The global electroweak fit at NNLO Prospects for LHC and ILC 80.46 - - PowerPoint PPT Presentation

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The global electroweak fit at NNLO Prospects for LHC and ILC 80.46 - - PowerPoint PPT Presentation

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University of Birmingham / Warwick, UK Max Baak (CERN), January 14 th / 15 th , 2015 on behalf of the Gfitter group (*) EPJC 74, 3046 (2014), arXiv:1407.3792 http://cern.ch/Gfitter The global electroweak fit at NNLO Prospects for LHC and ILC

slide-1
SLIDE 1

Max Baak (CERN) Global Fit of electroweak SM and beyond

Max Baak (CERN),

  • n behalf of the Gfitter group (*)

(*) M. Baak, J. Cuth, J. Haller, A. Höcker, R. Kogler, K. Mönig, M. Schott, J. Stelzer

The global electroweak fit at NNLO Prospects for LHC and ILC

http://cern.ch/Gfitter

1

EPJC 74, 3046 (2014), arXiv:1407.3792

University of Birmingham / Warwick, UK January 14th / 15th, 2015

[GeV]

t

m

140 150 160 170 180 190

[GeV]

W

M

80.25 80.3 80.35 80.4 80.45 80.5

68% and 95% CL contours measurements

t

and m

W

fit w/o M measurements

H

and M

t

, m

W

fit w/o M measurements

t

and m

W

direct M

σ 1 ± world comb.

W

M 0.015 GeV ± = 80.385

W

M σ 1 ± world comb.

t

m = 173.34 GeV

t

m = 0.76 GeV σ GeV

theo

0.50 ⊕ = 0.76 σ = 1 2 5 . 1 4 G e V

H

M = 5 G e V

H

M = 3 G e V

H

M = 6 G e V

H

M

G fitter SM

Jul ’14

)

eff l

θ (

2

sin

0.231 0.2311 0.2312 0.2313 0.2314 0.2315 0.2316 0.2317 0.2318 0.2319

[GeV]

W

M

80.32 80.34 80.36 80.38 80.4 80.42 80.44 80.46

68% and 95% CL fit contour ) measurements

eff f

θ (

2

and sin

W

w/o M Present SM fit Prospect for LHC Prospect for ILC/GigaZ Present measurement ILC precision LHC precision σ 1 ±

W

M σ 1 ± )

eff f

θ (

2

sin

G fitter SM

Jul ’14
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SLIDE 2

Max Baak (CERN)

Outline This presentation:

§ Introduction to the Electroweak Fit

  • Inputs to the electroweak fit
  • Full set of 2-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 2

slide-3
SLIDE 3

Max Baak (CERN) The ElectroWeak fit of Standard Model

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: http://cern.ch/Gfitter

  • (Most) results of this presentation: EPJC 74, 3046 (2014)

§ 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, 2HDM,

multiple BSM models, ...

3

slide-4
SLIDE 4

Max Baak (CERN)

The global electroweak fit of the SM

The ElectroWeak fit of Standard Model 4

slide-5
SLIDE 5

Max Baak (CERN)

Idea behind electroweak fits

ü Observables receive quantum loop corrections from ‘unseen’ virtual effects. ü If system is over-constrained, fit for unknown parameters

  • r 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

slide-6
SLIDE 6

Max Baak (CERN)

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.

The ElectroWeak fit of Standard Model

§ Top mass predictions from loop effects available since ~1990.

  • Official LEPEW fit since 1993.

§ The EW fits have always been able to predict the top mass correctly!

6

slide-7
SLIDE 7

Max Baak (CERN)

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].

7 The ElectroWeak fit of Standard Model 1 2 3 4 5 6 100 30 300

mH !GeV" !"2

Excluded

Preliminary

!#had = !#(5)

0.02758#0.00035 0.02749#0.00012

  • incl. low Q2 data

Theory uncertainty

March 2008

mLimit = 160 GeV

§ Fits of the different groups agree very well. § 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.)
slide-8
SLIDE 8

Max Baak (CERN)

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: § The impact of loop corrections

  • Absorbed into EW form factors: ρ, κ, Δr
  • Effective couplings at the Z-pole
  • Quadraticly dependent on mt,

logarithmic dependence on MH

8

Cross Section [pb] √s [GeV]

MW

2

M Z

2 cosθW 2 =1

The electroweak fit at NNLO – Status and Prospects

slide-9
SLIDE 9

Max Baak (CERN)

The SM fit with Gfitter, including the Higgs

9

§ 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: MH = 125.14 ± 0.24 GeV

  • ATLAS: MH = 125.36 ± 0.37 ± 0.18 GeV

CMS: MH = 125.03 ± 0.27 ± 0.14 GeV

[arXiv:1406.3827, CMS-PAS-HIG-14-009]

§ Change in average between fully uncorrelated and fully correlated systematic uncertainties is minor: δMH : 0.24 → 0.32 GeV

  • EW fit unaffected at this level of precision

The electroweak fit at NNLO – Status and Prospects (GeV)

H

m

123 124 125 126 127

ln L ∆

  • 2

1 2 3 4 5 6 7 8 9 10

Combined tagged γ γ → H ZZ tagged → H Combined tagged γ γ → H ZZ tagged → H

CMS

Preliminary

(7 TeV)

  • 1

(8 TeV) + 5.1 fb

  • 1

19.7 fb

ZZ → + H γ γ → H

(ggH,ttH),

γ γ

µ ,

ZZ

µ (VBF,VH)

γ γ

µ

slide-10
SLIDE 10

Max Baak (CERN)

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 MH. 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

slide-11
SLIDE 11

Max Baak (CERN)

√s [GeV] X-Section [pb]

Measurements at the Z-pole (1/2)

§ Total cross-section of e-e+→Z→ff

  • Expressed in terms of partial decay width of initial and final width:
  • Full width:
  • (Correlated set of measurements.)

§ Set of input (width) parameters to EW fit:

  • Z mass and width: MZ , ΓZ
  • Hadronic pole cross section:
  • Three leptonic ratios (lepton univ.):
  • Hadronic-width ratios:

The ElectroWeak fit of Standard Model

with

Corrected for QED radiation

11

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SLIDE 12

Max Baak (CERN)

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:

The ElectroWeak fit of Standard Model 12

slide-13
SLIDE 13

Max Baak (CERN)

Latest averages for MW and mtop

The ElectroWeak fit of Standard Model Latest Tevatron result from: arXiv:1204.0042 Top mass WA (March 2014): arXiv:1403.4427 13

Tevatron (Jul’14): arXiv:1457.2682 174.34 ± 0.64 GeV/c2 173.34 ± 0.76 GeV/c2

slide-14
SLIDE 14

Max Baak (CERN)

The electromagnetic coupling

§ The EW fit requires precise knowledge of α(MZ) – better than 1% level

  • Enters various places: hadr. radiator functions, predictions of MW and sin2θf

eff

§ Conventionally parametrized as (α(0) = fine structure constant) : § Evolution with renormalization scale:

The ElectroWeak fit of Standard Model 14

slide-15
SLIDE 15

Max Baak (CERN)

The electromagnetic coupling

§ The EW fit requires precise knowledge of α(MZ) – better than 1% level

  • Enters various places: hadr. radiator functions, predictions of MW and sin2θf

eff

§ Conventionally parametrized as (α(0) = fine structure constant) : § Evolution with renormalization scale: § Leptonic term known up to four loops (for q2 ≫ ml

2)

§ Top quark contribution known up to 2 loops, small: -0.7x10-4

The ElectroWeak fit of Standard Model 15 [C.Sturm, arXiv: 1305.0581] [M. Steinhauser, PLB 429, 158 (1998)]

slide-16
SLIDE 16

Max Baak (CERN)

The electromagnetic coupling

§ The EW fit requires precise knowledge of α(MZ) – better than 1% level

  • Enters various places: hadr. radiator functions, predictions of MW and sin2θf

eff

§ Conventionally parametrized as (α(0) = fine structure constant) : § Evolution with renormalization scale: § Hadronic contribution (from the 5 light quarks) completely dominates

  • verall uncertainty on α(MZ).

