Constraints on Higgs physics from EW precision...

Satoshi Mishima (Univ. of Rome)1

Constraints on Higgs physics from EW precision measurements

/26

FFP14, Marseille, Jul. 15, 2014

Satoshi Mishima

Univ. of Rome “La Sapienza”

Satoshi Mishima (Univ. of Rome)2 /26

Outline

1. Introduction

2. SM fit

3. NP fit: Oblique parameters

4. NP fit: Epsilon parameters

!

5. NP fit: Dim. 6 operators

6. Summary

e.g., 2HDM, EW chiral Lagrangian, Composite Higgs models

e.g., MSSM with decoupled sparticles

1. Introduction


The precise measurement of the Higgs/W/top masses at Tevatron and LHC make improvement in EW fits.

Electroweak precision observables (EWPO) offer a very powerful handle on the mechanism of EWSB and allow us to strongly constrain NP models relevant to solve the hierarchy problem.

Theoretical calculations have been improved in recent years.

No free SM parameter in the fit

EW precision observables

4 Satoshi Mishima (Univ. of Rome)/26

Z-pole obs’ are given in terms of effective couplings:

MW , �W and 13 Z-pole observables

A0,fLR = Af =

2Re⇣gfV /gf

A

⌘

1 +hRe

⇣gfV /gf

A

⌘i2 A0,fFB =

3

4AeAf

P pol

⌧ = A⌧

(LEP/SLD)(LEP2/Tevatron)

(f = `, c, b)

�Z , �0h =

12⇡

M2Z

�e�h

�2Z

, R0` =

�h

�`, R0

c,b =�c,b

�h

)

)�f = �(Z ! ff) /

��gfA

��22

4��gfV

gfA

��

2

RfV + Rf

A

3

5

gfV , gf

A

gfV /gf

A

L =e

2sW cWZµ f

⇣gfV �µ � gf

A�µ�5

⌘f

sin2 ✓lepte↵ =

1

4|Q`|

"1 � Re

g`V

g`A

!#

Full fermionic EW two-loop corrections to the Z-boson partial widths have been calculated recently.

have been calculated with full EW two-loop (bosonic is missing for f=b) and leading higher-order contributions.

Theoretical status

Satoshi Mishima (Univ. of Rome)

Mw has been calculated with full EW two-loop and leading higher-order contributions.

See also Sirlin; Marciano&Sirlin; Bardin et al; Djouadi&Verzegnassi; Djouadi; Kniehl; Halzen&Kniehl; Kniehl&Sirlin; Barbieri et al; Fleischer et al; Djouadi&Gambino; Degrassi et al; Avdeev et al; Chetyrkin et al; Freitas et al; Awramik&Czakon; Onishchenko&Veretin; Van der Bij et al; Faisst et al; Awramik et al, and many other works

Awramik, Czakon, Freitas & Weiglein (04)

Awramik, Czakon & Freitas (06); Awramik, Czakon, Freitas & Kniehl (09)

sin2 ✓fe↵

Freitas & Huang (12); Freitas (13); Freitas (14)

5 /26

Up-to-date formulae are available in on-shell scheme.


Electroweak precision tests Ayres Freitas

MW GZ s0had Rb sin2 q `

effExp. error 15 MeV 2.3 MeV 37 pb 6.6⇥10�4 1.6⇥10�4

Theory error 4 MeV 0.5 MeV 6 pb 1.5⇥10�4 0.5⇥10�4

Table 1: Current experimental errors and theory uncertainties for the SM prediction of some of the mostimportant electroweak precision observables. Here R

b

⌘ G[Z ! bb]/G[Z ! hadrons].

2. Z-boson width at two loops

As a concrete example for the electroweak two-loop corrections to electroweak precision ob-servables, this section will discuss the calculation of the O(N

f

a2) contribution to the (partial)Z-boson width(s). The total Z-width is defined through the imaginary part of the complex pole ofthe Z-boson propagator,

s0 = M

2Z � iMZGZ. (2.1)

This definition leads to a Breit-Wigner function with constant width near the Z-pole, s µ|s� s0|�2 = [(s�M

2Z)

2 +M

2ZG2

Z]�1. Note that this differs from the Breit-Wigner function with

a running width used in the experimental analyses, so that one has to include a finite shift whenrelating MZ and GZ to the reported measured values:

MZ = M

expZ �34.1 MeV, GZ = Gexp

Z �0.9 MeV. (2.2)

Expanding (2.1) up to next-to-next-to-leading order (NNLO) and using the power counting GZ ⇠O(a)MZ, the result for GZ can be written as [8]1

GZ =1

MZImSZ(s0) =

1MZ

ImSZ

1+ReS0Z

�

s=M

2Z

+O(G3Z), (2.3)

where SZ is the Z self-energy. Using the optical theorem, the imaginary part of the self-energy canbe related to the decay process Z ! f f , resulting in

GZ = Âf

Gf

, Gf

=N

f

c

MZ

12p⇥R f

V

F

f

V

+R f

A

F

f

A

⇤s=M

2Z, F

f

V

⇡|v

f

|2

1+ReS0Z, F

f

A

⇡|a

f

|2

1+ReS0Z, (2.4)

where N

f

c

= 3(1) for quarks (leptons). Here the functions R f

V,A have been introduced, which captureeffects from final-state QED and QCD corrections. They are known up to O(a4

s ), O(aas) andO(a2) in the limit of massless fermions, while mass corrections are known up to three-loop order[10]. The electroweak corrections are contained in S0

Z and the effective Z f f vector and axial-vectorcouplings v

f

and a

f

. Note that v

f

and a

f

include contributions from photon-Z mixing. Eq. (2.4) isaccurate up to NNLO.

