Theorie-Seminar Universität Bielefeld, Mai 2005
Higgs Production at the LHC
Michael Krämer
(RWTH Aachen)
Introduction: from WW -scattering to the Higgs boson
Higgs-boson searches at the LHC
Higher-order corrections to signal and background processes
Michael Krämer Page 1 Universität Bielefeld, Mai 2005
Introduction: from WW -scattering to the Higgs boson
Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ− → e−ν̄eνµ
L = GF√2
[ν̄µγλ(1 − γ5)µ][ēγλ(1 − γ5)νe]
with GF ≈ 1.17 × 10−5 GeV−2 (Fermi coupling)
Fermi theory at high energies: M[ν̄µe− → µ−νe] ∼ GF2√
2πs
⇒ violates unitarity
Solution: interaction mediated by heavy vector boson W±
M[ν̄µe− → µ−νe] →GF s
2√
2π
M2WM2W − s
(with MW ≈ 100 GeV)
Michael Krämer Page 2 Universität Bielefeld, Mai 2005
Introduction: from WW -scattering to the Higgs boson
Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ− → e−ν̄eνµ
L = GF√2
[ν̄µγλ(1 − γ5)µ][ēγλ(1 − γ5)νe]
with GF ≈ 1.17 × 10−5 GeV−2 (Fermi coupling)
Fermi theory at high energies: M[ν̄µe− → µ−νe] ∼ GF2√
2πs
⇒ violates unitarity
Solution: interaction mediated by heavy vector boson W±
M[ν̄µe− → µ−νe] →GF s
2√
2π
M2WM2W − s
(with MW ≈ 100 GeV)
Michael Krämer Page 2 Universität Bielefeld, Mai 2005
Introduction: from WW -scattering to the Higgs boson
Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ− → e−ν̄eνµ
L = GF√2
[ν̄µγλ(1 − γ5)µ][ēγλ(1 − γ5)νe]
with GF ≈ 1.17 × 10−5 GeV−2 (Fermi coupling)
Fermi theory at high energies: M[ν̄µe− → µ−νe] ∼ GF2√
2πs
⇒ violates unitarity
Solution: interaction mediated by heavy vector boson W±
M[ν̄µe− → µ−νe] →GF s
2√
2π
M2WM2W − s
(with MW ≈ 100 GeV)
Michael Krämer Page 2 Universität Bielefeld, Mai 2005
Introduction: from WW -scattering to the Higgs boson
Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ− → e−ν̄eνµ
L = GF√2
[ν̄µγλ(1 − γ5)µ][ēγλ(1 − γ5)νe]
with GF ≈ 1.17 × 10−5 GeV−2 (Fermi coupling)
Fermi theory at high energies: M[ν̄µe− → µ−νe] ∼ GF2√
2πs
⇒ violates unitarity
Solution: interaction mediated by heavy vector boson W±
� ���� � �
� �� �
� ���� � �
� �
�
M[ν̄µe− → µ−νe] →GF s
2√
2π
M2WM2W − s
(with MW ≈ 100 GeV)
Michael Krämer Page 2 Universität Bielefeld, Mai 2005
Introduction: from WW -scattering to the Higgs boson
Consider WW → WW
�� �
�
� �
� ��
M[WLWL →WLWL] ∝ s ⇒ violates unitarity
Solution: − strong WW interaction at high energies or− new scalar particle H with gWWH ∝ MW
M → GFM2H
4√
2π
Unitarity ⇒ properties of H : − coupling gXXH ∝ particle mass MX− MH ∼< 1 TeV
Michael Krämer Page 3 Universität Bielefeld, Mai 2005
Introduction: from WW -scattering to the Higgs boson
Consider WW → WW
�� �
�
� ��
� ��
M[WLWL →WLWL] ∝ s ⇒ violates unitarity
Solution: − strong WW interaction at high energies or− new scalar particle H with gWWH ∝ MW
�� �
�
� M → GFM2H
4√
2π
Unitarity ⇒ properties of H : − coupling gXXH ∝ particle mass MX− MH ∼< 1 TeV
Michael Krämer Page 3 Universität Bielefeld, Mai 2005
Introduction: from WW -scattering to the Higgs boson
Consider WW → WW
�� �
�
� ��
� ��
M[WLWL →WLWL] ∝ s ⇒ violates unitarity
Solution: − strong WW interaction at high energies or− new scalar particle H with gWWH ∝ MW
�� �
�
� M → GFM2H
4√
2π
Unitarity ⇒ properties of H : − coupling gXXH ∝ particle mass MX− MH ∼< 1 TeV
Michael Krämer Page 3 Universität Bielefeld, Mai 2005
Introduction: The ABEGHHK’tH Mechanism(Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, ’t Hooft)
Spontaneous symmetry breaking through scalar isodoublet φ
Lφ = |Dµφ|2 + gdf ψ̄dLφfdR + guf ψ̄dLφ̃fuR − V (φ)
scalar potential V = µ2|φ|2 + λ|φ|4 � �� �
�� �
� �� �
introduce Higgs field H : φ →(
0(v+H)/
√2
)(unitary gauge)
Goldstone bosons → longitudinal components of W, Z
⇒ SM is renormalisable gauge field theory including W and Z boson massesand a physical Higgs particle
Michael Krämer Page 4 Universität Bielefeld, Mai 2005
Introduction: The Higgs boson
The Higgs mechanism is testable becauseall couplings are known:
− fermions: gffH =√
2mf/v
− gauge bosons: gV V H = 2MV /v
with vacuum expectation value
v2 = 1/√
2GF ≈ (246 GeV)2
The Higgs sector and the properties of theHiggs particle (lifetime, decay branching ratios,cross sections) are fixed in terms of theHiggs boson mass MH .Express Higgs potential in terms of (µ, λ) → (v2, MH)
Michael Krämer Page 5 Universität Bielefeld, Mai 2005
Introduction: The Higgs boson
The Higgs mechanism is testable becauseall couplings are known:
− fermions: gffH =√
2mf/v
− gauge bosons: gV V H = 2MV /v
with vacuum expectation value
v2 = 1/√
2GF ≈ (246 GeV)2
The Higgs sector and the properties of theHiggs particle (lifetime, decay branching ratios,cross sections) are fixed in terms of theHiggs boson mass MH .Express Higgs potential in terms of (µ, λ) → (v2, MH)
Michael Krämer Page 5 Universität Bielefeld, Mai 2005
Introduction: The Higgs boson
The Higgs mechanism is testable becauseall couplings are known:
− fermions: gffH =√
2mf/v
− gauge bosons: gV V H = 2MV /v
with vacuum expectation value
v2 = 1/√
2GF ≈ (246 GeV)2
The Higgs sector and the properties of theHiggs particle (lifetime, decay branching ratios,cross sections) are fixed in terms of theHiggs boson mass MH .Express Higgs potential in terms of (µ, λ) → (v2, MH)
Michael Krämer Page 5 Universität Bielefeld, Mai 2005
Higgs boson hunting: indirect searches
Quantum corrections to precision observables
�
!
