [arxiv: ] CMS measurement [arxiv: ] G fitter SM Jul 14 σ 1σ 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 0,b FB, and clearly visible The electroweak fit at NNLO Status and Prospects M H fit below only includes the given observable A l (LEP) A l (SLD) 0,b A FB Fit w/o M H LHC average G fitter SM Jul M H [GeV] [GeV] ± 0. 7

28 History of Higgs mass predictions The EW fits have always been able to predict the Higgs mass correctly! The ElectroWeak fit of Standard Model and Beyond

29 Prediction of W mass Scan of Δχ profile versus 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 χ SM fit w/o measurement measurement and M H SM fit w/o SM fit with minimal input world average [arxiv: ] G fitter SM Jul 14 3σ σ M H measurement allows for precise constraint on 1 Agreement at 1.4σ Fit result for indirect determination of (full fit w/o ): [GeV] 1σ More precise estimate of than the direct measurements! Uncertainty on world average measurement: 15 MeV Obtained with simple error propagation The electroweak fit at NNLO Status and Prospects 9

30 Prediction of 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 χ measurement SM fit with M H measurement SM fit w/o M H SM fit with minimal input LEP/SLD average [hep-ex/ ] G fitter SM Jul 14 3σ σ M H measurement allows for very precise constraint on sin θ l eff Fit result for indirect determination of sin θ l eff : sin (θ l ) eff 1σ More precise than direct determination (from LEP/SLD)! Uncertainty on LEP/SLD average: 1.6x10-4 Obtained with simple error propagation The electroweak fit at NNLO Status and Prospects 30

31 Prediction of top mass χ 10 9 SM fit w/o m t measurements G fitter SM Jul 14 3σ 8 SM fit w/o m t and M H measurements mkin t world average [arxiv: ] mkin t D0 measurement [arxiv: ] pole m t pole m t pole m t from Tevatron from CMS from ATLAS σ tt σ σ tt [arxiv: ] [arxiv: v3] tt [arxiv: ] σ 3 1 1σ [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 - Remember: fully obtained from radiative corrections! Indirect result: m t = GeV Tevatron+LHC: ± 0.76 GeV new Tevatron-only: ± 0.64 GeV The electroweak fit at NNLO Status and Prospects 31

32 State of the SM: W versus top mass Scan of 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] % and 95% CL contours fit w/o M fit w/o M direct M W W W and m t measurements, m and M measurements t H and m t measurements m t world comb. ± 1σ m t = GeV σ = 0.76 GeV σ = theo GeV world comb. ± 1σ = ± GeV M H = 50 GeV M H = GeV M H = 300 GeV M H = 600 GeV G fitter SM Jul m t [GeV] Observed agreement demonstrates impressive consistency of the SM! The electroweak fit at NNLO Status and Prospects 3

33 State of the SM: loop vs tree-level observables Scan of M H vs m top (left) and vs sin θ l eff (right), with direct measurements excluded from the fit. Again, significant reduction allowed indirect parameter space from Higgs mass measurement. [GeV] M H Observables from radiative corrections Tree-level observables 68% and 95% CL contours fit w/o M and m meas. H t direct M and m meas. H t m t world comb. ± 1σ m t = GeV σ = 0.76 GeV σ = GeV theo [GeV] % and 95% CL contours direct M and sin (θ f ) measurements W eff fit w/o M, sin (θ f ) and Z widths measurements W eff f eff f eff fit w/o M, sin (θ W fit w/o M, sin (θ W ) and M ), M f eff sin (θ ) LEP+SLC ± 1σ measurements H and Z widths measurements H M H M H private comb. ± 1σ = ± 0.4 GeV world comb. ± 1σ 50 G fitter SM [GeV] m t Jan G fitter SM sin (θ l ) eff Jul 14 and sin θ l eff have become the sensitive probes of new physics! Reason: both are tree-level SM predictions. The electroweak fit at NNLO Status and Prospects