For the calculation of the fermionic electroweak O(a2) corrections, Feynman diagrams havebeen generated with FeynArts 3.3 [11]. In addition to the diagrams for the Z ! f f vertex cor-rections, one also needs two-loop self-energy diagrams for the on-shell renormalization [12]. Inthe on-shell renormalization scheme used here, particle masses are defined through the (complex)

1Here a term µ ImS00Z has been omitted, since ImS00

Z = 0 at leading order for massless final-state fermions.

3

A. Freitas, 1406.6980

Theoretical status

Theory errors from missing higher-order corrections are safely below current experimental errors.


EW precision fitErler et al. (for PDG)

GAPP (Global Analysis of Particle Properties)

MSbar scheme & frequentistGfitter group

http://gfitter.desy.de

http://www.fisica.unam.mx/erler/GAPPP.html

on-shell scheme & frequentistGfitter (Generic fitting package)

Many other groups with ZFITTERon-shell scheme

We have been developing a new tool, which handles EWPO, Higgs, flavor, etc. in various NP models.

on-shell scheme & BayesianM. Ciuchini, E. Franco, S.M., L. Silvestrini and others …

EW+Higgs codes will be released soon.

http://zfitter.com

http://gfitter.desy.de

http://www.fisica.unam.mx/erler/GAPPP.html

http://zfitter.com

2. SM fit


Combination and SM fit

Very good agreement between indirect anddirect determinations

Global p-value ≈ 20%

Gfitter coll. ’14

[GeV]tm140 150 160 170 180 190

[GeV

]W

M

80.25

80.3

80.35

80.4

80.45

80.568% and 95% CL contours

measurementst and mWfit w/o M measurementsH and Mt, mWfit w/o M

measurementst and mWdirect M

σ 1± world comb. WMPhys. Rev. D 88052018 (2013)

σ 1± world comb. tmarXiv:1403.4427

= 125.7 GeV

HM = 50 GeV

HM = 300 GeV

HM = 600 GeV

HM G fitter SM

Jun '14

1.4σ

1.5σ

2.0σ

2.5σ


Data Fit Indirect Pull↵s(M2

Z) 0.1185 ± 0.0005 0.1185 ± 0.0005 0.1185 ± 0.0028 +0.0

�↵(5)

had

(M2

Z) 0.02750 ± 0.00033 0.02742 ± 0.00026 0.02727 ± 0.00042 �0.4MZ [GeV] 91.1875 ± 0.0021 91.1879 ± 0.0020 91.198 ± 0.011 +0.9mt [GeV] 173.34 ± 0.76 ± 1.00 173.8 ± 0.9 176.6 ± 2.5 +1.2mh [GeV] 125.5 ± 0.3 125.5 ± 0.3 100.4 ± 27.5 �0.7MW [GeV] 80.385 ± 0.015 80.368 ± 0.007 80.363 ± 0.008 �1.3�W [GeV] 2.085 ± 0.042 2.0892 ± 0.0006 2.0892 ± 0.0006 +0.1�Z [GeV] 2.4952 ± 0.0023 2.4946 ± 0.0005 2.4945 ± 0.0005 �0.3�0

h [nb] 41.540 ± 0.037 41.488 ± 0.003 41.488 ± 0.003 �1.4

sin2 ✓lept

e↵

(Qhad

FB

) 0.2324 ± 0.0012 0.23145 ± 0.00009 0.23144 ± 0.00009 �0.8P pol

⌧ 0.1465 ± 0.0033 0.1476 ± 0.0007 0.1477 ± 0.0007 +0.3A` (SLD) 0.1513 ± 0.0021 0.1476 ± 0.0007 0.1471 ± 0.0008 �1.9Ac 0.670 ± 0.027 0.6682 ± 0.0003 0.6682 ± 0.0003 �0.1Ab 0.923 ± 0.020 0.93466 ± 0.00006 0.93466 ± 0.00006 +0.6

A0,`FB

0.0171 ± 0.0010 0.0163 ± 0.0002 0.0163 ± 0.0002 �0.8A0,c

FB

0.0707 ± 0.0035 0.0740 ± 0.0004 0.0740 ± 0.0004 +0.9

A0,bFB

0.0992 ± 0.0016 0.1035 ± 0.0005 0.1039 ± 0.0005 +2.8R0

` 20.767 ± 0.025 20.752 ± 0.003 20.752 ± 0.004 �0.6R0

c 0.1721 ± 0.0030 0.17224 ± 0.00001 0.17224 ± 0.00001 +0.0R0

b 0.21629 ± 0.00066 0.21578 ± 0.00003 0.21578 ± 0.00003 �0.8�MW [GeV] [�0.004, 0.004]

� sin2 ✓lept

e↵

[�4.7, 4.7] · 10�5

��Z [GeV] [�5, 5] · 10�4

Table 1: SM fit.

