Electroweak Correction for the Study of Higgs Potential in LC

LAPTH-Minamitateya CollaborationLCWS05

2005.3.19, Stanford U.presented by K.Kato(Kogakuin U.)

Introduction

• LC ： high-precision experiments Requires the same level theoretical prediction = Needs higher order calculation

• Higgs study : Central target Interesting channels = multi-body final states

• 1-loop correction to e+e- 3, 4-bodies : Great Progress since Sept. 2002

Higgs@LC:tree cross sections

23,4 processes important

Main channels

WWH vs ZZH

Higgs Potential

Yukawa coupl.

number of diagrams (GRACE:NLG model)

tree 1-loop

4(1) 341(119)RADCOR / Loops & Legs Sept. 2002

12(2) 1350(249)

12(6) 2327(758)

27(6) 5417(1597)

42(2) 4470(510)

ee

H

ZHH

ZH

HttHee

A.Denner, J.Kublbeck, R.Mertig, M.Bohm, Z.Phys.C56(1992) 261;B.A.Kniehl, Z.Phys.C55(1992) 605.

with(without) e-scalar couplings

10 years required to

develop 23 tools

Automated Systems

Full 1-loop RC available

Httee

ZHHee

Hee GRACE, PLB559(2003)252Denner et al., NPB660(2003)289

GRACE, PLB571(2003)163You et al., PLB571(2003)85Denner et al., PLB575(2003)290

GRACE, PLB576(2003)152Zhang et al., PLB578(2004)349

Heeee

ee e ,

csduee , Denner etal., hep-ph/0502063

GRACE, PLB600(2004)65

GRACE, NIM A534(2004)334

HHee GRACE, Talk by Y.Yasui at Durham(Sep.2004)

Userinput

TheorymodelfileDiagram generator

amplitude generator

LibraryCHANEL, loop

Kinematics library

kinematics code

generated code

diagram description

convergence information

Make file etc.

symbolic codeREDUCE, Form etc.

PS file

Drawer

BASES(MC integral)

SPRING (EG manager)

parameter file

Diagrams(figure)

EventsCross sections distributions

TREELOOP

FORTRAN code

.fin .mdl .rin

Higgs Potential

H H

H

H H

HH

Something required to provide massKey for the structure of standard model

Window to New Physics

Double (triple) Higgs production Process

e+e- νν ＨＨ

tree

old parameter set

HHH coupling dependence

SM: δΛ ＝０

νν ＨＨ ｖｓ ＺＨＨ

ZHH/ nunuHH

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500

W

σ(a

b)

GeV 120HM

HH

Tree

ZHH

ZHHee

HHee

Low W

High W

dominant mechanism (approximation)

W

W

HH

FULL calculation

e+e- νν ＨＨ

W+W- HH

W W

H

Annihilation BosonExchange

ContactInteraction

H

H ,W

W+W- HH

• tree … 6 diagrams Annihilation, Boson exch., Contact int.B A, C … opposite sign

• 1-loop … 827 diagrams 13 groups A : vertex corr .HHH, WWH, AWW, ZWW B : vertex corr. WWH, WχH C : Box

Check : Cuv independence

Cuv=0 Cuv=10000Cuv=100

LGNLG Cuv=0 Cuv=0Cuv=100

Linear Gauge vs Non-Linear Gauge

leading mt formulas

22

4

23 HW

tC

wH MM

mN

sC

2

2

2

2

2 12

32

8 w

W

W

tC

wW s

s

M

mN

sC

2

2

2

2

24 6

38

8 w

W

W

tC

w s

s

M

mN

sC

A: CH+CW

B: 2CW

C: C4

MW=80.4163MZ=91.1876MH=120mt=180α=1/137.0359895

-0.11779616

-0.07033663

-0.02535196

)5,4,3,2,1( GeV 10180 )1( nm nt

proof of the formulas and the performance of GRACE system

real world : NOT mt >> W, MH, MZ,…

OK

WWHH(tree)

