Contents1. Introduction2. Analysis3. Results4. Conclusion

Presice measurement of the Higgs-boson electroweak couplings at Linear Collider and its physics impacts

Yu Matsumoto (GUAS,KEK) 2008,3,5 @TILCW,Z,γ

0H

W,Z,γ

In collaboration with K.Hagiwara (KEK) and S.Dutta (Univ. of Delhi)

1-1. Motivation

New Physics

SM

TeV scale Physics

・ Light Higgs

・ Heavy Higgs or Higgsless

SUSYLittle Higgs・・・

LHC LC

Tevatron LEP

Experiments

If the light Higgs exists, LC can probe the detail properties of the Higgs boson

Theory

W, Z, top discovery

W and Zmass & couplings

Higgs discoveryHiggs partner

WW scattering

Precise measurements of Higgs couplings

1-2. Effective Lagrangian with Higgs doublet

,8dim7dim6dim5dim LLLLLL SMeff

contribute to majonara neutrino mass

contribute to four fermion coupling (Proton decay, FCNC, etc) purely gauge term (Triple gauge coupling, etc) Higgs electroweak couplings

New physics can be represented by higher mass dimension operators

We can write the effective Lagrangian including Higgs doublet as

)6(2 i

i

iSMeff

fLL

New physics effects. Here we considered only dimension 6

and the operators are …

We focused on this physics

are calculable in each particular modelsif

1-3. dimension 6 operators including Higgs

Dimension 6 operators

2 point function, TGC, vertices include Higgs boson

Precision measurement (SLC, LEP, Tevatron)

Triple gauge couplings (LEP2,Tevatron)

LH

C

LC

.)].))()(((2

[

]))()(([

]))()((22

[

)1(2

)1( WWZZ)6(

2

chWWHWHc

WHWbm

g

AZHZHcAHZbm

g

ZZHZHc

ZHZb

m

g

WHWgmaZHZmg

af

LL

WWWW

Z

Z

ZZZ

Z

ZZZZ

Z

Z

WZZ

ii

iSMeff

We exchange the operators into HVV interaction vertices as the experimental observables

※ 　　　　　　　　　 　　　 are the linear function of

if

1-4. Operators and Vertices, Form Factors

WWWZZZ dbabcbcba ,,,,,,,,

： EW precision, S and T parameter

： Triple Gauge Couplings

jijiji

SM

ji

jijik

k kSM

kjki

jiji

k kkSM

ikkii

kkEXP

ikTH

kEXP

n

cVcdLccLcc

L

cL

N

cNNcc

,

1

,,

22

12

)( )(

)()(

)(

)()(

)(

)()(

),,(

1-5. Optimal observable methodThe differential cross section can be expressed by using non-SM couplings

can be expressed in terms of non-SM couplings

)()( i

iiSM c

d

d

number of event in the k-th bin for experiment and theory

2

,)( kkSMkEXP LN

if is given, we can calculate

1V iciii Vc

The large discrepancy between and

makes larger errors become small 1VSM )(i

kkii

ikkSMkTH cLLN )()(

ZZZWWZZZWWZZWWi cccbbbbaac ,,,,,,,,is 3-body phase space

2-0. Cross section

2-1 : WW-fusion → 250GeV-1000GeV

2-2: ZH production → 250GeV - 1000GeV

2-3: ZZ-fusion → 250GeV,1000GeV

WWWWWW cba ,, measurement

ZZZZZZZZ cbcba ,,,,

2-4: γγ-fusion → 500GeV,1000GeV

Zγ-fusion → very small effect～　 ILC phase I

phase II

GeVmH 120

bcbcba ZZZZZZZZ ,,,,,

b

bcb ZZ ,,

2-1. WW fusion process

The eigenvectors and eigenvalues of areV

a b c

GeVs 500 GeVs 1000

),(),(),(),( TcWWTbWWTaWWTSMT

pycpybpyapydydpd

In WW fusion process, the out going fermions are neutrinos.The observable distributions should be

y y y

Tp

The results combining each collision energy with beam polarization are 1100,250 fbLGeVs

1500,1 fbLTeVs

this means HWW coupling can be measured with 0.72% accuracy

There are strong correlation because there is a combination of anomalous couplings which has a large error at each energy experiment.