1

Gfitter (14), taken from A. Freitas’ talk at ICHEP2014

M. Ciuchini, E. Franco, S.M. & L. Silvestrini (13); M. Ciuchini, E. Franco, S.M., M. Pierini, L. Reina & L. Silvestrini, in preparation

Indirect: determined w/o using the corresponding experimental information

SM fit

mt = 174.34 ± 0.64cf. new CDF+D0 combination: 1407.2682

107 108109

1010

1011

10121013

1014

1016

120 122 124 126 128 130 132168

170

172

174

176

178

180

Higgs pole mass Mh in GeV

ToppolemassM

tinGeV

1017

1018

1019

1,2,3 s

Instability

Stability

Meta-stability

The measurement of the top mass is crucial for testing the stability of the SM vacuum.

Top mass vs. (meta-)stability

Satoshi Mishima (Univ. of Rome)10/26

Degrassi et al.(12); Buttazzo et al.(13)

Indirect determination from EW fit:

Tevatron/LHC pole(?) mass:

Pole from MSbar:

Caveat: Threshold corrections at the Planck scale alter the phase diagram.

176.6 ± 2.5 GeV

171.2 ± 2.4 GeV1405.4781

173.34 ± 0.76 GeV

mpole

t < 171.53 ± 0.42 GeV

extra uncertainty of O(1 GeV)

Branchina & Messina (13)

Ciuchini et al.

3. NP fit: Oblique parameters


Oblique parameters


S = �16⇡⇧030(0) = 16⇡

h⇧NP0

33 (0) � ⇧NP03Q (0)

i

T =4⇡

s2W c2WM2Z

⇥⇧NP

11 (0) � ⇧NP33 (0)

⇤

U = 16⇡⇥⇧NP0

11 (0) � ⇧NP033 (0)

⇤

Suppose that dominant NP effects appear in the vacuum polarizations of the gauge bosons:

Kennedy & Lynn (89); Peskin & Takeuchi (90,92)

When the EW symmetry is realized linearly, U is associated with a dim. 8 operator and thus small.

More general parameterization: S, T , W, Y (+ U, V, X)

Barbieri et al. (04)

EWPO depend on the 3 independents: ↵

4s2WS0 = bS � W +

X

sW cW� Y , ↵ T 0 = bT � W +

2sW

cWX �

s2Wc2W

Y , �↵

4s2WU 0 = bU � V � W +

2sW

cWX

Oblique parameters


U = 0U 6= 0

EWPO depend on the three combinations:

�MW , ��W / �S + 2c2W T +

(c2W � s2W )U

2s2W��Z / �10(3 � 8s2W )S + (63 � 126s2W � 40s4W ) T

others / S � 4c2W s2W T

Constraints on new physics

Two-Higgs-Doublet Model: Eberhardt, Nierste, Wiebusch ’13

Constraints on couplings of SM-like Higgs

0.3 1 10 30tan β

0.2π

0.3π

0.4π

0.5π

0.6π

β−

α

!!!!!gTHDMhV V

gSMhV V

!!!!! = sin(β − α),

!!!!!gTHDMhff

gSMhff

!!!!! =cosα

sinαor sinα

cosα

Oblique parameters:

S-0.3 -0.2 -0.1 0 0.1 0.2 0.3

T-0.3

-0.2

-0.1

0

0.1

0.2

0.368% and 95% CL fit contours for U=0

=173 GeV)t=126 GeV, mH: Href(SMPresent fitPresent uncertainties

SM Prediction 0.4 GeV± = 125.7 HM 0.76 GeV± = 173.34 tm

G fitter SM

Jun '14

Gfitter coll. ’14

αT =ΣWW(0)

MW−

ΣZZ(0)

MZ

α

4s2c2S =

ΣZZ(M2Z) − ΣZZ(0)

MZ

+s2 − c2

sc

ΣZγ(M2Z)

MZ−

Σγγ(M2Z)

MZ

Gfitter (14), taken from A. Freitas’ talk at ICHEP2014

S

-0.5 0 0.5

T

-0.5

0

0.5

3 Oblique parameters

Fit result CorrelationsS 0.08 ± 0.10 1.00T 0.10 ± 0.12 0.85 1.00U 0.00 ± 0.09 �0.49 �0.79 1.00

Table 5: STU fit.

Fit result CorrelationsS 0.08 ± 0.09 1.00T 0.10 ± 0.07 0.87 1.00

Table 6: ST fit with U = 0.

5

3 Oblique parameters

Fit result CorrelationsS 0.08 ± 0.10 1.00T 0.10 ± 0.12 0.85 1.00U 0.00 ± 0.09 �0.49 �0.79 1.00

Table 5: STU fit.

Fit result CorrelationsS 0.08 ± 0.09 1.00T 0.10 ± 0.07 0.87 1.00

Table 6: ST fit with U = 0.

