Post on 05-Feb-2016
description
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