Theoretical calculations for precise measurement of multi-final-state processes

Renyou ZHANG, Liang HANUSTC phenomenology group

Introduction on motivation

Hadron colliders as discovery machinary

Tevatron, LHC W boson, top quark, Higgs? SUSY?

SM precise test, eg W boson mass, top physics etc Higgs characteristic and couplings: Hff, HZZ, HWW, HHH, HHHH New physics, eg SUSY parameter determination

Precise measurement at linear colliders LC

ILC

Challenges for hep phenomenology

QCD & EW quantum effects, NLO, 2-loop calculations and NLL resummation multi-particle (>=3) final states, resonance effects

1.Higgs potential, self-coupling ( HHZ production, 5-point loop integral )

2. Charged Higgs production, Higgs gauge coupling (Φ0H+W-(Φ0 =h0,H0,A0) production, Higgs resonance )

3. Higgs Yukawa coupling ( ttH / bbH / tbH production, ttbb production, 6-point loop integral, phase space integral )

Outline

Higgs potential, self-coupling, e+e-ZHH

SM:

MSSM:

trilinear coupling :

quartic coupling :multi-Higgs boson production!

: 500~1000 GeV

: >1 TeV

Therefore, in the first stage of a LC, HHZ production is the most promising channel to measure the trilinear Higgs self-coupling.

• 0.1~0.2fb @ √s<1TeV, • 8% on HHH 10% precision on cross-section

N-point loop integral:

1 to 4-point integrals given in G.Passarino and M.Veltman, NPB160(1979)151

(N≤4)-point loop integrals

Passarino-Veltman reduction: 3-point integral as example

--- Decompose to Lorentz-covariant tensor + coefficient (Gram Matrix method)

New development on (N=5)-point integrals

5-point integral by A.Denner and S.Dittmaier, NPB658(2003)175

where

5-dimensional Cayley matrix Y used to replace Gram matrix

Cancellation of IR singularity: virtual + soft-photon radiation + hard photon radiation (m , E)

--- independence of m@ --- independence of cutoff

Conclusion :

--- O(10%) EW correction to intermediate(115-200GeV) HHZ production at LC

--- maximum cross-section in √s = 600~800GeV for intermediate Higgs

--- tendency of the QED and weak corrections:

consistency check given by G.Belanger et al (Grace group)

PLB578(2004)349

Charged Higgs production, Higgs gauge coupling

light charged Higgs production

heavy charged Higgs production, Higgs gauge coupling

WHhee 0

2

HM

1. charged Higgs resonance

2. double counting problem and gauge invariance

complex charged Higgs mass

Supersymmetry Parameter Analysis (SPA)

SPS1a’

Conclusion :

---EW relative correction decreases from 20% to -15% as the increment of MA PRD75 053007(2007)

Higgs Yukawa coupling

Higgs production associated with top pair

1. an important discovery mode for a Higgs boson around 120-130GeV at the LHC 2. Yukawa coupling of the top quark to the Higgs boson

5.5% (Yukawa coupling)

NLO calculation! K factor=?model: SM, MSSM

Major source of background: (QCD)

(EW)

resonance at 2 Mt

SM Higgs MSSM heavy CP-even Higgs

tree-level cross section

QCD correction (SM)

SM:

--- K factor > 1.4 @ √s=500 GeV

MSSM:

intermediate Higgs mass region, 2.5<tanbeta<50, 500GeV :

~ 0.75 fb CP even Higgs H,h

< 0.01 fb CP odd Higgs A

QCD correction (MSSM)

EW correction (MSSM)

renormalization of e : 128/1)(137/1)0( Z Mewew

xf=mZ , mf <mZ

--- EW correction: -15% ~ -30%

PRD72 033010(2005)

SM: suppressed due to the smallness of the bbh Yukawa coupling MSSM: Yukawa coupling is enhanced by large tanbeta

a large resonant contribution from

500 GeV, tanbeta = 40

contribution from Z boson exchange

MSSM, LO

bbH production (QCD corrected)

500 GeV, MS=500 GeV

Precise measurement of the product of the Higgs couplings:

MSSM:

--- QCD K factor: ~ -0.8(Tevatron) , 1.2(LHC) , insensitive to SUSY input parameters

hep-ph/0505086

SPS1b, mass = 250 GeV (LHC), 175 GeV (Tevatron)

--- QCD relative correction: ~ -50%(Tevatron) , -40%(LHC)

PRD73 015012(2006)

ttbb production: background of tth production !

6-point integral

1. Cayley matrix method:

2. Gram matrix method:

define:

4-body phase space integral

general method:

improved method:

QCD corrections

hard real gluon emission !

PLB654(2007)13

Summary

QCD and EW NLO corrections to Higgs property studies could be as significant as ~O(10%), which are at the same level to or larger than the expected experiment accuracy and have to be taken into account.

Precise measurements of interested multi-final-states processes at LHC/ILC eg HHZ, Htt, ttbb etc require good control of theoretical predictions, which would involve loop integrals with multi-legs, multi-body phase integral and resonance effects, and have to be treated case-by-case for stability of numerical calculations