1100,350 fbLGeVs1500,500 fbLGeVs

1100,250 fbLGeVs1100,350 fbLGeVs

1500,500 fbLGeVs

0,0 ee PP

There are still strong correlation

2-1-2. Combined Results(1)

2-2. ZH production process

・ other couplings does not change so much because cross section decrease

・ become more sensitive when is increase

)~()(

2

1)

~()(

2

1

iii

iSMSM cd

d

i

iiSM cd

d)()(

GeVs 250

GeVs 500

The differential cross section is expressed as

・ az cannot be measured independently

・ is most sensitive because its coefficient includes s

s

),,(~

),,(

qqjj

qqjj

here

for llZ

for qqZ

ZZZ cc ,

4 constraints for 5 couplings

Zc

2-3. eeH double-tag Z,Zγ,γγ fusion process

GeVs 500

GeVs 1000

Final fermions are electron. we can use full information of

)(i

i

iiSM cd

d)()(

995.0cos e GeVepT 1)( Double e+ e- tag

conditions ：

Because the distribution of is same to SM

ZZa

6 constraints for 6 couplings

→ all couplings can be measured independently

2-4. (ee)H no-tag γγ fusion processParametrize the cross section by using the equivalent real photon fusion

event contamination from WW fusion process

pTH resolution is set to 3 GeV

here

is SM 1-loop contribution

The effect of ZH production process @250GeV 1. cannot be measured independently at one energy experiment 2. New physics term is proportional to Correlation goes small by combining other processes

It is possible to measure HZZ coupling with 0.32% accuracy

)( ZZ cb

1100,350 fbLGeVs

1100,250 fbLGeVs

1500,500 fbLGeVs

1100,350 fbLGeVs

1100,250 fbLGeVs

1500,500 fbLGeVs1500,1 fbLTeVs

Combined results with ZH process and eeH double-tag, (ee)H single-tag process with beam polarization 0.0||,8.0|| ee PP

2-5. Combined results (2)

ZZa

Combine up to with

2-5. Combined results (3)Comparison with polarization and

0||,0.0|| ee PP 0.0||,8.0|| ee PP

0.0||,0.0|| ee PPTeVs 1Combine up to with

0.0||,8.0|| ee PPTeVs 1

・ Strong correlation disappears→ all couplings are measured independently

)%0004.0,002.0,02.0(),,(

)%006.0,03.0,3.0(),,(

bcb

cba

ZZ

ZZZZZZ

Each couplings are measured with below accuracy

)%14.0,76.0,72.0(),,( WWWWWW cba

・ dose not change by beam polarization

baZZ ,

・ The error of become much smaller when polarized beam is applied

ZZZZ cbc ,,

40/1

15/1

4/122

22

WBZ

WWWBBWZ

WWBWZZ

ffc

fcfsb

fcfsc

3-1. Constraints on dim6-Operators,

& Comparison with other experiments

Constraint from EW precision measurement

measurement @ ILC

Constraint fromTGC (LEP L3)

ILC results are enough.

EW precision measurement gives stronger constraint about a several factor.

ILC is required Luminosityat ab-1 scale to get comparable constraint

LC is hopeful for reducing the anomalous Triple Gauge Coupling

most constrained combination

(EWPM)

(ILC)

4. Conclusion

We obtain the sensitivity to the ILC experiment on HVV couplings by using Optimal observable method

The expected accuracy of the several dim6 operator combinations will be sensitive to quantum corrections 　

The t-channel and no-tag processes at high energy experiment are important to measure and couplings

HHZHWW ,

The polarization of electron beam make the constraint on much stronger. And the all couplings are measured very accurately with relating small correlation. 　　

),,( ZZZZ cbc

(EWPM)

(ILC)

)13.0(22.0

)02.0(059.01

BWf

f)11(026.0

)3.5(016.0

B

W

f

f

075.0)23(

35.0

14.0

24

ff

f

f

BB

WW

(EWPM)

(TGC)

3-2. Luminosity uncertainty

The luminosity error will dominate the statistic uncertainty

df become dominant error.To make statistic error and df to be same contribution, df<0.005 is required especially at ab-1 scale.

df < 1% is required to get the error of az around 1%

region1fb100L region1fb100L

※ If df → 0 ：

Redefine inverse of the covariance matrix with considering Luminosity uncertainty (=df)

GeVs 250

Comparison with polarization and

0.0||,0.0|| ee PP 0.0||,8.0|| ee PP

0.0||,0.0|| ee PP

0.0||,8.0|| ee PPwith

GeVs 250 with

Comparison with polarization and

0||,0.0|| ee PP 0||,8.0|| ee PP

TeVs 1

0.0||,0.0|| ee PP

0.0||,8.0|| ee PPwith

TeVs 1 with

2-5. e(e)H single-tag Zγfusion processParametrize the cross section by using the equivalent real photon for un-tagged side

For 500 GeV

For 1 TeV

Add the contribution of this process to the total Single-tag process is sensitive to and

totalV 1

b )( cb

3-3. ILC measurement Contribution to the Tz and Sz

When the ILC measurements is combined, it gives more strong constraint on the dSz and dTz