�
"�
∝ m2t ∝ logMH
140
160
180
200
10 102
103
mH [GeV]
mt
[GeV
]
Excluded Preliminary (a)
High Q2 except mt68% CL
mt (TEVATRON)
⇒ Experimental data consistent with SM
⇒MH < 260 GeV (95% CL) (LEPEWWG)
Note:
− Precision data also consistent with SUSY models− No evidence for ESWB through new strong
interactions (eg. technicolour)
Michael Krämer Page 6 Universität Bielefeld, Mai 2005
Higgs boson hunting: indirect searches
Quantum corrections to precision observables
#
$%
#
&#
∝ m2t ∝ logMH
140
160
180
200
10 102
103
mH [GeV]
mt
[GeV
]
Excluded Preliminary (a)
High Q2 except mt68% CL
mt (TEVATRON)
⇒ Experimental data consistent with SM
⇒MH < 260 GeV (95% CL) (LEPEWWG)
Note:
− Precision data also consistent with SUSY models− No evidence for ESWB through new strong
interactions (eg. technicolour)
Michael Krämer Page 6 Universität Bielefeld, Mai 2005
Higgs boson hunting: indirect searches
Quantum corrections to precision observables
'
()
'
*'
∝ m2t ∝ logMH
140
160
180
200
10 102
103
mH [GeV]
mt
[GeV
]
Excluded Preliminary (a)
High Q2 except mt68% CL
mt (TEVATRON)
⇒ Experimental data consistent with SM
⇒MH < 260 GeV (95% CL) (LEPEWWG)
Note:
− Precision data also consistent with SUSY models− No evidence for ESWB through new strong
interactions (eg. technicolour)
Michael Krämer Page 6 Universität Bielefeld, Mai 2005
Higgs boson hunting: indirect searches
Quantum corrections to precision observables
+
,-
+
.+
∝ m2t ∝ logMH
140
160
180
200
10 102
103
mH [GeV]
mt
[GeV
]
Excluded Preliminary (a)
High Q2 except mt68% CL
mt (TEVATRON)
⇒ Experimental data consistent with SM
⇒MH < 260 GeV (95% CL) (LEPEWWG)
Note:
− Precision data also consistent with SUSY models− No evidence for ESWB through new strong
interactions (eg. technicolour)
Michael Krämer Page 6 Universität Bielefeld, Mai 2005
Higgs boson hunting
To establish the Higgs mechanism we need to
– discover the Higgs boson directly at a high-energy collider
– measure the couplings gXXφ ∝ MX– reconstruct the Higgs potential
Michael Krämer Page 7 Universität Bielefeld, Mai 2005
Higgs boson hunting: collider searches
Higgs decay modes and branching ratios
[HDECAY: M. Spira et al.]
BR(H)
bb_
τ+τ−
cc_
gg
WW
ZZ
tt-
γγ Zγ
MH [GeV]50 100 200 500 1000
10-3
10-2
10-1
1
102
103
⇒ dominant decay into
bb̄ for MH ∼< 130 GeV
WW, ZZ for MH ∼> 130 GeV
Michael Krämer Page 8 Universität Bielefeld, Mai 2005
Higgs boson hunting: past and present colliders
search at the CERN LEP2 (e+e− collider with√s ∼< 200 GeV)
e+e− −→/ ZH ⇒ MH > 114.4 GeV (95% CL) (LEPHIGGSWG)
search at the Fermilab Tevatron (pp̄ collider with√s = 2 TeV)
current∫L = 0.7 fb−1
expectation in 2008:∫L = 4 − 6 fb−1
Michael Krämer Page 9 Universität Bielefeld, Mai 2005
Higgs boson hunting: past and present colliders
search at the CERN LEP2 (e+e− collider with√s ∼< 200 GeV)
e+e− −→/ ZH ⇒ MH > 114.4 GeV (95% CL) (LEPHIGGSWG)
search at the Fermilab Tevatron (pp̄ collider with√s = 2 TeV)
current∫L = 0.7 fb−1
expectation in 2008:∫L = 4 − 6 fb−1
Michael Krämer Page 9 Universität Bielefeld, Mai 2005
The Large Hadron Collider LHC
− pp collider located at CERN− circumference 27 km−√s = 14 TeV− ∫L = 10 − 100 fb−1/year− in operation from April 2007
Michael Krämer Page 10 Universität Bielefeld, Mai 2005
We will start in 2007We will start in 2007
CMS HB-1 CMS HB+1
Installation of readout boxes started
source calibration in 2005.
Insertion in vacuum tank: Summer 2005.
Michael Krämer Page 11 Universität Bielefeld, Mai 2005
Higgs boson search at the LHC
The days of the Higgs boson are numbered!