§ Difficult to calculate, cannot be obtained from pQCD alone.

  • Analysis of low-energy e+e- data
  • Usage of pQCD if lack of data

§ Similar analysis to evaluation of hadronic contribution to (g-2)µ

The ElectroWeak fit of Standard Model [M. Davier et al., Eur. Phys. J. C71, 1515 (2011)]

( )

  • 4

) 5 (

10 . 1 9 . 274 ) ( ⋅ ± = Δ

Z had M

α

16

slide-17
SLIDE 17

Max Baak (CERN)

Theoretical inputs at NNLO

§ Radiative corrections are important!

  • E.g. consider tree-level EW unification relation:
  • This predicts:

MW = (79.964 ± 0.005) GeV

  • Experiment:

MW = (80.385 ± 0.015) GeV

§ Without loop corrections: shift of 400 MeV, 27σ discrepancy!

The ElectroWeak fit of Standard Model

MW

2 tree-level = MZ 2

2 ⋅ 1+ 1− 8πα GFMZ

2

% & ' ' ( ) * *

17

slide-18
SLIDE 18

Max Baak (CERN)

Theoretical inputs at NNLO

§ Radiative corrections are important!

  • E.g. consider tree-level EW unification relation:
  • This predicts:

MW = (79.964 ± 0.005) GeV

  • Experiment:

MW = (80.385 ± 0.015) GeV

§ Without loop corrections: shift of 400 MeV, 27σ discrepancy! 1. Experimental precision (<1%), better than typical loop factor (α≈1/137) → Requires radiative corrections at 2-loop level. 2. Before Higgs discovery: uncertainty on MH largest uncertainty in EW fit. → After: inclusion of all relevant theoretical uncertainties. (Part of focus of this talk …)

MW

2 tree-level = MZ 2

2 ⋅ 1+ 1− 8πα GFMZ

2

% & ' ' ( ) * *

18 The electroweak fit at NNLO – Status and Prospects

slide-19
SLIDE 19

Max Baak (CERN)

Theoretical inputs at NNLO

§ Radiative corrections are important!

  • E.g. consider tree-level EW unification relation:
  • This predicts:

MW = (79.964 ± 0.005) GeV

  • Experiment:

MW = (80.385 ± 0.015) GeV

§ Without loop corrections: shift of 400 MeV, 27σ discrepancy! § In EW fit with Gfitter we use state-of-the-art calculations:

  • sin2θfeff

Effective weak mixing angle [M. Awramik et al., JHEP 11, 048 (2006),

  • M. Awramik et al., Nucl.Phys.B813:174-187 (2009)]
  • Full two-loop + leading beyond-two-loop form factor corrections
  • MW

Mass of the W boson [M. Awramik et al., arXiv:0311148v2]

  • Full two-loop + leading beyond-two-loop + 4-loop QCD correction

[Kuhn et al., hep-hp/0504055,0605201,0606232]

  • Γhad

QCD Adler functions at N3LO [P. A. Baikov et al., PRL108, 222003 (2012)]

  • N3LO prediction of the hadronic cross section
  • Γi

Partial Z decay widths [A. Freitas, JHEP04, 070 (2014)]

§ New: all EWPOs(*) now described at 2-loop level or better!

The ElectroWeak fit of Standard Model

MW

2 tree-level = MZ 2

2 ⋅ 1+ 1− 8πα GFMZ

2

% & ' ' ( ) * *

19

New! full fermionic 2-loop calc. New!

slide-20
SLIDE 20

Max Baak (CERN)

Theory uncertainties from unknown H.O. terms

Most important

  • bservables:

Theory uncertainties accounted for in EW fit

(w/ Gauss constraints):

§ Old setup: two nuisance pars for theoretical uncertainties:

  • δMW (4 MeV), δsin2θ l

eff (4.7x10-5)

Newly included in EW fit setup: § Full fermionic 2-loop corrections of partial Z decay widths (A. Freitas)

  • 6 corresponding nuisance parameters. (δΓZ = 0.5 MeV)

§ Γhad QCD Adler functions at N3LO

  • 2 nuisance parameters.

§ Top quark mass: conversion from measurement to pole to MS-bar mass

  • Agnostic value used here: δtheo mt = 0.5 GeV.

The electroweak fit at NNLO – Status and Prospects

New in EW fit

(more later)

slide-21
SLIDE 21

Max Baak (CERN)

Electroweak Fit – Experimental inputs

§ Latest experimental inputs:

  • Z-pole observables: from LEP / SLC

[ADLO+SLD, Phys. Rept. 427, 257 (2006)]

  • MW and ΓW from LEP/Tevatron

[arXiv:1204.0042, arXiv:1302.3415]

  • mtop latest avg from Tevatron+LHC

[arXiv:1403.4427]

  • mc, mb world averages (PDG)

[PDG, J. Phys. G33,1 (2006)]

  • Δαhad

(5)(MZ 2) including αS dependency

[Davier et al., EPJC 71, 1515 (2011)]

  • MH from LHC

[arXiv:1406.3827, CMS-PAS-HIG-14-009]

§ 7 (+10) free fit parameters:

  • MH, MZ, αS(MZ

2), Δαhad (5)(MZ 2),

mt, mc, mb

  • 10 theory nuisance parameters
  • e.g. δMW (4 MeV), δsin2θl

eff (4.7x10-5)

21 Tevatron + LHC Tevatron LHC LEP SLC LEP SLC The electroweak fit at NNLO – Status and Prospects

slide-22
SLIDE 22

Max Baak (CERN)

Electroweak Fit – SM Fit Results

§ From the Gfitter group: www.cern.ch /gfitter § Left: full fit result § Middle: fit excluding the row § Right: not

  • incl. theory

errors

22 The ElectroWeak fit of Standard Model

Free w/o exp. input w/o exp. input Parameter Input value in fit Fit Result in line in line, no theo. unc MH [GeV](◦) 125.14 ± 0.24 yes 125.14 ± 0.24 93+25

−21

93+24

−20

MW [GeV] 80.385 ± 0.015 – 80.364 ± 0.007 80.358 ± 0.008 80.358 ± 0.006 ΓW [GeV] 2.085 ± 0.042 – 2.091 ± 0.001 2.091 ± 0.001 2.091 ± 0.001 MZ [GeV] 91.1875 ± 0.0021 yes 91.1880 ± 0.0021 91.200 ± 0.011 91.2000 ± 0.010 ΓZ [GeV] 2.4952 ± 0.0023 – 2.4950 ± 0.0014 2.4946 ± 0.0016 2.4945 ± 0.0016 σ0

had [nb]

41.540 ± 0.037 – 41.484 ± 0.015 41.475 ± 0.016 41.474 ± 0.015 R0

ℓ

20.767 ± 0.025 – 20.743 ± 0.017 20.722 ± 0.026 20.721 ± 0.026 A0,ℓ

FB

0.0171 ± 0.0010 – 0.01626 ± 0.0001 0.01625 ± 0.0001 0.01625 ± 0.0001 Aℓ (⋆) 0.1499 ± 0.0018 – 0.1472 ± 0.0005 0.1472 ± 0.0005 0.1472 ± 0.0004 sin2θℓ

eff(QFB)