5

S-0.5 0 0.5

T

-0.5

0

0.5

U=0

AllWM

0,fFB, Af, APol

τ, Plepteffθ2sin

ZΓ


[GeV]0H

M

200 300 400 500 600 700 800 900 1000

[G

eV

]0

AM

200

300

400

500

600

700

800

900

1000Two-Higgs Doublet Model

68%, 95%, 99% CL fit contours (allowed)/2π = α-β

= 250 GeV±H

= 120 GeV, M0h

M

= 500 GeV±H

= 120 GeV, M0h

M

= 750 GeV±H

= 120 GeV, M0h

M

[GeV]0H

M

200 300 400 500 600 700 800 900 1000

[G

eV

]0

AM

200

300

400

500

600

700

800

900

1000


Gfitter, EPJC72, 2003 (2012)

Example 1: Two Higgs doublet models

V =g2HDMhV V

gSMhV V

= sin(� � ↵)

5 physical Higgs bosons: h,H,A,H±

6 parameters: mh,mH ,mA,mH± , ↵, tan� = v2/v1

Several models (Type-I, Type-II, …) FCNC

Same S, T and U among the models at one-loop.

mH ⇡ mH± mA ⇡ mH±or

Many recent studies with Higgs and flavor data.

EWPO alone cannot fix all the parameters.

Example 2: EW chiral Lagrangian


Barberi, Bellazzini, Rychkov & Varagnolo (07)

No new state below cutoff + custodial symmetry:

⌃ : Goldstone bosons

V V

h

V

The HVV coupling contributes to S and T at one-loop.

V = 1 in the SM

⇤ = 4⇡v/q|1 � 2

V |

L =v2

4Tr

�Dµ⌃

†Dµ⌃� ✓

1 + 2Vh

v+ · · ·

◆+ · · ·

S =1

12⇡(1 � 2

V ) ln

✓⇤2

m2h

◆

T = �3

16⇡c2W(1 � 2

V ) ln

✓⇤2

m2h

◆

+V V

G

V

ln(⇤2/M2Z) � 2

V ln(⇤2/m2h)

Example 2: EW chiral Lagrangian


⇤ & 18 TeV @95% for V < 1

Vκ

0.9 1 1.1

Pro

ba

bili

ty d

en

sity

0

5

10

15

20

V = 1.025 ± 0.021

.

Falkowski, Rychkov & Urbano (12)

WLWL scattering is dominated by isospin 2 channelV > 1

1 � 2

V =v2

6⇡

Z 1

0

ds

s

�2�tot

I=0

(s) + 3�tot

I=1

(s) � 5�tot

I=2

(s)�


Vκ0.8 0.9 1 1.1 1.2

fκ

0.6

0.8

1

1.2

1.4EW+HiggsEWHiggs

EWPO constraint on Kv is stronger than Higgs one, but no constraint on Kf.

Vκ

0.9 1 1.1 1.2

[Te

V]

Λ

1

2

3

4

Vκ

0.9 0.95 1 1.05 1.1 1.15

[Ge

V]

WM

80.35

80.4

80.45

S

-0.2 -0.1 0 0.1 0.2 0.3

T

-0.2

-0.1

0

0.1

0.2

0.3

Vκ

1.15

1.10

1.05

1.00

0.95

0.90

0.85


68%, 95% & 99%

⇤ <4⇡v

p|1 � 2

V |

Example 2: EW chiral LagrangianM. Ciuchini, E. Franco, S.M. & L. Silvestrini (13); M. Ciuchini, E. Franco, S.M., M. Pierini, L. Reina & L. Silvestrini, in preparation

smaller Mw smaller Kv

Kv is tightly constrained for the scale compatible with direct searches.

17/26

Composite Higgs models typically generate .

Example 2’: Composite Higgs models


Extra contributions to S and T are required to fix the EW fit under .

Grojean et al. (13)

Fermionic resonances

x=0 HSMLx=0.1x=0.2x=0.25

UV con tr.

fermioncon tr.

IRcon tr.

-2 -1 0 1 2 3

-1

0

1

2

S`¥ 103

T`¥10

3

V < 1

V < 1

e.g. Minimal Composite Higgs Models (MCHM) based on SO(5)/SO(4)

V =p

1 � ⇠ ⇠ =

✓v

f

◆2

f : scale of compositeness

IR contribution

UV cont’ from heavy vector resonances+

+

Agashe, Contino & Pomarol (05)

4. NP fit: Epsilon parameters


Epsilon parameters


Unlike STU, involve non-oblique vertex corrections.

Altarelli et al. (91,92,93)

20/26

✏1

= �⇢0 (2)

✏2

= c20

�⇢0 +s20

c20

� s20

�rW � 2s20

�0 (3)

✏3

= c20

�⇢0 + (c20

� s20

)�0 (4)

s2W c2W =⇡↵(M2

Z)p2GµM

2

Z(1 � �rW )(5)

pRe ⇢e

Z = 1 +�⇢0

2(6)

sin2 ✓ee↵

= (1 + �0) s20

(7)

s20

c20

=⇡↵(M2

Z)p2GµM

2

Z

(8)

9

✏1

= �⇢0 (2)

✏2

= c20

�⇢0 +s20

c20

� s20

�rW � 2s20

�0 (3)