1
10
10 2
102
103
mH (GeV)
Sig
nal s
igni
fican
ce H → γ γ ttH (H → bb) H → ZZ(*) → 4 l
H → ZZ → llνν H → WW → lνjj
H → WW(*) → lνlν
Total significance
5 σ
∫ L dt = 30 fb-1
(no K-factors)
ATLAS
Michael Krämer Page 12 Universität Bielefeld, Mai 2005
Higgs boson searches at the LHC
0.1 1 1010-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
108
109
σjet(ETjet > √s/4)
LHCTevatron
σttbar
σHiggs(MH = 500 GeV)
σZ
σjet(ETjet > 100 GeV)
σHiggs(MH = 150 GeV)
σW
σjet(ETjet > √s/20)
σbbar
σtot
σ (n
b)
√s (TeV)
even
ts/s
ec f
or L
= 1
033 c
m-2
s-1
−→ QCD background: σbb̄ ≈ 108 pb
−→ Higgs signal: σH+X ≈ 10 pb↪→≈ 3 × 105 Higgs bosons/year
(∫L = 30 fb−1)
−→ Higgs-search through associate production or/and through rare decays
Michael Krämer Page 13 Universität Bielefeld, Mai 2005
Higgs boson searches at the LHC: cross section predictions
σ(pp → H + X) [pb]√s = 14 TeVNLO / NNLO
MRST
gg → H (NNLO)
qq → Hqqqq
_' → HW
qq_ → HZ
gg/qq_ → tt
_H (NLO)
MH [GeV]
10-4
10-3
10-2
10-1
1
10
10 2
100 200 300 400 500 600 700 800 900 1000
/01
1
2 34
55
55
2 34 /
2 3 4
565
7 89/
11
060
/
Michael Krämer Page 14 Universität Bielefeld, Mai 2005
Higgs boson searches at the LHC: signal significance
1
10
10 2
100 120 140 160 180 200 mH (GeV/c
2)
Sig
nal s
igni
fican
ce H → γ γ ttH (H → bb) H → ZZ(*) → 4 l H → WW(*) → lνlν qqH → qq WW(*)
qqH → qq ττ
Total significance
5 σ
∫ L dt = 30 fb-1
(no K-factors)ATLAS
MH ∼< 2MZ →
gg → H (H → γγ, ZZ∗,WW (∗))gg/qq̄ → tt̄H (H → bb̄, ττ)qq → qqH (H → γγ,WW ∗, ττ)qq̄′ →WH (H → γγ)
MH ∼> 2MZ →{
gg → H (H → ZZ,WW )qq → qqH (H → ZZ,WW )
[ + diffractive Higgs production]
Michael Krämer Page 15 Universität Bielefeld, Mai 2005
Higgs boson searches at the LHC: why precision calculations?
Higgs discovery through resonance peak, eg. H → γγ
10000
12500
15000
17500
20000
105 120 135mγγ (GeV)
Eve
nts
/ 2 G
eV
0
500
1000
1500
105 120 135mγγ (GeV)
Sign
al-b
ackg
roun
d, e
vent
s / 2
GeV
However, need precision calculations for signal and background processes
– for Higgs discovery in WW decay channels (no reconstruction of mass peak possible)
– for a reliable determination of the discovery/exclusion significance
– for a precise measurement of the Higgs couplings
↪→ test of the Higgs mechanism↪→ discrimination between SM and BSM (eg. SUSY)
Michael Krämer Page 16 Universität Bielefeld, Mai 2005
Higgs boson searches at the LHC: why precision calculations?
Higgs discovery through resonance peak, eg. H → γγ
10000
12500
15000
17500
20000
105 120 135mγγ (GeV)
Eve
nts
/ 2 G
eV
0
500
1000
1500
105 120 135mγγ (GeV)
Sign
al-b
ackg
roun
d, e
vent
s / 2
GeV
However, need precision calculations for signal and background processes
– for Higgs discovery in WW decay channels (no reconstruction of mass peak possible)
– for a reliable determination of the discovery/exclusion significance
– for a precise measurement of the Higgs couplings
↪→ test of the Higgs mechanism↪→ discrimination between SM and BSM (eg. SUSY)
Michael Krämer Page 16 Universität Bielefeld, Mai 2005
Higgs boson searches at the LHC: why precision calculations?
Example: MSSM Higgs sector
two Higgs doublets to give mass to up- and down-quarks → 5 physical states: h, H , A, H±
MSSM Higgs sector determined by tanβ = v2/v1 and MA
Consider
σMSSM(gg→h→γγ)
σSM(gg→h→γγ)
→ differences ∼< 10%
Needs precision measure-
ments & calculations for
production cross sections
and branching ratios
[Dedes, Heinemeyer, Su, Weiglein]
0 200 400 600 800 1000 1200 1400 1600 1800 20000
10
20
30
40
50
60
MA (GeV)
tanβ
mSUGRA gg−>h−>γγ
< 0.50.5−0.80.8−1.01.0−1.21.2−1.5>1.5
Michael Krämer Page 17 Universität Bielefeld, Mai 2005
Higgs boson searches at the LHC: why precision calculations?