0.2324 ± 0.0012 – 0.23150 ± 0.00006 0.23149 ± 0.00007 0.23150 ± 0.00005 Ac 0.670 ± 0.027 – 0.6680 ± 0.00022 0.6680 ± 0.00022 0.6680 ± 0.00016 Ab 0.923 ± 0.020 – 0.93463 ± 0.00004 0.93463 ± 0.00004 0.93463 ± 0.00003 A0,c

FB

0.0707 ± 0.0035 – 0.0738 ± 0.0003 0.0738 ± 0.0003 0.0738 ± 0.0002 A0,b

FB

0.0992 ± 0.0016 – 0.1032 ± 0.0004 0.1034 ± 0.0004 0.1033 ± 0.0003 R0

c

0.1721 ± 0.0030 – 0.17226 +0.00009

−0.00008

0.17226 ± 0.00008 0.17226 ± 0.00006 R0

b

0.21629 ± 0.00066 – 0.21578 ± 0.00011 0.21577 ± 0.00011 0.21577 ± 0.00004 mc [GeV] 1.27 +0.07

−0.11

yes 1.27 +0.07

−0.11

– – mb [GeV] 4.20 +0.17

−0.07

yes 4.20 +0.17

−0.07

– – mt [GeV] 173.34 ± 0.76 yes 173.81 ± 0.85(▽) 177.0 +2.3

−2.4 (▽)

177.0 ± 2.3 ∆α(5)

had(M 2 Z)(†△)

2757 ± 10 yes 2756 ± 10 2723 ± 44 2722 ± 42 αs(M 2

Z)

– yes 0.1196 ± 0.0030 0.1196 ± 0.0030 0.1196 ± 0.0028

slide-23
SLIDE 23

Max Baak (CERN)

Electroweak Fit – SM Fit Results

The ElectroWeak fit of Standard Model 23

§ 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!

slide-24
SLIDE 24

Max Baak (CERN)

Electroweak Fit – SM Fit Results

The ElectroWeak fit of Standard Model 24

§ 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!

slide-25
SLIDE 25

Max Baak (CERN)

Electroweak Fit – SM Fit Results

§ No individual value exceeds 3σ § Largest deviations in b-sector: A0,b

FB with 2.5σ

  • à largest contribution to χ2

§ Small pulls for MH, MZ, Δαhad

(5)(MZ 2),

mc, mb indicate that input accuracies exceed fit requirements § Small changes from switching between 1 and 2-loop calc. for partial Z widths and small MW correction.

  • χ2

min(complete setup) = 17.8

  • χ2

min(1-loop Z width) = 18.0

  • χ2

min(no MW correction) = 17.4

  • χ2

min(no extra theory errors) = 18.2

25 The ElectroWeak fit of Standard Model

slide-26
SLIDE 26

Max Baak (CERN)

Goodness of Fit

§ Toy analysis: p-value for wrongly rejecting the SM = 21 ± 2 (theo) %

  • p-value is equivalent to 0.8σ
  • Evaluated with 20k pseudo experiments – follows χ2 with 14 d.o.f.
  • For comparison: χ2

min= 17.8 à Prob(χ2 min, 14) = 21 %

§ Large value of χ2

min not due to inclusion of MH measurement.

  • Without MH measurement: χ2

min= 16.3 à Prob(χ2 min, 13) = 23%

26 The ElectroWeak fit of Standard Model

min 2

χ

5 10 15 20 25 30 35 40 45

Number of toy experiments

200 400 600 800 1000 1200 1400 =14

dof

distribution for n

2

χ Toy analysis incl. theo. errors Toy analysis excl. theo. errors p-value incl. theo. errors p-value excl. theo. errors

) SM | data p-value for (

0.2 0.4 0.6 0.8 1 = 17.87

min,data 2

χ 0.003 ± p-value = 0.210 0.003 ± p-value = 0.193

slide-27
SLIDE 27

Max Baak (CERN)

[GeV]

H

M

60 70 80 90 100 110 120 130 140

2

χ ∆

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 σ 1 σ 2

measurement

H

SM fit with M measurement

H

SM fit w/o M ATLAS measurement [arXiv:1406.3827] CMS measurement [arXiv:1407.0558]

G fitter SM

Jul ’14

Higgs results of the EW fit

fit below only includes the given observable

§ Scan of Δχ2 profile versus MH

  • Grey band: fit w/o MH measurement
  • Blue line: full SM fit, with MH meas.
  • Fit w/o MH measurement gives:

MH = 93+25

  • 21 GeV
  • Consistent at 1.3σ with

LHC measurements.

§ Bottom plot: impact of other most sensitive Higgs observables

  • Determination of MH removing

all sensitive observables except the given one.

  • Known tension (2.5σ)

between Al(SLD), A0,b

FB,

and MW clearly visible.

27 The electroweak fit at NNLO – Status and Prospects

[GeV]

H

M 6 10 20

2

10

2

10 × 2

3

10 LHC average

H

Fit w/o M

W

M

0,b FB

A (SLD)

l

A (LEP)

l

A 0.2 ± 125.1

  • 21

+25

93

  • 34

+47

77

  • 263

+628

503

  • 24

+45

38

  • 95

+254

143

G fitter

SM Jul ’14
slide-28
SLIDE 28

Max Baak (CERN)

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

slide-29
SLIDE 29

Max Baak (CERN)

[GeV]

W

M

80.32 80.33 80.34 80.35 80.36 80.37 80.38 80.39 80.4 80.41

2

χ ∆

1 2 3 4 5 6 7 8 9 10 σ 1 σ 2 σ 3

measurement

W

SM fit w/o M measurement

H

and M

W

SM fit w/o M SM fit with minimal input world average [arXiv:1204.0042]

W

M

G fitter SM

Jul ’14

Prediction of W mass

§ Scan of Δχ2 profile versus MW

  • Also shown: SM fit with

minimal inputs: MZ, GF, Δαhad

(5)(MZ), αs(MZ),

MH, and fermion masses

  • Good consistency between

total fit and SM w/ minimal inputs

§ MH measurement allows for precise constraint on MW

  • Agreement at 1.4σ

§ Fit result for indirect determination of MW (full fit w/o MW): § More precise estimate of MW than the direct measurements!

  • Uncertainty on world average measurement: 15 MeV

29 The electroweak fit at NNLO – Status and Prospects Obtained with simple error propagation

slide-30
SLIDE 30

Max Baak (CERN)

)

eff l

θ (

2

sin

0.2309 0.231 0.2311 0.2312 0.2313 0.2314 0.2315 0.2316 0.2317 0.2318

2

χ ∆

2 4 6 8 10 σ 1 σ 2 σ 3

measurement

H

SM fit with M measurement

H

SM fit w/o M SM fit with minimal input LEP/SLD average [hep-ex/0509008]

G fitter SM

Jul ’14

Prediction of effective weak mixing angle

§ Right: scan of Δχ2 profile versus sin2θl

eff

  • All sensitive measurements

removed from the SM fit.

  • Also shown: SM fit with

minimal inputs

§ MH measurement allows for very precise constraint

  • n sin2θl

eff

§ Fit result for indirect determination of sin2θl

eff :

§ More precise than direct determination (from LEP/SLD) !

  • Uncertainty on LEP/SLD average: 1.6x10-4

30 The electroweak fit at NNLO – Status and Prospects Obtained with simple error propagation

slide-31
SLIDE 31

Max Baak (CERN)

Prediction of top mass

§ Shown: scan of Δχ2 profile versus mt (without mt measurement)

  • MH measurement allows for significant better constraint of mt
  • Indirect determination consistent with direct measurements
  • Remember: fully obtained from radiative corrections!