✏3

= c20

�⇢0 + (c20

� s20

)�0 (4)

s2W c2W =⇡↵(M2

Z)p2GµM

2

Z(1 � �rW )(5)

pRe ⇢e

Z = 1 +�⇢0

2(6)

sin2 ✓ee↵

= (1 + �0) s20

(7)

s20

c20

=⇡↵(M2

Z)p2GµM

2

Z

(8)

9

✏1

= �⇢0 (2)

✏2

= c20

�⇢0 +s20

c20

� s20

�rW � 2s20

�0 (3)

✏3

= c20

�⇢0 + (c20

� s20

)�0 (4)

s2W c2W =⇡↵(M2

Z)p2GµM

2

Z(1 � �rW )(5)

pRe ⇢e

Z = 1 +�⇢0

2(6)

sin2 ✓ee↵

= (1 + �0) s20

(7)

s20

c20

=⇡↵(M2

Z)p2GµM

2

Z

(8)

9

and ✏b

Moreover, also involve SM contributions.

✏1

= �⇢0 (2)

✏2

= c20

�⇢0 +s20

c20

� s20

�rW � 2s20

�0 (3)

✏3

= c20

�⇢0 + (c20

� s20

)�0 (4)

s2W c2W =⇡↵(M2

Z)p2GµM

2

Z(1 � �rW )(5)

pRe ⇢e

Z = 1 +�⇢0

2(6)

sin2 ✓ee↵

= (1 + �0) s20

(7)

s20

c20

=⇡↵(M2

Z)p2GµM

2

Z

(8)

�✏i = ✏i � ✏SMi (9)

9

involve the oblique corrections beyond S, T and U.

✏i

✏i

✏ii.e., W, Y, …


Fit result Correlations�✏

1

0.0007 ± 0.0010 1.00�✏

2

�0.0001 ± 0.0009 0.80 1.00�✏

3

0.0006 ± 0.0009 0.86 0.51 1.00�✏b 0.0003 ± 0.0013 �0.33 �0.32 �0.22 1.00

Table 9: �✏ fit.


1

0.0008 ± 0.0006 1.00�✏

3

0.0007 ± 0.0008 0.87 1.00

Table 10: �✏ fit with fixing �✏2

= 0 and �✏b = 0.

8


1

0.0007 ± 0.0010 1.00�✏

2

�0.0001 ± 0.0009 0.80 1.00�✏

3

0.0006 ± 0.0009 0.86 0.51 1.00�✏b 0.0003 ± 0.0013 �0.33 �0.32 �0.22 1.00

Table 9: �✏ fit.


1

0.0008 ± 0.0006 1.00�✏

3

0.0007 ± 0.0008 0.87 1.00

Table 10: �✏ fit with fixing �✏2

= 0 and �✏b = 0.

8

1εδ

-2 0 2 4

-310×

3ε

δ

-2

0

2

4

-310×

1εδ

-2 0 2 4

-310×

3ε

δ

-2

0

2

4

-310×

0=bεδ=2εδ

Modified epsilon parametersM. Ciuchini, E. Franco, S.M. & L. Silvestrini (13); M. Ciuchini, E. Franco, S.M., M. Pierini, L. Reina & L. Silvestrini, in preparation

gets the VEV v, while is its orthogonal.


R. Barbieri & A. Tesi, PRD89, 055019 (2014)

-0.05

-0.02

-0.01

-0.005

-0.002LHC14

0.25 10-5

0.5 10-5

1. 10-5

-1. 10-6

1. 10-6

2 4 6 8 10 12 14200

400

600

800

1000

tan b

mHêGe

V

Example: MSSM with decoupled sparticles

h = cos � hv � sin � h?v H = sin � hv + cos � h?

v

hv h?v

All sparticles are assumed to be sufficiently decoupled.

� =⇡

2� � + ↵

ghdd

gSMhdd

= cos � � tan� sin �ghV V

gSMhV V

= cos �,ghuu

gSMhuu

= cos � +

sin �

tan�,

�✏1 . 10�3

�✏1

sin �

Current bound:

EWPO are irrelevant.

Orange: excluded at 95% by the signal strengths of h

Red: excluded at 95% by search for A,H ! ⌧+⌧�

5. NP fit: Dimension-6 operators


24/26 Satoshi Mishima (Univ. of Rome)

Dim-6 operators

59 dimension-six operators (for one generation)Buchmuller & Wyler (86); Grzadkowski, Iskrzynski, Misiak & Rosiek (10)

Dimension-five operators violate B and/or L.

L = L(4)SM +

1

⇤

X

i

C(5)i O

(5)i +

1

⇤2

X

j

C(6)j O

(6)j + O

✓1

⇤3

◆

NP scale is assumed to be enough higher than the weak scale.

Contributions from higher-dimensional operators are suppressed.

Operators respect the SM gauge symmetries.

Right-handed

Left-handed


switch on one operator at a time

Buchmuller & Wyler (86); Barbieri & Strumia (99); Grzadkowski, Iskrzynski, Misiak & Rosiek (10)

!!

S parameterT parameter

! Fermi constant]

!

