Contents1. Introduction2. Analysis3. Results4. Conclusion

Constraint on new physics by measuring the HVV

Couplings at e+e- LC

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

Yu Matsumoto (GUAS,KEK) 2007,12,13 @KEKPH07

H

V

V

1-1. Motivation

New Physics

SM

TeV scale Physics

・ Light Higgs

・ Heavy Higgs or Higgsless

SUSYLittle Higgs・・・

LHC LC

Tevatron LEP

Experiments

LHC can probe light Higgs scenario

1-2. Effective Lagrangian with Higgs doublet

,8dim7dim6dim5dim LLLLLL SMeff

contribute to majonara neutrino mass

contribute to four fermion coupling (Proton decay, 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

TeVf

LL ii

iSMeff 1,)6(

2

New physics effects. Here we considered only dimension 6

and the operators are …

We focused on this physics

1-3. dimension 6 operators including Higgs

are calculable in each particular modelsif

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

[

]))()(([

)1(2

)1(

,

Wz)6(

2

chWWHWHd

WHWbm

g

VZHZHcVHZbm

g

WHWgmaZHZmg

af

LL

WW

Z

Z

ZVVV

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 kSM

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

,kSMkEXP LN

if is given, we can calculate

1V iciii Vc

The large discrepancy between and

makes larger errors become small 1VSM )(i

kii

ikSMkTH cLLN )(

WWWZZZi dbabcbcbac ,,,,,,,, is 3-body phase space

2-0. Cross section

2-1 : WW-fusion → 500GeV,1000GeV

2-2: ZH production → 250GeV - 1000GeV2-3: ZZ-fusion → 500GeV,1000GeV

WWW dba ,, measurement

bcbcba ZZZ ,,,,

2-1. WW fusion process

The eigenvectors and eigenvalues of areV

awbw dw

GeVs 500 GeVs 1000

),(),(),(),( TdwWTbwWTawWTSMT

pydpybpyapydydpd

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 are

1500,500 fbLGeVs 1500,1 fbLTeVs

this means HWW coupling can be measured with 0.72% accuracy

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

1500,500 fbLGeVs

2-2. ZH production process

・ All couplings are independent

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

・ cg 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

・ cg is most sensitive because its coefficient includes

s

s

),,(~

),,(

qqjj

qqjj

here

2-3. ZZ 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 ：

strong correlation

The effect of ZH production process @250GeV 1. az 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 0.44% accuracy

)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 ZZ-fusion process

3.Constraints on dim6-Operators, & Comparison with other

experiments

Constraint from EW precision measurement

Our results (measurement at ILC)

Constraint from TGC (LEP L3)

Our 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(LEP)

(Our result)

4.Conclusion

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

The expected accuracy of the measurements will be sensitive to quantum corrections 　

The t-channel processes

at high energy experiment are important, especially measure coupling 　　

Hee Heeee

H

3-3. Luminosity uncertainty

The luminosity error will dominate the statistic uncertainty

Erro

r of a

z

]fb[L/1 1

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)

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