§ Indirect result: mt = 177.0+2.3

  • 2.4 GeV

31

Tevatron+LHC: 173.34 ± 0.76 GeV new Tevatron-only: 174.34 ± 0.64 GeV

The electroweak fit at NNLO – Status and Prospects

[GeV]

t

m

160 165 170 175 180 185 190

2

χ ∆

1 2 3 4 5 6 7 8 9 10 σ 1 σ 2 σ 3

measurements

t

SM fit w/o m measurements

H

and M

t

SM fit w/o m world average [arXiv:1403.4427]

kin t

m D0 measurement [arXiv:1405.1756]

kin t

m [arXiv:1207.0980]

t t

σ from Tevatron

pole t

m [arXiv:1307.1907v3]

t t

σ from CMS

pole t

m [arXiv:1406.5375]

t t

σ from ATLAS

pole t

m

G fitter SM

Jul ’14
slide-32
SLIDE 32

Max Baak (CERN)

State of the SM: W versus top mass

§ Scan of MW vs mt, with the direct measurements excluded from the fit. § Results from Higgs measurement significantly reduces allowed indirect parameter space → corners the SM! § Observed agreement demonstrates impressive consistency of the SM!

32 The electroweak fit at NNLO – Status and Prospects

[GeV]

t

m

140 150 160 170 180 190

[GeV]

W

M

80.25 80.3 80.35 80.4 80.45 80.5

68% and 95% CL contours measurements

t

and m

W

fit w/o M measurements

H

and M

t

, m

W

fit w/o M measurements

t

and m

W

direct M

σ 1 ± world comb.

W

M 0.015 GeV ± = 80.385

W

M σ 1 ± world comb.

t

m = 173.34 GeV

t

m = 0.76 GeV σ GeV

theo

0.50 ⊕ = 0.76 σ = 1 2 5 . 1 4 G e V

H

M = 5 G e V

H

M = 3 G e V

H

M = 6 G e V

H

M

G fitter SM

Jul ’14
slide-33
SLIDE 33

Max Baak (CERN)

[GeV]

t

m

155 160 165 170 175 180 185 190

[GeV]

H

M

50 100 150 200 250

68% and 95% CL contours meas.

t

and m

H

fit w/o M meas.

t

and m

H

direct M

σ 1 ± private comb.

H

M 0.24 GeV ± = 125.14

H

M σ 1 ± world comb.

t

m = 173.34 GeV

t

m = 0.76 GeV σ GeV

theo

0.50 ⊕ = 0.76 σ

G fitter SM

Jan ’15

State of the SM: loop vs tree-level observables

§ Scan of MH vs mtop (left) and MW vs sin2θl

eff (right),

with direct measurements excluded from the fit. § Again, significant reduction allowed indirect parameter space from Higgs mass measurement. § MW and sin2θleff have become the sensitive probes of new physics!

§ Reason: both are ‘tree-level’ SM predictions.

The electroweak fit at NNLO – Status and Prospects

)

eff l

θ (

2

sin

0.2308 0.231 0.2312 0.2314 0.2316 0.2318 0.232 0.2322

[GeV]

W

M

80.32 80.34 80.36 80.38 80.4 80.42 80.44 80.46 80.48 80.5

68% and 95% CL contours ) measurements

eff f

θ (

2

and sin

W

direct M ) and Z widths measurements

eff f

θ (

2

, sin

W

fit w/o M measurements

H

) and M

eff f

θ (

2

, sin

W

fit w/o M and Z widths measurements

H

), M

eff f

θ (

2

, sin

W

fit w/o M

σ 1 ± world comb.

W

M σ 1 ± ) LEP+SLC

eff f

θ (

2

sin

G fitter SM

Jul ’14

Observables from radiative corrections “Tree-level” observables

slide-34
SLIDE 34

Max Baak (CERN)

Theoretical uncertainty on mtop

)

eff l

θ (

2

sin

0.2308 0.231 0.2312 0.2314 0.2316 0.2318 0.232 0.2322

[GeV]

W

M

80.32 80.34 80.36 80.38 80.4 80.42 80.44 80.46 80.48 80.5

95% CL contour for fit w/o ) and Z widths measurements

eff l

θ (

2

, sin

W

m = 1.5 GeV

t

m

theo

δ = 1.0 GeV

t

m

theo

δ = 0.5 GeV

t

m

theo

δ = 0.0 GeV

t

m

theo

δ

σ 1 ± world comb.

W

m σ 1 ± ) LEP+SLC

eff l

θ (

2

sin

G fitter SM

Jul ’14

§ δtheo mt : unc. on conversion of measured top mass to MS-bar mass

  • Sources: ambiguity top mass definition, fragmentation process, pole→MS conv.
  • Predictions for δtheo mt : between 0.25 – 0.9 GeV or greater.

[Moch etal, aX:1405.4781, Mangano: TOP’12, Buckley etal, aX:1101.2599, Juste etal: aX:1310.0799]

  • δtheo mt varied here between 0 and 1.5 GeV, in steps of 0.5 GeV.

§ Better assessment of δtheo mt of relevance for the EW fit. (see also backup)

The electroweak fit at NNLO – Status and Prospects default = 0.5 GeV

slide-35
SLIDE 35

Max Baak (CERN)

Prediction for αs(MZ) from Z→hadrons

§ Scan of Δχ2 versus αs

  • Also shown: SM fit with

minimal inputs: MZ, GF, Δαhad

(5)(MZ), αs(MZ),

MH, and fermion masses

§ Determination of αs at full N2LO and partial N3LO.

  • Most sensitive through

total hadronic cross- section σ0

had and

partial leptonic width R0

l

§ In good agreement with value from τ decays, at N3LO, and with WA.

  • (Improvements in precision only expected with ILC/GigaZ. See later.)

35 The electroweak fit at NNLO – Status and Prospects

)

Z

(M

S

α

0.112 0.114 0.116 0.118 0.12 0.122 0.124 0.126

2

χ ∆

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 σ 1 σ 2

SM fit

had

σ and

l

SM fit minimal input and R decays at 3NLO [Eur.Phys.J.C56,305 (2008)] τ ) from

Z

(M

S

α

G fitter SM

Jul ’14

Most affected by new theory uncertainties Before: δtheo = 0.0001

slide-36
SLIDE 36

Max Baak (CERN)

Beyond the SM

The ElectroWeak fit of Standard Model 36

slide-37
SLIDE 37

Max Baak (CERN)

X X’

Constraints on BSM models

§ Oblique corrections from New Physics described through STU parametrization

[Peskin and Takeuchi, Phys. Rev. D46, 1 (1991)]

Omeas = OSM,REF(mH,mt) + cSS + cTT +cUU § 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. B326, 276 (1994)] [Burgess et al., Phys. Rev. D49, 6115 (1994)]

§ 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:

MW

2, sin2θeff, GF, α, etc.

§ Electroweak fit sensitive to BSM physics through oblique corrections

  • Similar to

sensitivity to top and Higgs loop corrections.