34 Theoretical uncertainty on m top [GeV] % CL contour for fit w/o m W, sin (θ l ) and Z widths measurements = 1.5 GeV eff δ m theo t δ m theo t δ m theo t δ theo m t = 1.0 GeV = 0.5 GeV = 0.0 GeV sin (θ l eff ) LEP+SLC ± 1σ default = 0.5 GeV m W world comb. ± 1σ G fitter SM Jul sin (θ l ) eff δ theo m t : unc. on conversion of measured top mass to MS-bar mass Sources: ambiguity top mass definition, fragmentation process, pole MS conv. Predictions for δ theo m t : between GeV or greater. [Moch etal, ax: , Mangano: TOP 1, Buckley etal, ax: , Juste etal: ax: ] δ theo m t varied here between 0 and 1.5 GeV, in steps of 0.5 GeV. Better assessment of δ theo m t of relevance for the EW fit. (see also backup) The electroweak fit at NNLO Status and Prospects

35 Prediction for α s (M Z ) from Z hadrons Scan of Δχ 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 full N LO and partial N 3 LO. Most sensitive through total hadronic crosssection σ 0 had and partial leptonic width R 0 l χ SM fit SM fit minimal input and R α S (M ) from Z τ G fitter SM and σ 0 l had decays at 3NLO [Eur.Phys.J.C56,305 (008)] Jul 14 α S (M ) Z σ 1σ Most affected by new theory uncertainties Before: δ theo = In good agreement with value from τ decays, at N 3 LO, and with WA. (Improvements in precision only expected with ILC/GigaZ. See later.) The electroweak fit at NNLO Status and Prospects 35

36 Beyond the SM The ElectroWeak fit of Standard Model 36

37 Constraints on BSM models Oblique corrections from New Physics described through STU parametrization [Peskin and Takeuchi, Phys. Rev. D46, 1 (1991)] If energy scale of NP is high, BSM physics could appear dominantly through vacuum polarization corrections Aka, oblique corrections Oblique corrections reabsorbed into electroweak form factors Δρ, Δκ, Δr parameters, appearing in:, sin θ eff, G F, α, etc. Electroweak fit sensitive to BSM physics through oblique corrections Similar to sensitivity to top and 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: extended parameters (VWX), correction to Zà bb couplings. [Burgess et al., Phys. Lett. B36, 76 (1994)] [Burgess et al., Phys. Rev. D49, 6115 (1994)] The ElectroWeak fit of Standard Model 37

38 Fit results for S, T, U S,T,U parameters obtained directly from fit to the EW observables. SM: M H = 15 GeV, m t = 173 GeV This defines (S,T,U) = (0,0,0) S, T depend logarithmically on M H T fit contours for U=0 (SM : M H =15 GeV, m =173 GeV) ref t 68% and 95% CL for present fit 95% CL for asymmetries & sin θ l (Q ) eff FB 95% CL for Z widths 95% CL for & Γ W Fit result (with U floating): S = 0.05 ± 0.11 T = 0.09 ± 0.13 U = 0.01 ± 0.11 S T U S T U 1 Also results for Zà bb correction (see backup) SM Prediction M H = ± 0.4 GeV = ± 0.91 GeV m t G fitter SM Stronger constraints with U=0. Jul 14 S No indication for new physics. Use this to constrain 4 th gen, Ex-Dim, T-C, Higgs couplings (in backup) The electroweak fit at NNLO Status and Prospects 38

39 Modified Higgs couplings Study of potential deviations of Higgs couplings from SM. BSM modeled as extension of SM through effective Lagrangian. Consider leading corrections only. Popular benchmark model: Scaling of Higgs-vector boson (κ V ) and Higgs-fermion couplings (κ F ) with no invisible/undetectable width (Custodial symmetry is assumed.) Kappa parametrization Main effect on EWPO due to modified Higgs coupling to gauge bosons (κ V ) κ V κ V Involving the longitudinal d.o.f. κ V Most BSM models: κ V < 1 Additional Higgses typically give positive contribution to. The ElectroWeak fit of Standard Model 39

40 Modified Higgs couplings Main effect on EWPO due to Higgs coupling to gauge bosons (κ V ). Formulas from: Espinosa et al [arxiv: ] Cut-off scale Λ represents mass scale of new states that unitarize longitudinal gauge-boson scattering. (As required in this model.) T Higgs-vector boson couplings scaling B G fitter SM preliminary Aug 13 Espinosa et al [arxiv: ], Falkowski et al [arxiv: ], etc. λ is varied between 1 and 10 TeV, nominally fixed to 3 TeV (4πv) %, 95%, 99% CL fit contours (M = 16 GeV, m = 173 GeV, U = 0) H t [0,] λ [1,10] TeV κ V S The ElectroWeak fit of Standard Model 40