Example: MSSM Higgs sector
two Higgs doublets to give mass to up- and down-quarks → 5 physical states: h, H , A, H±
MSSM Higgs sector determined by tanβ = v2/v1 and MA
Consider
σMSSM(gg→h→γγ)
σSM(gg→h→γγ)
→ differences ∼< 10%
Needs precision measure-
ments & calculations for
production cross sections
and branching ratios
[Dedes, Heinemeyer, Su, Weiglein]
0 200 400 600 800 1000 1200 1400 1600 1800 20000
10
20
30
40
50
60
MA (GeV)
tanβ
mSUGRA gg−>h−>γγ
< 0.50.5−0.80.8−1.01.0−1.21.2−1.5>1.5
Michael Krämer Page 17 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Example: Drell-Yan process
:;=< ;?>
@@
ABDCB
EEC F=GHI JK FH JLM N N
Cross section: σpp→l+l− =∑
q
∫
dx1dx2 fq(x1) fq̄(x2) σ̂qq̄→l+l−
− fq,q̄(x) dx: probability to find (anti)quark with momentum fraction x→ process independent, measured in DIS
− σ̂qq̄→l+l− : hard scattering cross section→ calculable in perturbation theory
Michael Krämer Page 18 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Example: Drell-Yan process
OP=Q P?R
SS
TUDVU
WWV X=YZ[ \] XZ \^_ ` `
Cross section: σpp→l+l− =∑
q
∫
dx1dx2 fq(x1) fq̄(x2) σ̂qq̄→l+l−
− fq,q̄(x) dx: probability to find (anti)quark with momentum fraction x→ process independent, measured in DIS
− σ̂qq̄→l+l− : hard scattering cross section→ calculable in perturbation theory
Michael Krämer Page 18 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Example: Drell-Yan process
ab=c b?d
ee
fgDhg
iih j=klm no jl npq r r
Cross section: σpp→l+l− =∑
q
∫
dx1dx2 fq(x1) fq̄(x2) σ̂qq̄→l+l−
− fq,q̄(x) dx: probability to find (anti)quark with momentum fraction x→ process independent, measured in DIS
− σ̂qq̄→l+l− : hard scattering cross section→ calculable in perturbation theory
Michael Krämer Page 18 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Example: Drell-Yan process
st=u t?v
ww
xyDzy
{{z |=}~ |~
Cross section: σpp→l+l− =∑
q
∫
dx1dx2 fq(x1) fq̄(x2) σ̂qq̄→l+l−
− fq,q̄(x) dx: probability to find (anti)quark with momentum fraction x→ process independent, measured in DIS
− σ̂qq̄→l+l− : hard scattering cross section→ calculable in perturbation theory
Michael Krämer Page 18 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Factorization is non-trivial beyond leading order
− virtual corrections
→ UV divergences→ IR divergences
− real corrections
→ IR divergences→ collinear divergences
UV divergences → renormalization (αs(µren) etc.)IR divergences → cancel between virtual and real (KLN)collinear initial state divergences → can be absorbed in pdfs
Michael Krämer Page 19 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Factorization is non-trivial beyond leading order
− virtual corrections
→ UV divergences→ IR divergences
− real corrections
→ IR divergences→ collinear divergences
UV divergences → renormalization (αs(µren) etc.)IR divergences → cancel between virtual and real (KLN)collinear initial state divergences → can be absorbed in pdfs
Michael Krämer Page 19 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Factorization is non-trivial beyond leading order
− virtual corrections
→ UV divergences→ IR divergences
− real corrections
→ IR divergences→ collinear divergences
UV divergences → renormalization (αs(µren) etc.)IR divergences → cancel between virtual and real (KLN)collinear initial state divergences → can be absorbed in pdfs
Michael Krämer Page 19 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Factorization is non-trivial beyond leading order
− virtual corrections
→ UV divergences→ IR divergences
− real corrections
→ IR divergences→ collinear divergences
UV divergences → renormalization (αs(µren) etc.)IR divergences → cancel between virtual and real (KLN)collinear initial state divergences → can be absorbed in pdfs
Michael Krämer Page 19 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Initial state collinear singularities,eg.
¡
¢£ ¤
− process independent divergence in ∫ dk2T as k2T → 0
→ absorb singularity in parton densities:
fq(x, µfac) = fq(x) +{
divergent part of∫ µ2fac0 dk
2T
}
Hadron collider cross section
σ =∫
dx1fPi (x1, µF )
∫
dx2fPj (x2, µF )
×∑
n
αns (µR) Cn(µR, µF ) + O(ΛQCD/Q)
(Collins, Soper, Sterman ’82-’84 and many others)
Michael Krämer Page 20 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Initial state collinear singularities,eg.
¥
¦¦¦§
¨© ª
− process independent divergence in ∫ dk2T as k2T → 0→ absorb singularity in parton densities:
fq(x, µfac) = fq(x) +{
divergent part of∫ µ2fac0 dk
2T
}
Hadron collider cross section
σ =∫
dx1fPi (x1, µF )
∫
dx2fPj (x2, µF )
×∑
n
αns (µR) Cn(µR, µF ) + O(ΛQCD/Q)
(Collins, Soper, Sterman ’82-’84 and many others)
Michael Krämer Page 20 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Initial state collinear singularities,eg.
«
¬¬¬
®¯ °
− process independent divergence in ∫ dk2T as k2T → 0→ absorb singularity in parton densities:
fq(x, µfac) = fq(x) +{
divergent part of∫ µ2fac0 dk
2T
}
Hadron collider cross section
σ =∫
dx1fPi (x1, µF )
∫
dx2fPj (x2, µF )
×∑
n
αns (µR) Cn(µR, µF ) + O(ΛQCD/Q)
(Collins, Soper, Sterman ’82-’84 and many others)
Michael Krämer Page 20 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Scale dependence
σ =
∫
dx1fPi (x1, µF )
∫
dx2fPj (x2, µF )
×∑
n
αns (µR)Cn(µR, µF )
finite order in perturbation theory
→ artificial µ-dependence:
dσd ln µ2
R
=
N∑
n=0
αns (µR) Cn(µR, µF )
= O(αs(µR)N+1)
⇒ scale dependence ∼ theoreticaluncertainty due to HO corrections
Example: rapidity distribution in pp→W +X[Anastasiou, Dixon, Melnikov, Petriello ’03]
⇒ significant reduction of µ dependence at(N)NLO
Michael Krämer Page 21 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Scale dependence
σ =
∫
dx1fPi (x1, µF )
∫
dx2fPj (x2, µF )
×∑
n
αns (µR)Cn(µR, µF )
finite order in perturbation theory
→ artificial µ-dependence:
dσd ln µ2
R
=
N∑
n=0
αns (µR) Cn(µR, µF )
= O(αs(µR)N+1)
⇒ scale dependence ∼ theoreticaluncertainty due to HO corrections
Example: rapidity distribution in pp→W +X[Anastasiou, Dixon, Melnikov, Petriello ’03]
⇒ significant reduction of µ dependence at(N)NLO
Michael Krämer Page 21 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
pdf uncertainties
[Martin, Roberts, Stirling, Thorne ’03]
2.50
2.55
2.60
2.65
2.70
2.75
2.80
W @ Tevatron
NLO
Q2cut = 7 GeV2
Q2cut = 10 GeV2
NNLO
xcut = 0 0.0002 0.001 0.0025 0.005 0.01
σ W .