! Zff

Zff

OHWB = (H†⌧ IH)W Iµ⌫B

µ⌫

OHD = (H†DµH)⇤(H†DµH)

OLL = (L�µL)(L�µL)

O(3)

HL = (H†i !D I

µH)(L ⌧ I�µL)

O(1)

HL = (H†i !D µH)(L�µL)

O(3)

HQ = (H†i !D I

µH)(Q ⌧ I�µQ)

O(1)

HQ = (H†i !D µH)(Q�µQ)

OHe = (H†i !D µH)(eR�µeR)

OHu = (H†i !D µH)(uR�µuR)

OHd = (H†i !D µH)(dR�µdR)

17

M. Ciuchini, E. Franco, S.M., M. Pierini, L. Reina & L. Silvestrini, in preparation

There are flat directions in the fit. See, e.g., Han & Skiba (05)

Dim-6 operators


Z) 0.1185 ± 0.0005 0.1185 ± 0.0005 0.1185 ± 0.0028 +0.0

�↵(5)

had

(M2

Z) 0.02750 ± 0.00033 0.02742 ± 0.00026 0.02727 ± 0.00042 �0.4MZ [GeV] 91.1875 ± 0.0021 91.1879 ± 0.0020 91.198 ± 0.011 +0.9mt [GeV] 173.34 ± 0.76 ± 1.00 173.8 ± 0.9 176.6 ± 2.5 +1.2mh [GeV] 125.5 ± 0.3 125.5 ± 0.3 100.4 ± 27.5 �0.7MW [GeV] 80.385 ± 0.015 80.368 ± 0.007 80.363 ± 0.008 �1.3�W [GeV] 2.085 ± 0.042 2.0892 ± 0.0006 2.0892 ± 0.0006 +0.1�Z [GeV] 2.4952 ± 0.0023 2.4946 ± 0.0005 2.4945 ± 0.0005 �0.3�0

h [nb] 41.540 ± 0.037 41.488 ± 0.003 41.488 ± 0.003 �1.4

sin2 ✓lept

e↵

(Qhad

FB

) 0.2324 ± 0.0012 0.23145 ± 0.00009 0.23144 ± 0.00009 �0.8P pol

⌧ 0.1465 ± 0.0033 0.1476 ± 0.0007 0.1477 ± 0.0007 +0.3A` (SLD) 0.1513 ± 0.0021 0.1476 ± 0.0007 0.1471 ± 0.0008 �1.9Ac 0.670 ± 0.027 0.6682 ± 0.0003 0.6682 ± 0.0003 �0.1Ab 0.923 ± 0.020 0.93466 ± 0.00006 0.93466 ± 0.00006 +0.6

A0,`FB

0.0171 ± 0.0010 0.0163 ± 0.0002 0.0163 ± 0.0002 �0.8A0,c

FB

0.0707 ± 0.0035 0.0740 ± 0.0004 0.0740 ± 0.0004 +0.9

A0,bFB

0.0992 ± 0.0016 0.1035 ± 0.0005 0.1039 ± 0.0005 +2.8R0

` 20.767 ± 0.025 20.752 ± 0.003 20.752 ± 0.004 �0.6R0

c 0.1721 ± 0.0030 0.17224 ± 0.00001 0.17224 ± 0.00001 +0.0R0

b 0.21629 ± 0.00066 0.21578 ± 0.00003 0.21578 ± 0.00003 �0.8�MW [GeV] [�0.004, 0.004]

� sin2 ✓lept

e↵

[�4.7, 4.7] · 10�5

��Z [GeV] [�5, 5] · 10�4

Table 1: SM fit.

Ci/⇤2 [TeV�2] ⇤ [TeV]Coe�cient at 95% Ci = �1 Ci = 1CHWB [�0.010, 0.005] 9.9 14.7CHD [�0.031, 0.006] 5.7 13.0CLL [�0.010, 0.022] 9.9 6.8

C(3)

HL [�0.011, 0.006] 9.4 12.6

C(1)

HL [�0.005, 0.012] 14.1 9.3

C(3)

HQ [�0.011, 0.013] 9.4 8.7

C(1)

HQ [�0.027, 0.041] 6.1 5.0CHe [�0.017, 0.005] 7.7 13.6CHu [�0.070, 0.076] 3.8 3.6CHd [�0.14, 0.06] 2.7 4.0

Table 2: [Only EW including uncertainties in the SM input parameters] Fit results for the coe�cients

of the dimension six operators at 95% probability in units of 1/⇤2

TeV

�2

, where the fit is performed switching

on one operator at a time. The corresponding lower bounds on the NP scale in TeV obtained by setting

Ci = ±1 are also presented. Unlike the fit in the previous section, the tree-level SM quantities havebeen used in NP contributions.

1

Many (semi-)global studies with TGC and Higgs data

6. Summary


The constraining power of the EW fit have been improved by the recent experimental and theoretical progresses.

Future experiments (ILC/FCC-ee) will strengthen greatly the power of the EW fit.

Interplay between EWPO and Higgs data provides further constraints on TeV-scale NP.

2HDM and composite Higgs models are strongly constrained by EWPO.

MSSM with decoupled sparticles is insensitive to EWPO.

Backup


Our global fitting tool


Alternatively, one can use it as a library to compute observables in a given model.

We have been developing a computational framework to calculate various observables in the SM or in its extensions, and to constrain their parameter space.

One can use our tool as a stand-alone program to perform a Bayesian statistical analysis with MCMC based on the Bayesian Analysis Toolkit (BAT).