41 Reproduction of ATLAS and CMS results arxiv: CMS-PAS-HIG κ V κ V Approximate reproduction of ATLAS/CMS results within limited public-info available. The electroweak fit at NNLO Status and Prospects 41

42 Higgs coupling results Private LHC combination: κ V = κ F = Result from stand-alone EW fit: κ V = 1.03 ± 0.0 (using λ=3 TeV) Implies NP-scale of Λ 13 TeV. κ F Combination of ATLAS and CMS results. Average neglects correlations. LHC experiments 68% and 95% CL fit contours Standard Model prediction EW-fit + LHC experiments 68% and 95% CL fit contours [λ = 3 TeV] Fit minimum % CL contours w/o and κ V measurement λ = 10 TeV λ = 5 TeV λ = 1 TeV κ V private LHC average ± 1σ Λ = λ 1-κ V world comb. ± 1σ B G fitter SM Jul 14 κ V κ V Some dependency for κ V in central value [ ] and error [ ] on cut-off scale λ [1-10 TeV]. 1. EW fit sofar more precise result for κ V than current LHC experiments.. EW fit has positive deviation of κ V from 1.0. (Many BSM models: κ V < 1) % and 95% CL contours for direct M and κ V measurements W G fitter SM Jul 14 The electroweak fit at NNLO Status and Prospects 4

43 Prospects for the Standard Model fit The ElectroWeak fit of Standard Model 43

44 Two prospects scenarios: LHC, ILC/GigaZ Prospects of EW fit tested for two (three) scenarios: 1. LHC Phase-1 = before HL upgrade. ILC with GigaZ (*) 3. (FCC-ee in backup) (*) GigaZ: Operation of ILC at lower energies like Z-pole or WW threshold. Allows to perform precision measurements of EW sector of the SM. At Z-pole, several billion Z s can be studied within ~1- months. Physics of LEP1 and SLC can be revisited with few days of data. In following studies: central values of input measurements adjusted to M H = 15 GeV. (Except where indicated.) The electroweak fit at NNLO Status and Prospects

45 Prospects of EW fit for: ILC with Giga Z Future Linear Collider can improve precision of EWPO s tremendously. WW threshold scan + kinematic reconstruction, to obtain MW From threshold scan: δmw : 15 5 MeV ttbar threshold scan, to obtain mt Obtain mt indirectly from production cross section: δmt : GeV - Dominated by conversion from threshold to MSbar mass. 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 θ l eff : H ZZ and H WW couplings: measured at 1% precision. ILC prospects: from ILC TDR (Vol-). The electroweak fit at NNLO Status and Prospects 45

46 Prospects of EW fit for: LHC Phase-1 LHC Phase-1 (300/fb) W mass measurement : δmw : 15 8 MeV Final top mass measurement mt : δmt : GeV H ZZ and H WW couplings: measured at 3% precision. LHC prospects: possibly optimistic scenario, but not impossible. The electroweak fit at NNLO Status and Prospects

47 Prospects of EW fit LHC Phase-1 (300/fb) W mass measurement : δmw : 15 8 MeV Final top mass measurement mt : δmt : GeV H ZZ and H WW couplings: measured at 3% precision. For both LHC and ILC: Low-energy data results to improve Δαhad: ISR-based (BABAR), KLOE-II, VEPP-000 (at energy below cc resonance), and BESIII e + e - cross-section measurements (around cc resonance). Plus: improved αs (from reliable Lattice predictions): Δαhad: Assuming ~5% of today s theoretical uncertainties on and sin θ l eff Implies ambitions three-loop electroweak calculations! - δ (4 1 MeV), δsin θ l eff (4.7x10-5 1x10-5 ) (from Snowmass report) Partial Z decay widths at 3-loop level: factor 4 improvement LHC: top quark mass theo uncertainty: GeV The electroweak fit at NNLO Status and Prospects