Blν
(nb)
MRST NLO and NNLO partons
→ ∆ pdf ∼< 5% (CTEQ, MRST, Alekhin,...)
Michael Krämer Page 22 Universität Bielefeld, Mai 2005
Particle production at hadron colliders
Precision physics at hadron colliders requires
– the calculation of QCD corrections at (N)NLO;
– the precision determination of input pdfs;
– the resummation of large logarithmic corrections;
– matching of fixed order calculations with parton showers & hadronization;
– the inclusion of electroweak corrections.
Michael Krämer Page 23 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in gluon-gluon fusion
±²
³³
− NLO corrections: KNLO ≈ 1.7[Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman]
− NNLO corrections:KNNLO(mtop �MH) ≈ 2[Harlander, Kilgore; Anastasiou, Melnikov ’02; Ravindran et al. ’03]
consistent with calculations based on soft/collinear gluon
approximations [MK, Laenen, Spira; Catani et al.]
→ NNLO scale dependence ∼< 15%
[Harlander, Kilgore ’02]
1
10
102
100 120 140 160 180 200 220 240 260 280 300
σ(pp → H+X) [pb]
MH [GeV]
LONLONNLO
√s = 14 TeV
Michael Krämer Page 24 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in gluon-gluon fusion
´µ
¶¶
− NLO corrections: KNLO ≈ 1.7[Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman]
− NNLO corrections:KNNLO(mtop �MH) ≈ 2[Harlander, Kilgore; Anastasiou, Melnikov ’02; Ravindran et al. ’03]
consistent with calculations based on soft/collinear gluon
approximations [MK, Laenen, Spira; Catani et al.]
→ NNLO scale dependence ∼< 15%
[Harlander, Kilgore ’02]
1
10
102
100 120 140 160 180 200 220 240 260 280 300
σ(pp → H+X) [pb]
MH [GeV]
LONLONNLO
√s = 14 TeV
Michael Krämer Page 24 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in gluon-gluon fusion
·¸
¹¹
− NLO corrections: KNLO ≈ 1.7[Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman]
− NNLO corrections:KNNLO(mtop �MH) ≈ 2[Harlander, Kilgore; Anastasiou, Melnikov ’02; Ravindran et al. ’03]
consistent with calculations based on soft/collinear gluon
approximations [MK, Laenen, Spira; Catani et al.]
→ NNLO scale dependence ∼< 15%
[Harlander, Kilgore ’02]
1
10
102
100 120 140 160 180 200 220 240 260 280 300
σ(pp → H+X) [pb]
MH [GeV]
LONLONNLO
√s = 14 TeV
Michael Krämer Page 24 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in gluon-gluon fusion
º»
¼¼
− NLO corrections: KNLO ≈ 1.7[Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman]
− NNLO corrections:KNNLO(mtop �MH) ≈ 2[Harlander, Kilgore; Anastasiou, Melnikov ’02; Ravindran et al. ’03]
consistent with calculations based on soft/collinear gluon
approximations [MK, Laenen, Spira; Catani et al.]
→ NNLO scale dependence ∼< 15%
[Harlander, Kilgore ’02]
1
10
102
100 120 140 160 180 200 220 240 260 280 300
σ(pp → H+X) [pb]
MH [GeV]
LONLONNLO
√s = 14 TeV
Michael Krämer Page 24 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in gluon-gluon fusion
½¾
¿¿
− NLO corrections: KNLO ≈ 1.7[Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman]
− NNLO corrections:KNNLO(mtop �MH) ≈ 2[Harlander, Kilgore; Anastasiou, Melnikov ’02; Ravindran et al. ’03]
consistent with calculations based on soft/collinear gluon
approximations [MK, Laenen, Spira; Catani et al.]
→ NNLO scale dependence ∼< 15%
[Harlander, Kilgore ’02]
1
10
102
100 120 140 160 180 200 220 240 260 280 300
σ(pp → H+X) [pb]
MH [GeV]
LONLONNLO
√s = 14 TeV
Michael Krämer Page 24 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Vector boson fusion
À Á?Â
ÃÃ
ÃÃ
À Á? Ä
− discovery channel & measurement ofHiggs couplings[Kauer, Plehn, Rainwater, Zeppenfeld]
− NLO QCD corrections (cf DIS) ≈ +10%[Han, Valencia, Willenbrock]
Associated VH production
− crucial for Tevatron search (MH ∼< 130 GeV)− NLO QCD corrections ≈ +(30 − 40)%
[Han, Willenbrock]
− NNLO QCD corrections ≈ +10%[Brein, Djouadi, Harlander ’03]
− NLO electroweak corrections ≈ −10%[Ciccolini, Dittmaier, MK ’03]
Michael Krämer Page 25 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Vector boson fusion
Å Æ?Ç
ÈÈ
ÈÈ
Å Æ?Ç É
− discovery channel & measurement ofHiggs couplings[Kauer, Plehn, Rainwater, Zeppenfeld]
− NLO QCD corrections (cf DIS) ≈ +10%[Han, Valencia, Willenbrock]
Associated VH production
Ê ËÍÌ
ÎÏÎ
Ð ÑÓÒÔ
− crucial for Tevatron search (MH ∼< 130 GeV)− NLO QCD corrections ≈ +(30 − 40)%
[Han, Willenbrock]
− NNLO QCD corrections ≈ +10%[Brein, Djouadi, Harlander ’03]
− NLO electroweak corrections ≈ −10%[Ciccolini, Dittmaier, MK ’03]
Michael Krämer Page 25 Universität Bielefeld, Mai 2005
Associated WH and ZH production: QCD + EW corrections
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
80 100 120 140 160 180 200MH[GeV]
KW
H(L
HC
)
QCD+EW
QCD
NNLO
1
1.1
1.2
1.3
1.4
1.5
1.6
80 100 120 140 160 180 200MH[GeV]
KW
H(T
evat
ron)
QCD+EW
QCD
1
1.1
1.2
1.3
1.4
1.5
1.6
80 100 120 140 160 180 200MH[GeV]
KZ
H(L
HC
)
QCD+EW
QCD
1
1.1
1.2
1.3
1.4
1.5
1.6
80 100 120 140 160 180 200MH[GeV]
KZ
H(T
evat
ron)