37 The ElectroWeak fit of Standard Model

slide-38
SLIDE 38

Max Baak (CERN)

S

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4 0.5

T

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4 0.5

=173 GeV)

t

=125 GeV, m

H

: M

ref

fit contours for U=0 (SM 68% and 95% CL for present fit )

FB

(Q

eff l

θ

2

95% CL for asymmetries & sin 95% CL for Z widths

W

Γ &

W

95% CL for M SM Prediction 0.24 GeV ± = 125.14

H

M 0.91 GeV ± = 173.34

t

m

G fitter SM

Jul ’14

Fit results for S, T, U

§ S,T,U parameters obtained directly from fit to the EW observables. § SM: MH = 125 GeV, mt = 173 GeV

  • This defines (S,T,U) = (0,0,0)

§ S, T depend logarithmically on MH § Fit result (with U floating): § Also results for Zàbb correction (see backup) § No indication for new physics. § Use this to constrain 4th gen, Ex-Dim, T-C, Higgs couplings (in backup)

38

S T U S 1 +0.90

  • 0.59

T 1

  • 0.83

U 1

S = 0.05 ± 0.11 T = 0.09 ± 0.13 U = 0.01 ± 0.11

The electroweak fit at NNLO – Status and Prospects

§ Stronger constraints with U=0.

slide-39
SLIDE 39

Max Baak (CERN)

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 (κV)

and Higgs-fermion couplings (κF) with no invisible/undetectable width

  • (Custodial symmetry is assumed.)
  • “Kappa parametrization”

§ Main effect on EWPO due to modified Higgs coupling to gauge bosons (κV)

  • Involving the longitudinal d.o.f.

§ Most BSM models: κV < 1

  • Additional Higgses typically give positive contribution to MW.

The ElectroWeak fit of Standard Model 39 κV κV κV

2

slide-40
SLIDE 40

Max Baak (CERN)

S

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4 0.5

T

  • 0.5
  • 0.4
  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3 0.4 0.5 Higgs-vector boson couplings scaling

68%, 95%, 99% CL fit contours = 173 GeV, U = 0)

t

= 126 GeV, m

H

(M [0,2] ∈

V

κ [1,10] TeV ∈ λ

preliminary

G fitter SM

B

Aug 13

Modified Higgs couplings

§ Main effect on EWPO due to Higgs coupling to gauge bosons (κV).

  • Formulas from: Espinosa et al [arXiv:1202.3697]

§ Cut-off scale Λ represents mass scale of new states that unitarize longitudinal gauge-boson scattering.

  • (As required in this model.)

§ λ is varied between 1 and 10 TeV, nominally fixed to 3 TeV (4πv).

The ElectroWeak fit of Standard Model 40

Espinosa et al [arXiv:1202.3697], Falkowski et al [arXiv:1303.1812], etc.

slide-41
SLIDE 41

Max Baak (CERN)

Reproduction of ATLAS and CMS results

§ Approximate reproduction of ATLAS/CMS results within limited public-info available.

41 arXiv:1307.1427 CMS-PAS-HIG-14-009 κV κV The electroweak fit at NNLO – Status and Prospects

slide-42
SLIDE 42

Max Baak (CERN)

Higgs coupling results

§ Private LHC combination:

  • κV = 1.026+0.043
  • 0.043
  • κF = 0.88+0.10
  • 0.09

§ Some dependency for κV in central value [1.02-1.04] and error [0.02-0.03]

  • n cut-off scale λ [1-10 TeV].

1. EW fit sofar more precise result for κV than current LHC experiments. 2. EW fit has positive deviation of κV from 1.0.

  • (Many BSM models: κV < 1)

42

§ Result from stand-alone EW fit:

  • κV = 1.03 ± 0.02 (using λ=3 TeV)
  • Implies NP-scale of Λ ≿ 13 TeV.

V

κ

0.7 0.8 0.9 1 1.1 1.2 1.3

F

κ

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

LHC experiments 68% and 95% CL fit contours EW-fit + LHC experiments 68% and 95% CL fit contours = 3 TeV] λ [ Standard Model prediction Fit minimum Combination of ATLAS and CMS results. Average neglects correlations.

G fitter SM

B

Jul ’14

V

κ

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

W

M

80.25 80.3 80.35 80.4 80.45 80.5

95% CL contours measurement

V

κ and

W

w/o M = 10 TeV λ = 5 TeV λ = 1 TeV λ

σ 1 ± world comb.

W

M

68% and 95% CL contours for measurements

V

κ and

W

direct M

σ 1 ± private LHC average

V

κ |

2 V

κ |1- λ = Λ

G fitter SM

Jul ’14

The electroweak fit at NNLO – Status and Prospects

slide-43
SLIDE 43

Max Baak (CERN)

Prospects for the Standard Model fit

The ElectroWeak fit of Standard Model 43

slide-44
SLIDE 44

Max Baak (CERN)

Two prospects scenarios: LHC, ILC/GigaZ

Prospects of EW fit tested for two (three) scenarios: 1. LHC Phase-1 = before HL upgrade 2. 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 ~1-2 months.

  • Physics of LEP1 and SLC can be revisited with few days of data.

In following studies: central values of input measurements adjusted to MH = 125 GeV.

  • (Except where indicated.)

The electroweak fit at NNLO – Status and Prospects

slide-45
SLIDE 45

Max Baak (CERN)

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 : 0.8 → 0.1 GeV
  • Dominated by conversion from threshold to MSbar mass.

§ Z pole measurements

  • High statistics: 109 Z decays: δR0lep : 2.5⋅10−2 → 4⋅10−3
  • With polarized beams, uncertainty on δA0,fLR: 10−3 →10−4,

which translates to δsin2θleff : 1.6⋅10−4 → 1.3⋅10−5

§ H→ZZ and H→WW couplings: measured at 1% precision.

45

ILC prospects: from ILC TDR (Vol-2).

The electroweak fit at NNLO – Status and Prospects

slide-46
SLIDE 46

Max Baak (CERN)

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 : 0.8 → 0.6 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

slide-47
SLIDE 47

Max Baak (CERN)

Prospects of EW fit

LHC Phase-1 (300/fb) § W mass measurement : δMW : 15 → 8 MeV § Final top mass measurement mt : δmt : 0.8 → 0.6 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-2000 (at energy below cc resonance),

and BESIII e+e- cross-section measurements (around cc resonance).

  • Plus: improved αs (from reliable Lattice predictions): Δαhad: 10−4 → 5⋅10−5

§ Assuming ~25% of today’s theoretical uncertainties on MW and sin2θleff

  • Implies ambitions three-loop electroweak calculations!
  • δMW (4→1 MeV), δsin2θ 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: 0.50 → 0.25 GeV

The electroweak fit at NNLO – Status and Prospects

slide-48
SLIDE 48

Max Baak (CERN)

[GeV]

H

M

60 80 100 120 140 160 180 200

2

χ ∆

5 10 15 20 25 σ 1 σ 2 σ 3 σ 4 σ 5

Present SM fit Prospects for LHC = Rfit)

theo

δ Prospects for ILC/GigaZ ( = Gauss)

theo

δ Prospects for ILC/GigaZ (

G fitter SM

Aug 13

[GeV]

H

M

60 80 100 120 140 160 180 200

2

χ ∆

5 10 15 20 25 σ 1 σ 2 σ 3 σ 4 σ 5

Present SM fit Present uncertainties Prospects for LHC Prospects for ILC/GigaZ

G fitter SM

Jul ’14

Prospects of EW fit

§ Indirect prediction MH dominated by experimental uncertainties.

  • Present:

σ(MH) = +31

  • 26 (exp) +10
  • 8 (theo) GeV
  • LHC:

σ(MH) = +20

  • 18 (exp) +3.9
  • 3.8 (theo) GeV
  • ILC:

σ(MH) = +6.9

  • 6.6 (exp) +2.5
  • 2.3 (theo) GeV

§ Logarithmic dependency on MH → cannot compete with direct MH meas. § If EWP-data central values unchanged, i.e. keep favoring low value of Higgs mass (93 GeV), ~5σ discrepancy with measured Higgs mass.