48 Prospects of EW fit χ 5 0 Present SM fit Present uncertainties Prospects for LHC Prospects for ILC/GigaZ G fitter SM χ Jul 14 5σ 5 Present SM fit M H avg G fitter SM 15 GeV 0 Prospects for LHC 93 GeV Prospects for ILC/GigaZ (δ = Rfit) theo Aug 13 5σ 15 4σ 15 Prospects for ILC/GigaZ (δ = Gauss) theo 4σ σ 3σ 5 5 σ σ 0 1σ M H [GeV] 1σ M H [GeV] Indirect prediction M H dominated by experimental uncertainties. Present: σ(m H ) = (exp) (theo) GeV LHC: σ(m H ) = (exp) (theo) GeV ILC: σ(m H ) = (exp) (theo) GeV Logarithmic dependency on M H cannot compete with direct M H meas. If EWP-data central values unchanged, i.e. keep favoring low value of Higgs mass (93 GeV), ~5σ discrepancy with measured Higgs mass. The electroweak fit at NNLO Status and Prospects 48

49 Prospects of EW fit [GeV] % and 95% CL fit contour and m t w/o Present SM fit measurements Prospect for LHC Prospect for ILC/GigaZ Present measurement m t ± 1 σ [GeV] % and 95% CL fit contour w/o M and sin (θ f ) measurements W eff Present SM fit Prospect for LHC Prospect for ILC/GigaZ Present measurement sin (θ f ) eff ± 1 σ ILC precision LHC precision ILC precision LHC precision ± 1 σ ± 1 σ G fitter SM Jul G fitter SM Jul [GeV] m t sin (θ l ) eff Huge reduction of uncertainty on indirect determinations of m t, m W, and sin θ l eff, by a factor of 3 or more. Assuming central values of m t and do not change, (at ILC) a deviation between the SM prediction and the direct measurements would be prominently visible. The electroweak fit at NNLO Status and Prospects 49

50 Impact of individual uncertainties Breakdown of individual contributions to errors of and sin θ l eff and sin θ l eff are sensitive probes of new physics! For all scenarios. At ILC/GigaZ, precision of M Z will become important again. The electroweak fit at NNLO Status and Prospects

51 BSM prospects of EW fit T % and 95% CL fit contours for U=0 (SM : M H =15 GeV, m =173 GeV) ref t Present uncertainties Prospects for LHC Prospects for ILC/GigaZ % and 95% CL contours measurement and κ V w/o Present SM fit Prospect for LHC Prospect for ILC/GigaZ Present measurement ILC precision LHC precision κ V private LHC average Λ = 4πv 1-κ V ± 1σ SM Prediction M H = ± 0.4 GeV = ± 0.91 GeV m t world comb. ± 1σ G fitter SM S Jul G fitter SM κ V Jul 14 For STU parameters, improvement of factor of >3 is possible at ILC. Again, at ILC a deviation between the SM predictions and direct measurements would be prominently visible. Competitive results between EW fit and Higgs coupling measurements! (At level of 1%.) The electroweak fit at NNLO Status and Prospects 51

52 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: 1% (pseudo-experiments) New: N LO calcs and theo. uncertainties for all relevant observables. δ theo m t starting to become relevant. Knowledge of M H dramatically improves SM prediction of key observables (8 8 MeV), sin θ l eff (.3x x10-5 ), m t (6..5 GeV) Improved accuracies set benchmark for new direct measurements! δ (indirect) = 8 MeV Large contributions to δ from top and unknown higher-order EW corrections δ (direct) = 15 MeV δtheo δαs δδαhad Including new data electroweak fits δmz remain very interesting in the next years! Latest results always available at: 6% 5% 4% δmtop 31% 10% 4% δ theo mtop Thanks! The electroweak fit at NNLO Status and Prospects 5

53 Backup A Generic Fitter Project for HEP Model Testing Backup The ElectroWeak fit of Standard Model 53

54 Input correlations of the EW fit Input correlation coefficients between Z pole measurements The ElectroWeak fit of Standard Model 54

55 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 ~0.15 MeV, compared with experimental uncertainty of.0 MeV. The ElectroWeak fit of Standard Model [D. Bardin, G. Passarino, The Standard Model in the Making, Clarendon Press (1999)] O(αs 3 ) O(αs 4 ) O(αs) O(αs ) [P. Baikov et al., Phys. Rev. Lett. 108, 003 (01)] [P. Baikov et al Phys. Rev. Lett. 104, (010)] 55