QCD+EW
QCD
Michael Krämer Page 26 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
ÕÕ
Ö×Ö
Ø
− σ(tt̄H) ∼< 1 pb (LHC, MH > 115 GeV)but: distinctive final state:
pp→ t(→W+b) t̄(→W−b̄) H(→ bb̄)→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Müller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeVMH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ00.2 0.5 1 2 5
200
400
600
800
1000
1200
1400
1
Michael Krämer Page 27 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
ÙÙ
ÚÛÚ
Ü
− σ(tt̄H) ∼< 1 pb (LHC, MH > 115 GeV)but: distinctive final state:
pp→ t(→W+b) t̄(→W−b̄) H(→ bb̄)→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Müller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeVMH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ00.2 0.5 1 2 5
200
400
600
800
1000
1200
1400
1
Michael Krämer Page 27 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
ÝÝ
ÞßÞ
à
− σ(tt̄H) ∼< 1 pb (LHC, MH > 115 GeV)but: distinctive final state:
pp→ t(→W+b) t̄(→W−b̄) H(→ bb̄)→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Müller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeVMH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ00.2 0.5 1 2 5
200
400
600
800
1000
1200
1400
1
Michael Krämer Page 27 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
áá
âãâ
ä
− σ(tt̄H) ∼< 1 pb (LHC, MH > 115 GeV)but: distinctive final state:
pp→ t(→W+b) t̄(→W−b̄) H(→ bb̄)→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Müller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeVMH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ00.2 0.5 1 2 5
200
400
600
800
1000
1200
1400
1
Michael Krämer Page 27 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
åå
æçæ
è
− σ(tt̄H) ∼< 1 pb (LHC, MH > 115 GeV)but: distinctive final state:
pp→ t(→W+b) t̄(→W−b̄) H(→ bb̄)→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Müller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeVMH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ00.2 0.5 1 2 5
200
400
600
800
1000
1200
1400
1
Michael Krämer Page 27 Universität Bielefeld, Mai 2005
Higgs production cross sections: theoretical status
Recent progress for SM Higgs production includes
– NNLO QCD calculations for pp → H[Harlander, Kilgore; Anastasiou, Melnikov; Ravindran, Smith, van Neerven; Anastasiou, Melnikov, Petriello;Blümlein, Ravindran; . . . (02-05)]
– NNLO QCD calculations for pp → HZ, HW[Brein, Djouadi, Harlander (04)]
– (N)NLO QCD calculations for pp → QQ̄H[Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas; Dawson, Jackson, Orr, Reina, Wackeroth; Harlander, Kilgore;Campbell, Ellis, Maltoni, Willenbrock; . . . (01-05)]
– NLO QCD calculations for pp → qqH[Figy, Oleari, Zeppenfeld; Berger, Campbell (03-04)]
– NLO EWK calculations for pp → HZ, HW[Ciccolini, Dittmaier, MK (03)]
– (N)NLL resummation for pp → H[Kulesza, Sterman, Vogelsang; Berger, Qiu; Catani, de Florian, Grazzini; . . . (03-04)]
– matching of NLO calculation with parton shower MC Herwig for pp → H[Frixione, Webber (04)];
– NNLO splitting functions and PDF fits, error estimates for PDF fits[Moch, Vermaseren, Vogt; MRST; CTEQ (02-05)].
Michael Krämer Page 28 Universität Bielefeld, Mai 2005
Higgs production in the MSSM: associated bb̄h production
Associated bb̄h/H production is crucial for MSSM Higgs searches at large tan β
Bottom-Higgs Yukawa coupling:
gMSSMbbh = − sin αcos β gSMbbH
gMSSMbbH =cos αcos β
gSMbbH
}
tan β � 1-
{
tan β gSMbbH (Mh'MA'MZ)
tan β gSMbbH (MH'MA�MZ)
At tanβ � 1 associated bb̄h/H pro-duction becomes the dominant MSSM
Higgs production mechanism
[Spira]
10-3
10-2
10-1
1
10
10 2
10 3
10 4
102
gg→H (SM)
gg→H
Hbb–
Htt–
Hqq
HZ HW
tan β = 30Maximal mixing
Ù H
Ù
h
mh/H (GeV)
Cro
ss-s
ectio
n (p
b)
Michael Krämer Page 29 Universität Bielefeld, Mai 2005
Higgs production in the MSSM: associated bb̄h production
Associated bb̄h/H production is crucial for MSSM Higgs searches at large tan β
Bottom-Higgs Yukawa coupling:
gMSSMbbh = − sin αcos β gSMbbH
gMSSMbbH =cos αcos β
gSMbbH
}
tan β � 1-
{
tan β gSMbbH (Mh'MA'MZ)
tan β gSMbbH (MH'MA�MZ)
At tanβ � 1 associated bb̄h/H pro-duction becomes the dominant MSSM
Higgs production mechanism
[Spira]
10-3
10-2
10-1
1
10
10 2
10 3
10 4
102
gg→H (SM)
gg→H
Hbb–
Htt–
Hqq
HZ HW
tan β = 30Maximal mixing
Ù HÙ
h
mh/H (GeV)
Cro
ss-s
ectio
n (p
b)
Michael Krämer Page 29 Universität Bielefeld, Mai 2005
Associated bb̄h production mechanism
At leading order
︸ ︷︷ ︸ ︸ ︷︷ ︸ ︸ ︷︷ ︸
MQ � MH : ∼ α2s ln2(MH/MQ) ∼ α2s ln(MH/MQ) ∼ α2s
Summation of ln(MH/MQ) terms by using heavy quark PDFs[Collins, Olness, Tung; Barnett, Haber, Soper; Dicus, Willenbrock,. . . ]
MQ �MH-
Michael Krämer Page 30 Universität Bielefeld, Mai 2005
Associated bb̄h production mechanism
At leading order
︸ ︷︷ ︸ ︸ ︷︷ ︸ ︸ ︷︷ ︸
MQ � MH : ∼ α2s ln2(MH/MQ) ∼ α2s ln(MH/MQ) ∼ α2s