Caldwell, Kollar & Kroninger

One can add his/her favorite models as well as observables to our tool as external modules.

The codes are written in C++, supporting MPI.

M. Ciuchini, E. Franco, S.M., L. Silvestrini and others …


EW+Higgs codes will be released soon.

M. Ciuchini, E. Franco, S.M., L. Silvestrini and others …

Models:- Standard Model (tested)- Some NP extensions for model-independent studies of EW and Higgs (tested)

The outcomes are presented in this talk.- general MSSM (under testing)

Observables:- EW precision observables (tested)

- Higgs signal strengths (tested)

- Flavor: �F = 2, UT, b ! s�, b ! s`` (under testing)

- LEP2 x-sections, LFV obs’ (under construction/testing)

Our global fitting tool

Parametric uncertainties


and are the most important sources of parametric uncertainty. �↵(5)

had(M2Z)

1 Standard Model


Z) 0.1185 ± 0.0005 0.1185 ± 0.0005 0.1185 ± 0.0028 +0.0

�↵(5)

had

(M2

Z) 0.02750 ± 0.00033 0.02741 ± 0.00026 0.02727 ± 0.00042 �0.4MZ [GeV] 91.1875 ± 0.0021 91.1879 ± 0.0020 91.198 ± 0.011 +0.9mt [GeV] 173.34 ± 0.76 173.6 ± 0.7 176.6 ± 2.5 +1.2mh [GeV] 125.5 ± 0.3 125.5 ± 0.3 99.9 ± 26.6 �0.8MW [GeV] 80.385 ± 0.015 80.367 ± 0.006 80.363 ± 0.007 �1.3�W [GeV] 2.085 ± 0.042 2.0892 ± 0.0005 2.0892 ± 0.0005 +0.1�Z [GeV] 2.4952 ± 0.0023 2.4945 ± 0.0004 2.4944 ± 0.0004 �0.3�0

h [nb] 41.540 ± 0.037 41.488 ± 0.003 41.488 ± 0.003 �1.4

sin2 ✓lept

e↵

(Qhad

FB

) 0.2324 ± 0.0012 0.23145 ± 0.00009 0.23144 ± 0.00009 �0.8P pol

⌧ 0.1465 ± 0.0033 0.1476 ± 0.0007 0.1477 ± 0.0007 +0.3A` (SLD) 0.1513 ± 0.0021 0.1476 ± 0.0007 0.1471 ± 0.0007 �1.9Ac 0.670 ± 0.027 0.6682 ± 0.0003 0.6682 ± 0.0003 �0.1Ab 0.923 ± 0.020 0.93466 ± 0.00006 0.93466 ± 0.00006 +0.6

A0,`FB

0.0171 ± 0.0010 0.0163 ± 0.0002 0.0163 ± 0.0002 �0.8A0,c

FB

0.0707 ± 0.0035 0.0740 ± 0.0004 0.0740 ± 0.0004 +0.9

A0,bFB

0.0992 ± 0.0016 0.1035 ± 0.0005 0.1039 ± 0.0005 +2.8R0

` 20.767 ± 0.025 20.752 ± 0.003 20.752 ± 0.003 �0.6R0

c 0.1721 ± 0.0030 0.17224 ± 0.00001 0.17224 ± 0.00001 +0.0R0

b 0.21629 ± 0.00066 0.21578 ± 0.00003 0.21578 ± 0.00003 �0.8

Table 1: SM fit.

Prediction ↵s �↵(5)

had

MZ mt

MW [GeV] 80.363 ± 0.008 ±0.000 ±0.006 ±0.003 ±0.005�W [GeV] 2.0889 ± 0.0007 ±0.0002 ±0.0005 ±0.0002 ±0.0004�Z [GeV] 2.4943 ± 0.0005 ±0.0002 ±0.0003 ±0.0002 ±0.0002�0

h [nb] 41.488 ± 0.003 ±0.002 ±0.000 ±0.002 ±0.001

sin2 ✓lept

e↵

(Qhad

FB

) 0.23149 ± 0.00012 ±0.00000 ±0.00012 ±0.00001 ±0.00002P pol

⌧ 0.1473 ± 0.0009 ±0.0000 ±0.0009 ±0.0001 ±0.0002A` (SLD) 0.1473 ± 0.0009 ±0.0000 ±0.0009 ±0.0001 ±0.0002Ac 0.6680 ± 0.0004 ±0.0000 ±0.0004 ±0.0001 ±0.0001Ab 0.93464 ± 0.00008 ±0.00000 ±0.00007 ±0.00001 ±0.00001

A0,`FB

0.0163 ± 0.0002 ±0.0000 ±0.0002 ±0.0000 ±0.0000A0,c

FB

0.0738 ± 0.0005 ±0.0000 ±0.0005 ±0.0001 ±0.0001

A0,bFB

0.1032 ± 0.0007 ±0.0000 ±0.0006 ±0.0001 ±0.0001R0

` 20.751 ± 0.004 ±0.003 ±0.002 ±0.000 ±0.000R0

c 0.17223 ± 0.00001 ±0.00001 ±0.00001 ±0.00000 ±0.00001R0

b 0.21579 ± 0.00003 ±0.00001 ±0.00000 ±0.00000 ±0.00003

Table 2: SM predictions computed using the theoretical expressions for EWPO without the experimentalconstraints on the observables, and individual uncertainties associated with each input parameter: ↵s(M2

Z) =

0.1185± 0.0005, �↵(5)

had

(M2

Z) = 0.02750± 0.00033, MZ = 91.1875± 0.0021 GeV and mt = 173.34±0.76 GeV, where the uncertainty associated to mh = 125.5 ± 0.3 GeV is always negligible.