56 Calculation of 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 s ), O(α ferm ), O(α bos ), O(α α s m t4 ), O(α 3 m t6 ) Uncertainty estimate: Missing terms of order O(α α s ): about 3 MeV (from O(α α s m t4 )) Electroweak three-loop correction O(α 3 ): < MeV Three-loop QCD corrections O(α s3 ): < MeV Total: δ 4 MeV [M Awramik et al., Phys. Rev. D69, (004)] [M Awramik et al., Phys. Rev. Lett. 89, (00)] [A Freitas et al., Phys. Lett. B495, 338 (000)] The ElectroWeak fit of Standard Model 56

57 Calculation of sin (θ l eff ) Effective mixing angle: [M Awramik et al, Phys. Rev. Lett. 93, (004)] [M Awramik et al., JHEP 11, 048 (006)] 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 of: δsin (θ l eff ) = 4.7x10-5 The ElectroWeak fit of Standard Model 57

58 Uncertainty in Top mass definition Difficult to define a pole mass for heavy, unstable and colored particle. Single top decays before hadronizing. To have colorless final states, additional quarks needed. Non-perturb. color-reconnection effects in fragmentation biases in simulation. Renormalon ambiguity in top mass definition. - For pole mass, not for MS-bar scheme. Impact of finite top width effects. Result: m exp t m pole t, and event-dependent. The top mass extracted in hadron collisions is not well defined below a precision of O(Γ t ) ~ 1 GeV Hard to estimate additional theo. uncertainties. With 0.5 GeV on m t : M H = GeV, = ±0.013 GeV, sin θ l eff = ± Sofar only small deterioration in precision. The ElectroWeak fit of Standard Model

59 Interesting Top pole mass measurement From: ATLAS-CONF : top-quark pole mass measurement from ttbar+1jet events Through study of inverse of invariant mass of ttbar+1jet system (quantity: ρ S ). ) s,ρ pole R (m t ATLAS Preliminary -1 s=7 TeV, 4.6 fb Data tt+1-jet, m tt+1-jet, m pole t pole t =170 GeV =180 GeV Free of MC pole mass conversion uncertainty m pole t = ± 1.5 (stat) ± 1.4 (syst) (theo) GeV Great to see these efforts ongoing! Similar measurements / tests ongoing at CMS ρ [parton level] s The ElectroWeak fit of Standard Model and Beyond

60 Moriond 011: Prediction for Higgs mass LEP + Tevatron (Fall 010) : CLs s+b central value ±1σ: M H = σ interval: lnq : 115,15 LEP + Tevatron (Moriond 011) : s CL s+b central value ±1σ: M H = σ interval: lnq : 115,138 CL s+b CL s+b [ ] GeV [ ] GeV sided : 114,155 sided : 114,149 Fit with LEP + Tevatron + LHC (Hè WW) searches (Moriond 011) : Central value unchanged σ interval: [ ] GeV [ ] GeV lnq : 115,137 CL sided s+b : 114,14? [ ] GeV [ ] [ 15,155] GeV GeV +1.3 GeV "! "! Global Fit of electroweak SM and beyond Direct searches $! = -ln(q) LEP 95% CL Tevatron 95% CL LHC: H% WW only. Average neglects correlations LEP + Tevatron + ATLAS + CMS LEP + Tevatron G fitter SM LEP + Tevatron (Fall 010) Direct searches $! = -ln(q) LEP 95% CL Tevatron 95% CL M H [GeV] LHC: H% WW only. Average neglects correlations Theory uncertainty G fitter SM Fit including theory errors Fit excluding theory errors M H MOR 11 MOR 11 [GeV] 4# 3# # 1# 4# 3# # 1# 60

61 Low energy observables Low energy observables with interesting precision will soon become available. The ElectroWeak fit of Standard Model

62 Two prospects scenarios: LHC, ILC/GigaZ Uncertainty estimates used: ILC prospects from: ILC TDR (Vol-). Theoretical uncertainty estimates from recent Snowmass report Central values of input measurements adjusted to M H = 16 GeV. The ElectroWeak fit of Standard Model and Beyond

63 FCC-ee prospects From TLEP prospects: arxiv: Global Fit of electroweak SM and beyond

64 Experimental inputs Predicted uncertainties FCC-ee scenario: Preliminary estimates Clearly not the same level of understanding as LHC or ILC. Uncertainties may turn out completely different. From arxiv: , and Snowmass report. - Of these two, we take most conservative estimate. Note: top mass dominated by theoretical uncertainty. Higher statistics From beam energy precision: improved M Z and Γ Z The ElectroWeak fit of Standard Model and Beyond