0

1

2

3

4

5

6

0 500 1000 1500 2000

W

σ(p

b) tree+leading mt correction

full EW correction (w/o QED)

δ (EW) & δ (mt)

- 5%

0%

5%

10%

15%

20%

0 500 1000 1500 2000

W

δ(%

)

W+W- HH

WWHH 1- loop corrections

- 100%

- 80%

- 60%

- 40%

- 20%

0%

20%

40%

0 500 1000 1500 2000

W

δ(%

)

δV

λ=10-12 Gev δV QED

δW δW(Gm)

e+e- νν ＨＨ

• number of diagrams

νe ... tree= 81 loop=19638

(prod. set = 12 x 3416) 50M lines of Fortran code

νmu ... tree= 27 loop=8292 (prod. set = 6 x 1754)

e+e- νν ＨＨ

ZHHee

hep-ph/030910Phys.Lett.B 576(2003)152.

“s-channel”

e+e- νν ＨＨ

nunuHH

0

5

10

15

20

25

0 500 1000 1500 2000 2500

W

δ（％

）)EW(

)G(

nunuHH(tree)

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500

W

σ(a

b)

Full calculation

MH=120GeV

e+e- νν ＨＨ

GeV 120HM

W=0.5TeV

W=2.5TeV

W=2.0TeV

W=1.5TeV

W=1.0TeV

M(HH) (TeV)

Tree

Invariant mass of HH

• Higgs Potential channel eeνν ＨＨ cross section and its EW correction is calculated. σ ＝Ｏ（１００ ａｂ） and greater than eeZHH in high-E LC region ( 1TeV). δ(Gmu) is ≧~10% for >700GeV. Large diviation from eeZHH dominated by s-channel.

• WWHH is studied to check the t-channel structure of eeνν ＨＨ and has shown validity and limitation of the leading mt formulas.

Summary

s

s

e+e- νν ＨＨ

Hee

)(W s

hep-ph/0212261Phys.Lett.B 559(2003) 252.

s,t channels show different behaviorgenuine weak correction in G-scheme is -2 ～ -4%

total)(O

GW

W)(W t

1.5%16

522

2

HWW WW

t

Ms

M

Httee hep-ph/0307029Phys.Lett.B 571(2003) 163.

system components

• Diagram generation for input process

• Amplitude/Matrix element generation• Kinematics and Integration (efficiency)

• Event generation (efficiency & weight)

• Peripheral tools: rule generator, diagram selection, QED radiation, PDF, loop integral library, multi-process, color flow and interface for hadronization, etc.

5-point functions

43210

5 DDDDDdGI

jjj XrD

XD

22

02

0

FDEN

4

)(

rank M

BOX rank M-1

002 XD

4

0

)]([1

Drba jj

scalar 5-pnt

BOX

jijijiij rArgrrA 1

][)( 001

211

jjijijiji XXDDArrAr

N

δ(QED), δ(EW)

)1(0 WQED

W

hardQED

softQED

VQEDQED

LLf

hard LLLL

vQEDQED fddfdd 0100

~~

phase space subtraction =radiator

non-QED virtural corrections

Non-linear gauge fixing terms

22

2

1

2

11 AZ

ZWGF FFFFL

3~

2

~

2

~~

WWWW

W

W

se

iHse

M

WZsec

iAieF

33

~2

H

cse

MZFWW

WZZ

AF A

Samples of NLG Feynman rules

)])(/~1(

))(/~1(

)([

12

33

21

gpgp

gpgp

ppge

AWW

W

W

gieM

AW

W )~1(

ge

WAcc A

~2

WW

A

sie

Hcc

~

2

12

ghost-ghost- vector-vector / ghost-ghost-scalar-scalar

modified

• Numerator structure is the same as Feynman gauge Loop integral library

• Vertices modified• general values #diagrams

Non-linear gauge

~,~,~

,~

,~

)1for ( g

AW no 1~

Check gauge invariance Independence on gauge parameters

“old” usagereduce #diagram