48

MH

avg

125 GeV 93 GeV

The electroweak fit at NNLO – Status and Prospects

slide-49
SLIDE 49

Max Baak (CERN)

Prospects of EW fit

§ Huge reduction of uncertainty on indirect determinations of mt, mW, and sin2θleff, by a factor of 3 or more. § Assuming central values of mt and MW do not change, (at ILC) a deviation between the SM prediction and the direct measurements would be prominently visible.

49 The electroweak fit at NNLO – Status and Prospects

[GeV]

t

m

160 165 170 175 180 185

[GeV]

W

M

80.32 80.34 80.36 80.38 80.4 80.42 80.44 80.46

68% and 95% CL fit contour measurements

t

and m

W

w/o M Present SM fit Prospect for LHC Prospect for ILC/GigaZ Present measurement ILC precision LHC precision σ 1 ±

W

M σ 1 ±

t

m

G fitter SM

Jul ’14

)

eff l

θ (

2

sin

0.231 0.2311 0.2312 0.2313 0.2314 0.2315 0.2316 0.2317 0.2318 0.2319

[GeV]

W

M

80.32 80.34 80.36 80.38 80.4 80.42 80.44 80.46

68% and 95% CL fit contour ) measurements

eff f

θ (

2

and sin

W

w/o M Present SM fit Prospect for LHC Prospect for ILC/GigaZ Present measurement ILC precision LHC precision σ 1 ±

W

M σ 1 ± )

eff f

θ (

2

sin

G fitter SM

Jul ’14
slide-50
SLIDE 50

Max Baak (CERN)

Impact of individual uncertainties

§ Breakdown of individual contributions to errors of MW and sin2θleff § MW and sin2θleff are sensitive probes of new physics! For all scenarios. § At ILC/GigaZ, precision of MZ will become important again.

The electroweak fit at NNLO – Status and Prospects

slide-51
SLIDE 51

Max Baak (CERN)

BSM prospects of EW fit

§ 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%.)

51 The electroweak fit at NNLO – Status and Prospects

S

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

T

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

68% and 95% CL fit contours for U=0 =173 GeV)

t

=125 GeV, m

H

: M

ref

(SM Present uncertainties Prospects for LHC Prospects for ILC/GigaZ SM Prediction 0.24 GeV ± = 125.14

H

M 0.91 GeV ± = 173.34

t

m

G fitter SM

Jul ’14

V

κ

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

W

M

80.25 80.3 80.35 80.4 80.45 80.5

68% and 95% CL contours measurement

V

κ and

W

w/o M Present SM fit Prospect for LHC Prospect for ILC/GigaZ

Present measurement ILC precision LHC precision σ 1 ± world comb.

W

M σ 1 ± private LHC average

V

κ |

2 V

κ |1- v π 4 = Λ

G fitter SM

Jul ’14
slide-52
SLIDE 52

Max Baak (CERN)

Conclusion and Today’s prospects

§ Including MH measurement, for first time SM is fully over-constrained!

  • MH consistent at 1.3σ with indirect prediction from EW fit.
  • p-Value of global electroweak fit of SM: 21% (pseudo-experiments)

§ New: N2LO calcs and theo. uncertainties for all relevant observables.

  • δtheo mt starting to become relevant.

§ Knowledge of MH dramatically improves SM prediction of key observables

  • MW (28→8 MeV), sin2θleff (2.3x10-5→0.7x10-5), mt (6.2→2.5 GeV)

§ Improved accuracies set benchmark for new direct measurements! § δMW (indirect) = 8 MeV

  • Large contributions to δMW from

top and unknown higher-order EW corrections

§ δMW (direct) = 15 MeV § Including new data electroweak fits remain very interesting in the next years! § Latest results always available at: http://cern.ch/Gfitter

31% 24% 10% 5% 6% 24%

δmtop δtheoMW δMZ δΔαhad δαs

52

Thanks!

The electroweak fit at NNLO – Status and Prospects

δtheomtop

slide-53
SLIDE 53

Max Baak (CERN)

Backup

Backup

A Generic Fitter Project for HEP Model Testing

53 The ElectroWeak fit of Standard Model

slide-54
SLIDE 54

Max Baak (CERN)

Input correlations of the EW fit

§ Input correlation coefficients between Z pole measurements

The ElectroWeak fit of Standard Model 54

slide-55
SLIDE 55

Max Baak (CERN)

Radiator Functions

§ Partial widths are defined inclusively: contain both QCD and QED contributions. § Corrections expressed as so-called radiator functions RA,f and RV,f § High sensitivity to the strong coupling αs § Recently, full four-loop calculation of QCD Adler function became available (N3LO) § Much-reduced scale dependence! § Theoretical uncertainty of ~0.15 MeV, compared with experimental uncertainty

  • f 2.0 MeV.

The ElectroWeak fit of Standard Model [P. Baikov et al., Phys. Rev. Lett. 108, 222003 (2012)] [P. Baikov et al Phys. Rev. Lett. 104, 132004 (2010)] O(αs3) O(αs4) O(αs) O(αs2) [D. Bardin, G. Passarino, “The Standard Model in the Making”, Clarendon Press (1999)] 55

slide-56
SLIDE 56

Max Baak (CERN)

Calculation of MW

§ 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(ααs), O(ααs

2), O(α2 ferm),

O(α2

bos), O(α2αsmt 4), O(α3mt 6)

§ Uncertainty estimate:

  • Missing terms of order O(α2αs):

about 3 MeV (from O(α2αsmt

4))

  • Electroweak three-loop

correction O(α3): < 2 MeV

  • Three-loop QCD corrections

O(αs

3): < 2 MeV

§ Total: δMW ≈ 4 MeV

The ElectroWeak fit of Standard Model [M Awramik et al., Phys. Rev. D69, 053006 (2004)] [M Awramik et al., Phys. Rev. Lett. 89, 241801 (2002)] [A Freitas et al., Phys. Lett. B495, 338 (2000)] 56

slide-57
SLIDE 57

Max Baak (CERN)

Calculation of sin2(θl

eff)

§ Effective mixing angle: § Two-loop EW and QCD correction to Δκ known, leading terms of higher

  • rder QCD corrections.

§ Fermionic two-loop correction about 10−3, whereas bosonic one 10−5. § Uncertainty estimate obtained with different methods, geometric progression, leading to total of: δsin2(θl

eff) = 4.7x10-5

The ElectroWeak fit of Standard Model [M Awramik et al, Phys. Rev. Lett. 93, 201805 (2004)] [M Awramik et al., JHEP 11, 048 (2006)] 57

slide-58
SLIDE 58

Max Baak (CERN)

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: mt

exp ≢ mt pole,

and event-dependent. § The top mass extracted in hadron collisions is not well defined below a precision of O(Γt) ~ 1 GeV § Hard to estimate additional theo. uncertainties. With 0.5 GeV on mt:

  • MH = 90+34
  • 21 GeV, MW = 80.359±0.013 GeV, sin2θleff = 0.23148±0.00010.
  • → Sofar only small deterioration in precision.

The ElectroWeak fit of Standard Model

slide-59
SLIDE 59

Max Baak (CERN)

Interesting Top pole mass measurement

§ From: ATLAS-CONF-2014-053: “top-quark pole mass measurement from ttbar+1jet events”

  • Through study of inverse of

invariant mass of ttbar+1jet system (quantity: ρS).

  • Free of MC→pole mass

conversion uncertainty.

§ ⇒ mt

pole = 173.7 ± 1.5 (stat) ± 1.4 (syst) +1.0

  • 0.5 (theo) GeV

§ Great to see these efforts ongoing!