Summation of ln(MH/MQ) terms by using heavy quark PDFs[Collins, Olness, Tung; Barnett, Haber, Soper; Dicus, Willenbrock,. . . ]
MQ �MH-
Michael Krämer Page 30 Universität Bielefeld, Mai 2005
Associated bb̄h production mechanism
At leading order
︸ ︷︷ ︸ ︸ ︷︷ ︸ ︸ ︷︷ ︸
MQ � MH : ∼ α2s ln2(MH/MQ) ∼ α2s ln(MH/MQ) ∼ α2s
Summation of ln(MH/MQ) terms by using heavy quark PDFs[Collins, Olness, Tung; Barnett, Haber, Soper; Dicus, Willenbrock,. . . ]
MQ �MH-
Michael Krämer Page 30 Universität Bielefeld, Mai 2005
Associated bb̄h production: two calculational schemes
4-flavour scheme
+ exact g → bb̄ splitting & mass effects
− no summation of ln(MH/Mb) terms
5-flavour scheme
+ summation of ln(MH/Mb) terms
− LL approximation to g → bb̄ splitting
The 4- and 5-flavour schemes
– are both theoretically consistent & well-defined
– represent different ways of ordering perturbation theory
– should agree at sufficiently high order
– do not match exactly at finite order
Michael Krämer Page 31 Universität Bielefeld, Mai 2005
Associated bb̄h production: two calculational schemes
4-flavour scheme
+ exact g → bb̄ splitting & mass effects
− no summation of ln(MH/Mb) terms
5-flavour scheme
+ summation of ln(MH/Mb) terms
− LL approximation to g → bb̄ splitting
The 4- and 5-flavour schemes
– are both theoretically consistent & well-defined
– represent different ways of ordering perturbation theory
– should agree at sufficiently high order
– do not match exactly at finite order
Michael Krämer Page 31 Universität Bielefeld, Mai 2005
Associated bb̄h production: two calculational schemes
4-flavour scheme
+ exact g → bb̄ splitting & mass effects
− no summation of ln(MH/Mb) terms
5-flavour scheme
+ summation of ln(MH/Mb) terms
− LL approximation to g → bb̄ splitting
The 4- and 5-flavour schemes
– are both theoretically consistent & well-defined
– represent different ways of ordering perturbation theory
– should agree at sufficiently high order
– do not match exactly at finite order
Michael Krämer Page 31 Universität Bielefeld, Mai 2005
Associated bb̄h production: two calculational schemes
4-flavour scheme
+ exact g → bb̄ splitting & mass effects
− no summation of ln(MH/Mb) terms
5-flavour scheme
+ summation of ln(MH/Mb) terms
− LL approximation to g → bb̄ splitting
The 4- and 5-flavour schemes
– are both theoretically consistent & well-defined
– represent different ways of ordering perturbation theory
– should agree at sufficiently high order
– do not match exactly at finite order
Michael Krämer Page 31 Universität Bielefeld, Mai 2005
Associated bb̄h production: two calculational schemes
Comparison at leading order
→ strong scale dependence
→ σ(bb̄→ H) � σ(gg → bb̄H) at µ = MH
→ discrepancy reduced at µF = MH/4 (→ Harlander, Kilgore)[see also Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn]
Michael Krämer Page 32 Universität Bielefeld, Mai 2005
Associated bb̄h production: two calculational schemes
Comparison at leading order
→ strong scale dependence
→ σ(bb̄→ H) � σ(gg → bb̄H) at µ = MH
→ discrepancy reduced at µF = MH/4 (→ Harlander, Kilgore)[see also Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn]
Michael Krämer Page 32 Universität Bielefeld, Mai 2005
Associated bb̄h production: two calculational schemes
Comparison at leading order
→ strong scale dependence
→ σ(bb̄→ H) � σ(gg → bb̄H) at µ = MH→ discrepancy reduced at µF = MH/4 (→ Harlander, Kilgore)
[see also Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn]
Michael Krämer Page 32 Universität Bielefeld, Mai 2005
Associated bb̄h production: (N)NLO corrections
Comparison of 4- and 5-flavour schemes at (N)NLO (SM Higgs, LHC)
[Harlander, Kilgore; Dittmaier, MK, Spira]
σ(pp → bb_
h + X) [fb]
√s = 14 TeVµ = (2mb + Mh)/4
Mh [GeV]
bb_
→ h (NNLO)
gg → bb_
h (NLO)10
10 2
10 3
100 150 200 250 300 350 400
Michael Krämer Page 33 Universität Bielefeld, Mai 2005
Higgs background calculations
Example: pp → H → γγ/WW backgrounds
γγ background
– NLO parton level MC program pp→ γγ (DIPHOX) [Binoth, Guillet, Heinrich, Pilon, Werlen]– gg → γγ at NLO (2-loop) [Bern, De Freitas, Dixon, Schmidt ’02]
WW background
– jet veto effects [Catani, De Florian, Grazzini]
– NLO parton level MC program pp→W+W− [Frixione, Nason, Ridolfi; Baur, Han, Ohnemus]– NLO spin correlations in leptonic W decays [Dixon, Kunszt, Signer]
– tt̄ backgrounds including finite width effects [Kauer, Zeppenfeld]
– NLO parton level MC program pp→W/Z + bb̄ [Campbell, Ellis, Veseli]– gluon-gluon induced contributions to pp→WW → lνlν [Binoth, Ciccolini, Kauer, MK ’05]
Michael Krämer Page 34 Universität Bielefeld, Mai 2005
WW production: a background to Higgs searches
pp → H → WW → lν̄ l̄′ν ′ is an important Higgs search channel– WW pair production is the dominant background: σ× BR ≈ 5 times larger than signal
– a Higgs mass peak cannot be reconstructed from leptonic W decays
⇒ theoretical control of the background is important (≈ 5%!)