65 χ Prospects of the EW fit: Higgs mass (16 GeV) Present SM fit Present uncertainties Prospects for LHC Present / LHC / ILC FCC-ee scenario Prospects for ILC/GigaZ (δ = Rfit) theo = Gauss) Prospects for ILC/GigaZ (δ theo G fitter SM χ Aug 13 5σ 5 0 4σ 15 Future scenario: δm H = 0.1 GeV, δm Z = 0.1 MeV, δγ Z = 0.1 MeV, δ = 1.3 MeV, δm t = 80 MeV, -6-3 theo theo -5 δsin (θ ) = 3 10, δr = , δ = 1 MeV, δsin (θ ) = 1 10 eff 0,lep eff Future scenario Present SM fit Present uncertainties 5σ 4σ σ 3σ σ 1σ M H [GeV] σ 1σ M H [GeV] Logarithmic dependency on M H cannot compete with direct M H meas. Indirect prediction M H dominated by theory uncertainties. ILC with (without) theory errors: M H = (±7) GeV ILC with present-day theory uncertainties: M H = GeV FCC-ee with (without) theory errors: M H = 16 ± 5 (±3) GeV The ElectroWeak fit of Standard Model and Beyond

66 χ Prospects of the EW fit: Higgs mass (94 GeV) 5 0 Present SM fit Prospects for LHC Present / LHC / ILC FCC-ee scenario Prospects for ILC/GigaZ (δ = Rfit) theo M H avg G fitter SM 94 GeV χ Aug 13 5σ 5 0 Future scenario: δm H = 0.1 GeV, δm Z = 0.1 MeV, δγ Z = 0.1 MeV, δ = 1.3 MeV, -6 lep -3-5 δm t = 80 MeV, δsin (θ ) = 3 10, δr = , δ α = , eff 0 had th th -5 δ = 1 MeV, δ sin (θ eff ) = 1 10 = 94 MeV Future scenario M H 94 GeV 5σ 15 Prospects for ILC/GigaZ (δ = Gauss) theo 4σ 15 Present SM fit 4σ σ 3σ 5 5 σ σ 0 1σ M H [GeV] 1σ M H [GeV] If EWP-data central values are unchanged, i.e. they keep favoring low value of Higgs mass (94 GeV), >5σ discrepancy with measured Higgs mass. In both ILC and FCC-ee scenarios. The ElectroWeak fit of Standard Model and Beyond

67 χ Prospects of the EW fit: W mass and sin θ l eff Present SM fit Prospects for LHC Present / LHC / ILC Prospectes for ILC/GigaZ (δ = Rfit) theo Prospects for ILC/GigaZ (δ = Gauss) theo Direct measurement (present / LHC / ILC) G fitter SM Aug 13 5σ 4σ χ Future scenario: δm H = 0.1 GeV, δm Z = 0.1 MeV, δγ Z = 0.1 MeV, δ = 1.3 MeV, -6 lep -3-5 δm t = 80 MeV, δsin (θ ) = 3 10, δr = , δ α = , eff 0 had th th -5 δ = 1 MeV, δ sin (θ eff ) = 1 10 Future scenario Present SM fit FCC-ee scenario Direct measurement (present / future) 5σ 4σ 10 3σ 10 3σ 5 σ 5 σ 1σ [GeV] 1σ Future scenario: δm H = 0.1 GeV, δm Z = 0.1 MeV, δγ Z = 0.1 MeV, δ = 1.3 MeV, -6 lep -3-5 δm t = 80 MeV, δsin (θ ) = 3 10, δr = , δ α = , eff 0 had th th -5 δ = 1 MeV, δ sin (θ eff ) = 1 10 Future scenario Present uncertainties Direct measurement (present / future) [GeV] 5σ 4σ 10 3σ 5 σ The ElectroWeak fit of Standard Model and Beyond 1σ sin l (θ eff )