  • Similar measurements / tests ongoing at CMS.

The ElectroWeak fit of Standard Model and Beyond ] parton level [

s

ρ

0.2 0.4 0.6 0.8 1

)

s

ρ ,

pole t

m ( R

0.5 1 1.5 2 2.5 3 3.5 4 4.5 Data =170 GeV

pole t

+1-jet, m t t =180 GeV

pole t

+1-jet, m t t

ATLAS Preliminary

  • 1

=7 TeV, 4.6 fb s

slide-60
SLIDE 60

Max Baak (CERN)

Moriond 2011: Prediction for Higgs mass

Global Fit of electroweak SM and beyond

−2lnQ : 115,137

[ ] GeV

[GeV]

H

M

100 150 200 250 300

2

! "

2 4 6 8 10 12 14 16 18 20 22

LEP 95% CL Tevatron 95% CL

# 1 # 2 # 3 # 4

LEP + Tevatron + ATLAS + CMS LEP + Tevatron LEP + Tevatron (Fall 2010) = -2ln(Q)

2

! $ Direct searches WW only. Average neglects correlations % LHC: H

G fitter SM

MOR 11

[GeV]

H

M

100 150 200 250 300

2

! "

2 4 6 8 10 12 14 16 18 20 22

LEP 95% CL Tevatron 95% CL

# 1 # 2 # 3 # 4

= -2ln(Q)

2

! $ Direct searches WW only. Average neglects correlations % LHC: H

Theory uncertainty Fit including theory errors Fit excluding theory errors

G fitter SM

MOR 11

§ LEP + Tevatron (Fall 2010) :

  • CLs+b central value ±1σ:
  • 2σ interval:

§ LEP + Tevatron (Moriond 2011) :

  • CLs+b central value ±1σ:
  • 2σ interval:

§ Fit with LEP + Tevatron + LHC (HèWW) searches (Moriond 2011) :

  • Central value unchanged
  • 2σ interval:

M H =120.2−4.7

+12.3 GeV

CLs+b

2−sided :

114,149

[ ]∪ 152,155 [ ] GeV

−2lnQ : 115,138

[ ] GeV

60

M H =120.2−5.2

+17.9 GeV

CLs+b

2−sided :

114,155

[ ] GeV

−2lnQ : 115,152

[ ] GeV

2s 2s

CLs+b

2−sided :

114,14?

[ ] GeV

slide-61
SLIDE 61

Max Baak (CERN)

Low energy observables

§ Low energy observables with interesting precision will soon become available.

The ElectroWeak fit of Standard Model

slide-62
SLIDE 62

Max Baak (CERN)

Two prospects scenarios: LHC, ILC/GigaZ

§ Uncertainty estimates used:

  • ILC prospects from: ILC TDR (Vol-2).
  • Theoretical uncertainty estimates from recent Snowmass report

§ Central values of input measurements adjusted to MH = 126 GeV.

The ElectroWeak fit of Standard Model and Beyond

slide-63
SLIDE 63

Max Baak (CERN)

FCC-ee prospects

Global Fit of electroweak SM and beyond

§ From TLEP prospects: arXiv:1308.6176

slide-64
SLIDE 64

Max Baak (CERN)

Experimental inputs – Predicted uncertainties

FCC-ee scenario: § Preliminary estimates § Clearly not the same level

  • f understanding as LHC
  • r ILC.

§ Uncertainties may turn out completely different.

  • From arXiv:1308.6176,
  • 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 MZ and ΓZ

The ElectroWeak fit of Standard Model and Beyond

slide-65
SLIDE 65

Max Baak (CERN)

Prospects of the EW fit: Higgs mass (126 GeV)

The ElectroWeak fit of Standard Model and Beyond

[GeV]

H

M

60 80 100 120 140 160 180 200

2

χ ∆

5 10 15 20 25 σ 1 σ 2 σ 3 σ 4 σ 5

Future scenario: = 80 MeV,

t

m δ = 1.3 MeV,

W

M δ = 0.1 MeV,

Z

Γ δ = 0.1 MeV,

Z

M δ = 0.1 GeV,

H

M δ

  • 5

10 × = 1

theo

)

eff

θ (

2

sin δ = 1 MeV,

theo W

M δ ,

  • 3

10 × = 1.25

0,lep

R δ ,

  • 6

10 × ) = 3

eff

θ (

2

sin δ Future scenario Present SM fit Present uncertainties

[GeV]

H

M

60 80 100 120 140 160 180 200

2

χ ∆

5 10 15 20 25 σ 1 σ 2 σ 3 σ 4 σ 5

Present SM fit Present uncertainties Prospects for LHC = Rfit)

theo

δ Prospects for ILC/GigaZ ( = Gauss)

theo

δ Prospects for ILC/GigaZ (

G fitter SM

Aug 13

§ Logarithmic dependency on MH → cannot compete with direct MH meas. § Indirect prediction MH dominated by theory uncertainties.

  • ILC with (without) theory errors:

MH = 126+10

  • 9 (±7) GeV
  • ILC with present-day theory uncertainties:

MH = 126+20

  • 17 GeV
  • FCC-ee with (without) theory errors:

MH = 126 ± 5 (±3) GeV

Present / LHC / ILC FCC-ee scenario

slide-66
SLIDE 66

Max Baak (CERN)

[GeV]

H

M

60 80 100 120 140 160 180 200

2

χ ∆

5 10 15 20 25 σ 1 σ 2 σ 3 σ 4 σ 5

= 1.3 MeV,

W

M δ = 0.1 MeV,

Z

Γ δ = 0.1 MeV,

Z

M δ = 0.1 GeV,

H

M δ Future scenario: ,

  • 5

10 × = 4.7

had

α ∆ δ ,

  • 3

10 × = 1.25

lep

R δ ,

  • 6

10 × ) = 3

eff

θ (

2

sin δ = 80 MeV,

t

m δ

  • 5

10 × ) = 1

eff

θ (

2

sin

th

δ = 1 MeV,

W

M

th

δ = 94 MeV

H

Future scenario M Present SM fit

Prospects of the EW fit: Higgs mass (94 GeV)

The ElectroWeak fit of Standard Model and Beyond

[GeV]

H

M

60 80 100 120 140 160 180 200

2

χ ∆

5 10 15 20 25 σ 1 σ 2 σ 3 σ 4 σ 5

Present SM fit Prospects for LHC = Rfit)

theo

δ Prospects for ILC/GigaZ ( = Gauss)

theo

δ Prospects for ILC/GigaZ (

G fitter SM

Aug 13

MH

avg

94 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.