experimental selection cuts to enhance the signal/background ratio may amplifythe importance of higher-order corrections for background processes
example: gg →WW → lν̄ l̄′ν′ [Binoth, Ciccolini, Kauer, MK (05)]
W−
νµ
µ+
W+
e−
ν̄e γ, Z
ν̄e
e−
νµ
µ+
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
g W+
νµ
µ+
e−
ν̄e
d
d u
W−d
→ formally NNLO→ but enhanced by Higgs search cuts
gg qq̄ (NLO) corr.
σtot 54 fb 1373 fb 4%
σbkg 1.39 fb 4.8 fb 30%
Michael Krämer Page 35 Universität Bielefeld, Mai 2005
WW production: a background to Higgs searches
pp → H → WW → lν̄ l̄′ν ′ is an important Higgs search channel– WW pair production is the dominant background: σ× BR ≈ 5 times larger than signal
– a Higgs mass peak cannot be reconstructed from leptonic W decays
⇒ theoretical control of the background is important (≈ 5%!)
experimental selection cuts to enhance the signal/background ratio may amplifythe importance of higher-order corrections for background processes
example: gg →WW → lν̄ l̄′ν′ [Binoth, Ciccolini, Kauer, MK (05)]
W−
νµ
µ+
W+
e−
ν̄e γ, Z
ν̄e
e−
νµ
µ+
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
g W+
νµ
µ+
e−
ν̄e
d
d u
W−d
→ formally NNLO→ but enhanced by Higgs search cuts
gg qq̄ (NLO) corr.
σtot 54 fb 1373 fb 4%
σbkg 1.39 fb 4.8 fb 30%
Michael Krämer Page 35 Universität Bielefeld, Mai 2005
WW production: a background to Higgs searches
pp → H → WW → lν̄ l̄′ν ′ is an important Higgs search channel– WW pair production is the dominant background: σ× BR ≈ 5 times larger than signal
– a Higgs mass peak cannot be reconstructed from leptonic W decays
⇒ theoretical control of the background is important (≈ 5%!)
experimental selection cuts to enhance the signal/background ratio may amplifythe importance of higher-order corrections for background processes
example: gg →WW → lν̄ l̄′ν′ [Binoth, Ciccolini, Kauer, MK (05)]
W−
νµ
µ+
W+
e−
ν̄e γ, Z
ν̄e
e−
νµ
µ+
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
g W+
νµ
µ+
e−
ν̄e
d
d u
W−d
→ formally NNLO→ but enhanced by Higgs search cuts
gg qq̄ (NLO) corr.
σtot 54 fb 1373 fb 4%
σbkg 1.39 fb 4.8 fb 30%
Michael Krämer Page 35 Universität Bielefeld, Mai 2005
Summary and Conclusions
The LHC will find the (or a or various) Higgs boson(s) (or some new strong inter-
actions in the gauge boson sector)
Higgs physics is exciting:
– reveals the mechanism of electroweak symmetry breaking
– points towards physics beyond the SM (hierarchy problem)
Exploring Higgs physics at the LHC needs precision measurements and precision
calculations
– signal cross sections are now known within 15% or better
– more work is needed to improve prediction of background processes
Exciting times ahead!
Michael Krämer Page 36 Universität Bielefeld, Mai 2005
Summary and Conclusions
The LHC will find the (or a or various) Higgs boson(s) (or some new strong inter-
actions in the gauge boson sector)
Higgs physics is exciting:
– reveals the mechanism of electroweak symmetry breaking
– points towards physics beyond the SM (hierarchy problem)
Exploring Higgs physics at the LHC needs precision measurements and precision
calculations
– signal cross sections are now known within 15% or better
– more work is needed to improve prediction of background processes
Exciting times ahead!
Michael Krämer Page 36 Universität Bielefeld, Mai 2005
Summary and Conclusions
The LHC will find the (or a or various) Higgs boson(s) (or some new strong inter-
actions in the gauge boson sector)
Higgs physics is exciting:
– reveals the mechanism of electroweak symmetry breaking
– points towards physics beyond the SM (hierarchy problem)
Exploring Higgs physics at the LHC needs precision measurements and precision
calculations
– signal cross sections are now known within 15% or better
– more work is needed to improve prediction of background processes
Exciting times ahead!
Michael Krämer Page 36 Universität Bielefeld, Mai 2005
Summary and Conclusions
The LHC will find the (or a or various) Higgs boson(s) (or some new strong inter-
actions in the gauge boson sector)
Higgs physics is exciting:
– reveals the mechanism of electroweak symmetry breaking
– points towards physics beyond the SM (hierarchy problem)
Exploring Higgs physics at the LHC needs precision measurements and precision
calculations
– signal cross sections are now known within 15% or better
– more work is needed to improve prediction of background processes
Exciting times ahead!
Michael Krämer Page 36 Universität Bielefeld, Mai 2005
Summary and Conclusions
The LHC will find the (or a or various) Higgs boson(s) (or some new strong inter-
actions in the gauge boson sector)
Higgs physics is exciting:
– reveals the mechanism of electroweak symmetry breaking
– points towards physics beyond the SM (hierarchy problem)
Exploring Higgs physics at the LHC needs precision measurements and precision
calculations
– signal cross sections are now known within 15% or better
– more work is needed to improve prediction of background processes
Exciting times ahead!
Michael Krämer Page 36 Universität Bielefeld, Mai 2005
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