68 [GeV] Prospects of the EW fit: W mass versus sin θ l eff % and 95% CL fit contours w/o M W and sin (θ Present SM fit l eff Prospects for LHC ) measurements Prospects for ILC/GigaZ Present measurement ILC precision LHC precision ± 1σ Present / LHC / ILC FCC-ee scenario l sin (θeff ) ± 1σ G fitter SM sin [GeV] Oct 13 l (θ eff ) Future scenario: δm H = 0.1 GeV, δm Z = 0.1 MeV, δγ Z = 0.1 MeV, δ = 1.3 MeV, -6 lep -3-5 δm t = 80 MeV, δsin (θ ) = 3 10, δr = , δ α = , eff 0 had th th -5 δ = 1 MeV, δ sin (θ eff ) = 1 10 Present measurement Future scenario 68% and 95% CL fit contours w/o and m t measurements Present SM fit Future scenario l (θ eff ) ± 1σ sin sin ± 1σ l (θ eff ) Huge reduction of uncertainty on indirect determinations of m W, and sin θ l eff, by a factor of 3 ( 4-5) at ILC (FCC-ee). Assuming central values of and sin θ l eff do not change, a deviation between the SM prediction and the direct measurements would be prominently visible, at both ILC and FCC-ee. But also in LHC-300 scenario, from improved theory uncertainties. The ElectroWeak fit of Standard Model and Beyond

69 Confrontation of measurement and prediction Breakdown of individual contributions to errors of and sin θ l eff Parametric uncertainties (not the full fit). and sin θ l eff are sensitive probes of new physics! In all scenarios. At ILC/GigaZ, precision of M Z will become important again. At FCC-ee ( Future ), limited by external inputs: theory errors and Δα had The ElectroWeak fit of Standard Model and Beyond

70 [GeV] Prospects of the EW fit: W versus top mass % and 95% CL fit contours w/o and m t measurements Present SM fit Prospects for LHC Prospects for ILC/GigaZ Present measurement ILC precision LHC precision ± 1σ Present / LHC / ILC FCC-ee scenario mt ± 1σ G fitter SM Oct 13 [GeV] Future scenario: δm H = 0.1 GeV, δm Z = 0.1 MeV, δγ Z = 0.1 MeV, δ = 1.3 MeV, -6 lep -3-5 δm t = 80 MeV, δsin (θ ) = 3 10, δr = , δ α = , eff 0 had th th -5 δ = 1 MeV, δ sin (θ eff ) = 1 10 Present measurement Future scenario 68% and 95% CL fit contours w/o and m t measurements Present SM fit Future scenario m t ± 1σ ± 1σ m t [GeV] m t [GeV] Huge reduction of uncertainty on indirect determinations of m t and m W by a factor of 3 ( 5) at ILC (FCC-ee). Assuming central values of m t and do not change, a deviation between the SM prediction and the direct measurements would be prominently visible. The ElectroWeak fit of Standard Model and Beyond

71 T Prospects of EW fit: S versus T % and 95% CL fit contours for U=0 (SM : M H =16 GeV, m =173 GeV) ref t Present fit Present uncertainties Prospects for LHC Prospects for ILC/GigaZ Present / LHC / ILC FCC-ee scenario T Future scenario: δm H = 0.1 GeV, δm Z = 0.1 MeV, δγ Z = 0.1 MeV, δ = 1.3 MeV, -6 lep -3-5 δm t = 80 MeV, δsin (θ ) = 3 10, δr = , δ α = , eff 0 had th th -5 δ = 1 MeV, δ sin (θ eff ) = % and 95% CL fit contours for U=0 (SM : M H =16 GeV, m =173 GeV) ref t Present SM fit Present uncertainties Future scenario SM Prediction M H = 15.7 ± 0.4 GeV = ± 0.87 GeV m t B G fitter SM Oct 13 S S For STU parameters, improvement of factor of 4 ( 10) is possible at ILC (FCC-ee). Again, at both ILC and FCC-ee a deviation between the SM predictions and direct measurements would be prominently visible. The ElectroWeak fit of Standard Model and Beyond

72 Predicted uncertainties from EW fit Breakdown of uncertainties derived from EW fit. (Note: correlated errors.) Compared to parametric breakdown: reduced experimental, but increased theory errors. Slightly smaller total errors. The ElectroWeak fit of Standard Model and Beyond

73 Hunt for the Higgs Gfitter group, EPJC 7, 003 (01) χ LEP 95% CL Tevatron 95% CL Early 01 3σ 5 4 σ 3 Theory uncertainty Fit including theory errors Fit excluding theory errors 1 1σ M H [GeV] M H was last missing input parameter of the electroweak fit Indirect determination from EW fit (01): M H = GeV With direct limits incorporated in the EW fit: M H = GeV The ElectroWeak fit of Standard Model 73