94 GeV Present / LHC / ILC FCC-ee scenario

slide-67
SLIDE 67

Max Baak (CERN)

[GeV]

W

M

80.33 80.34 80.35 80.36 80.37 80.38 80.39 80.4

2

χ ∆

5 10 15 20 25 σ 1 σ 2 σ 3 σ 4 σ 5

= 1.3 MeV,

W

M δ = 0.1 MeV,

Z

Γ δ = 0.1 MeV,

Z

M δ = 0.1 GeV,

H

M δ Future scenario: ,

  • 5

10 × = 4.7

had

α ∆ δ ,

  • 3

10 × = 1.25

lep

R δ ,

  • 6

10 × ) = 3

eff

θ (

2

sin δ = 80 MeV,

t

m δ

  • 5

10 × ) = 1

eff

θ (

2

sin

th

δ = 1 MeV,

W

M

th

δ Future scenario Present SM fit Direct measurement (present / future)

Prospects of the EW fit: W mass and sin2θl

eff

The ElectroWeak fit of Standard Model and Beyond

[GeV]

W

M

80.33 80.34 80.35 80.36 80.37 80.38 80.39 80.4

2

χ ∆

5 10 15 20 25 σ 1 σ 2 σ 3 σ 4 σ 5

Present SM fit Prospects for LHC = Rfit)

theo

δ Prospectes for ILC/GigaZ ( = Gauss)

theo

δ Prospects for ILC/GigaZ ( Direct measurement (present / LHC / ILC)

G fitter SM

Aug 13

)

l eff

θ (

2

sin

0.2312 0.2313 0.2314 0.2315 0.2316 0.2317 0.2318

χ ∆

5 10 15 20 25 σ 1 σ 2 σ 3 σ 4 σ 5

= 1.3 MeV,

W

M δ = 0.1 MeV,

Z

Γ δ = 0.1 MeV,

Z

M δ = 0.1 GeV,

H

M δ Future scenario: ,

  • 5

10 × = 4.7

had

α ∆ δ ,

  • 3

10 × = 1.25

lep

R δ ,

  • 6

10 × ) = 3

eff

θ (

2

sin δ = 80 MeV,

t

m δ

  • 5

10 × ) = 1

eff

θ (

2

sin

th

δ = 1 MeV,

W

M

th

δ Future scenario Present uncertainties Direct measurement (present / future)

Present / LHC / ILC FCC-ee scenario

slide-68
SLIDE 68

Max Baak (CERN)

Prospects of the EW fit: W mass versus sin2θl

eff

The ElectroWeak fit of Standard Model and Beyond

)

l eff

θ (

2

sin

0.231 0.2311 0.2312 0.2313 0.2314 0.2315 0.2316 0.2317 0.2318 0.2319

[GeV]

W

M

80.3 80.32 80.34 80.36 80.38 80.4 80.42 80.44 80.46

68% and 95% CL fit contours ) measurements

l eff

θ (

2

and sin

W

w/o M Present SM fit Prospects for LHC Prospects for ILC/GigaZ ILC precision LHC precision Present measurement σ 1 ±

W

M σ 1 ± )

eff l

θ (

2

sin

G fitter SM

Oct 13

)

l eff

θ (

2

sin

0.231 0.2311 0.2312 0.2313 0.2314 0.2315 0.2316 0.2317 0.2318 0.2319

W

80.32 80.34 80.36 80.38 80.4 80.42 80.44 80.46

68% and 95% CL fit contours measurements

t

and m

W

w/o M Present SM fit Future scenario Present measurement Future scenario σ 1 ± )

l eff

θ (

2

sin σ 1 ±

W

M = 1.3 MeV,

W

M δ = 0.1 MeV,

Z

Γ δ = 0.1 MeV,

Z

M δ = 0.1 GeV,

H

M δ Future scenario: ,

  • 5

10 × = 4.7

had

α ∆ δ ,

  • 3

10 × = 1.25

lep

R δ ,

  • 6

10 × ) = 3

eff

θ (

2

sin δ = 80 MeV,

t

m δ

  • 5

10 × ) = 1

eff

θ (

2

sin

th

δ = 1 MeV,

W

M

th

δ

§ Huge reduction of uncertainty on indirect determinations of mW, and sin2θleff, by a factor of ≳3 (≳4-5) at ILC (FCC-ee). § Assuming central values of MW and sin2θleff 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.

Present / LHC / ILC FCC-ee scenario

slide-69
SLIDE 69

Max Baak (CERN)

Confrontation of measurement and prediction

§ Breakdown of individual contributions to errors of MW and sin2θleff § Parametric uncertainties (not the full fit).

The ElectroWeak fit of Standard Model and Beyond

§ MW and sin2θleff are sensitive probes of new physics! In all scenarios. § At ILC/GigaZ, precision of MZ will become important again. § At FCC-ee (‘Future’), limited by external inputs: theory errors and Δαhad

slide-70
SLIDE 70

Max Baak (CERN)

[GeV]

t

m

160 165 170 175 180 185

[GeV]

W

M

80.32 80.34 80.36 80.38 80.4 80.42 80.44 80.46

68% and 95% CL fit contours measurements

t

and m

W

w/o M Present SM fit Future scenario Present measurement Future scenario σ 1 ±

t

m σ 1 ±

W

M = 1.3 MeV,

W

M δ = 0.1 MeV,

Z

Γ δ = 0.1 MeV,

Z

M δ = 0.1 GeV,

H

M δ Future scenario: ,

  • 5

10 × = 4.7

had

α ∆ δ ,

  • 3

10 × = 1.25

lep

R δ ,

  • 6

10 × ) = 3

eff

θ (

2

sin δ = 80 MeV,

t

m δ

  • 5

10 × ) = 1

eff

θ (

2

sin

th

δ = 1 MeV,

W

M

th

δ

Prospects of the EW fit: W versus top mass

The ElectroWeak fit of Standard Model and Beyond

[GeV]

t

m

160 165 170 175 180 185

[GeV]

W

M

80.3 80.32 80.34 80.36 80.38 80.4 80.42 80.44 80.46

68% and 95% CL fit contours measurements

t

and m

W

w/o M Present SM fit Prospects for LHC Prospects for ILC/GigaZ ILC precision LHC precision Present measurement σ 1 ±

W

M σ 1 ±

t

m

G fitter SM

Oct 13

§ Huge reduction of uncertainty on indirect determinations of mt and mW by a factor of ≳3 (≳5) at ILC (FCC-ee). § Assuming central values of mt and MW do not change, a deviation between the SM prediction and the direct measurements would be prominently visible. Present / LHC / ILC FCC-ee scenario

slide-71
SLIDE 71

Max Baak (CERN)

Prospects of EW fit: S versus T

The ElectroWeak fit of Standard Model and Beyond

S

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

T

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

68% and 95% CL fit contours for U=0 =173 GeV)

t

=126 GeV, m

H

: M

ref

(SM Present SM fit Present uncertainties Future scenario = 1.3 MeV,

W

M δ = 0.1 MeV,

Z

Γ δ = 0.1 MeV,

Z

M δ = 0.1 GeV,

H

M δ Future scenario: ,

  • 5

10 × = 4.7

had

α ∆ δ ,

  • 3

10 × = 1.25

lep

R δ ,

  • 6

10 × ) = 3

eff

θ (

2

sin δ = 80 MeV,

t

m δ

  • 5

10 × ) = 1

eff

θ (

2

sin

th

δ = 1 MeV,

W

M

th

δ

S

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

T

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

68% and 95% CL fit contours for U=0 =173 GeV)

t

=126 GeV, m

H

: M

ref

(SM Present fit Present uncertainties Prospects for LHC Prospects for ILC/GigaZ SM Prediction 0.4 GeV ± = 125.7

H

M 0.87 GeV ± = 173.20

t

m

G fitter SM

B

Oct 13

§ 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. Present / LHC / ILC FCC-ee scenario

slide-72
SLIDE 72

Max Baak (CERN)

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

slide-73
SLIDE 73

Max Baak (CERN) [GeV]

H

M

50 100 150 200 250 300

2

χ ∆

1 2 3 4 5 6 7 8 9 10

LEP 95% CL Tevatron 95% CL

σ 1 σ 2 σ 3

Theory uncertainty Fit including theory errors Fit excluding theory errors

Hunt for the Higgs

§ MH was last missing input parameter of the electroweak fit § Indirect determination from EW fit (2012): MH = 96+31

  • 24 GeV
  • With direct limits incorporated in the EW fit: MH = 120+12
  • 5 GeV

The ElectroWeak fit of Standard Model Gfitter group, EPJC 72, 2003 (2012)

Early 2012

73