1

mt


68% & 95% prob. regions


Direct and indirect measurements


[GeV]WM

80.34 80.36 80.38 80.4 80.42

[Ge

V]

)W

(Mσ

0

0.005

0.01

0.015

0.02

1

2

3

4

5

6σ

σ

σ

σ

σ

σ

lA

0.145 0.15 0.155

) l(A

σ

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

1

2

3

4

5

6σ

σ

σ

σ

σ

σ

b0R

0.215 0.216 0.217 0.218

)b0

(Rσ

0

0.0002

0.0004

0.0006

0.0008

1

2

3

4

5

6σ

σ

σ

σ

σ

σ

0,bFBA

0.096 0.098 0.1 0.102 0.104

)0

,bF

B(A

σ

0

0.0005

0.001

0.0015

0.002

1

2

3

4

5

6σ

σ

σ

σ

σ

σ

Pulls in the SM fit



Non-universal vertex corrections


4 Epsilon parameters

The SM predictions for the ✏ parameters are given by:

✏SM1

= (5.22 ± 0.07) 10�3 ([5.08, 5.35] 10�3 @95% prob.) ,

✏SM2

= �(7.38 ± 0.02) 10�3 ([�7.42,�7.33] 10�3 @95% prob.) ,

✏SM3

= (5.279 ± 0.004) 10�3 ([5.271, 5.286] 10�3 @95% prob.) ,

✏SMb = �(6.95 ± 0.15) 10�3 ([�7.24,�6.66] 10�3 @95% prob.) . (1)

Fit result Correlations✏1

0.0056 ± 0.0009 1.00✏2

�0.0078 ± 0.0009 0.79 1.00✏3

0.0056 ± 0.0009 0.86 0.50 1.00✏b �0.0058 ± 0.0013 �0.32 �0.31 �0.21 1.00

Table 7: ✏ fit.


0.0060 ± 0.0006 1.00✏3

0.0058 ± 0.0008 0.87 1.00

Table 8: ✏ fit with fixing ✏2

and ✏b to their SM values.

6

4 Epsilon parameters

The SM predictions for the ✏ parameters are given by:

✏SM1

= (5.22 ± 0.07) 10�3 ([5.08, 5.35] 10�3 @95% prob.) ,

✏SM2

= �(7.38 ± 0.02) 10�3 ([�7.42,�7.33] 10�3 @95% prob.) ,

✏SM3

= (5.279 ± 0.004) 10�3 ([5.271, 5.286] 10�3 @95% prob.) ,

✏SMb = �(6.95 ± 0.15) 10�3 ([�7.24,�6.66] 10�3 @95% prob.) . (1)


0.0056 ± 0.0009 1.00✏2

�0.0078 ± 0.0009 0.79 1.00✏3

0.0056 ± 0.0009 0.86 0.50 1.00✏b �0.0058 ± 0.0013 �0.32 �0.31 �0.21 1.00

Table 7: ✏ fit.


0.0060 ± 0.0006 1.00✏3

0.0058 ± 0.0008 0.87 1.00

Table 8: ✏ fit with fixing ✏2

and ✏b to their SM values.

6

1ε

2 4 6 8

-310×

3ε

2

4

6

8

-310×

SMbε=bε, SM

2ε=2ε

w/o nonuniversal corrections

SM prediction [95%]

1ε

2 4 6 8

-310×

3ε

2

4

6

8

-310×

w/o nonuniversal corrections

SM prediction [95%]


Four solutions from Z-pole data, while two of them are disfavored by off Z-pole data for AFBb.

Zbb couplings


Choudhury et al. (02)

The solution closer to the SM:

See also Batell et al. (13) Deviation from the SM due to

�V ⇡ 0.06

V 2 [1.05, 1.22] @ 68%

V 2 [0.81, 0.97] @ 68%

Ab

A0,bFB

�R0

b ⇠ 6.6 ⇥ 10�4 ! �R0

b ⇠ 6 ⇥ 10�5

5

6 Zbb

Fit result Correlations�gb

R 0.018 ± 0.007 1.00�gb

L 0.0029 ± 0.0014 0.90 1.00�gb

V 0.021 ± 0.008 1.00�gb

A �0.015 ± 0.006 �0.98 1.00

Table 11: Fit results for the shifts in the Zbb couplings.

9

bRgδ

-0.04 -0.02 0 0.02 0.04 0.06

b Lgδ

-0.04

-0.02

0

0.02

0.04Allb0R0,bFBAbA

bVgδ

0 0.02 0.04

b Ag

δ

-0.04

-0.02

0

0.02

gbi = (gb

i )SM + �gbi


Constraints on Higgs physics from EW precision...

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