Page 1
Theorie-Seminar Universitat Bielefeld, Mai 2005
Higgs Production at the LHC
Michael Kramer
(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 Kramer Page 1 Universitat Bielefeld, Mai 2005
Page 2
Introduction: from WW -scattering to the Higgs boson
Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ− → e−νeνµ
L =GF√
2[νµγλ(1 − γ5)µ][eγλ(1 − γ5)νe]
with GF ≈ 1.17 × 10−5 GeV−2 (Fermi coupling)
Fermi theory at high energies: M[νµe− → µ−νe] ∼ GF
2√
2πs
⇒ violates unitarity
Solution: interaction mediated by heavy vector boson W±
M[νµe− → µ−νe] →
GF s
2√
2π
M2W
M2W − s
(with MW ≈ 100 GeV)
Michael Kramer Page 2 Universitat Bielefeld, Mai 2005
Page 3
Introduction: from WW -scattering to the Higgs boson
Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ− → e−νeνµ
L =GF√
2[νµγλ(1 − γ5)µ][eγλ(1 − γ5)νe]
with GF ≈ 1.17 × 10−5 GeV−2 (Fermi coupling)
Fermi theory at high energies: M[νµe− → µ−νe] ∼ GF
2√
2πs
⇒ violates unitarity
Solution: interaction mediated by heavy vector boson W±
M[νµe− → µ−νe] →
GF s
2√
2π
M2W
M2W − s
(with MW ≈ 100 GeV)
Michael Kramer Page 2 Universitat Bielefeld, Mai 2005
Page 4
Introduction: from WW -scattering to the Higgs boson
Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ− → e−νeνµ
L =GF√
2[νµγλ(1 − γ5)µ][eγλ(1 − γ5)νe]
with GF ≈ 1.17 × 10−5 GeV−2 (Fermi coupling)
Fermi theory at high energies: M[νµe− → µ−νe] ∼ GF
2√
2πs
⇒ violates unitarity
Solution: interaction mediated by heavy vector boson W±
M[νµe− → µ−νe] →
GF s
2√
2π
M2W
M2W − s
(with MW ≈ 100 GeV)
Michael Kramer Page 2 Universitat Bielefeld, Mai 2005
Page 5
Introduction: from WW -scattering to the Higgs boson
Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ− → e−νeνµ
L =GF√
2[νµγλ(1 − γ5)µ][eγλ(1 − γ5)νe]
with GF ≈ 1.17 × 10−5 GeV−2 (Fermi coupling)
Fermi theory at high energies: M[νµe− → µ−νe] ∼ GF
2√
2πs
⇒ violates unitarity
Solution: interaction mediated by heavy vector boson W±
� ���� � �
� �� �
� ���� � �
� �
�
M[νµe− → µ−νe] →
GF s
2√
2π
M2W
M2W − s
(with MW ≈ 100 GeV)
Michael Kramer Page 2 Universitat Bielefeld, Mai 2005
Page 6
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 Kramer Page 3 Universitat Bielefeld, Mai 2005
Page 7
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 Kramer Page 3 Universitat Bielefeld, Mai 2005
Page 8
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 Kramer Page 3 Universitat Bielefeld, Mai 2005
Page 9
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 ψ
dLφf
dR + gu
f ψdLφf
uR − 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 masses
and a physical Higgs particle
Michael Kramer Page 4 Universitat Bielefeld, Mai 2005
Page 10
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 Kramer Page 5 Universitat Bielefeld, Mai 2005
Page 11
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 Kramer Page 5 Universitat Bielefeld, Mai 2005
Page 12
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 Kramer Page 5 Universitat Bielefeld, Mai 2005
Page 13
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 mt
68% 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 Kramer Page 6 Universitat Bielefeld, Mai 2005
Page 14
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 mt
68% 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 Kramer Page 6 Universitat Bielefeld, Mai 2005
Page 15
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 mt
68% 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 Kramer Page 6 Universitat Bielefeld, Mai 2005
Page 16
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 mt
68% 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 Kramer Page 6 Universitat Bielefeld, Mai 2005
Page 17
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 Kramer Page 7 Universitat Bielefeld, Mai 2005
Page 18
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
bb for MH ∼< 130 GeV
WW, ZZ for MH ∼> 130 GeV
Michael Kramer Page 8 Universitat Bielefeld, Mai 2005
Page 19
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 (pp collider with√s = 2 TeV)
current∫L = 0.7 fb−1
expectation in 2008:∫L = 4 − 6 fb−1
Michael Kramer Page 9 Universitat Bielefeld, Mai 2005
Page 20
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 (pp collider with√s = 2 TeV)
current∫L = 0.7 fb−1
expectation in 2008:∫L = 4 − 6 fb−1
Michael Kramer Page 9 Universitat Bielefeld, Mai 2005
Page 21
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 Kramer Page 10 Universitat Bielefeld, Mai 2005
Page 22
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 Kramer Page 11 Universitat Bielefeld, Mai 2005
Page 23
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 Kramer Page 12 Universitat Bielefeld, Mai 2005
Page 24
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: σbb ≈ 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 Kramer Page 13 Universitat Bielefeld, Mai 2005
Page 25
Higgs boson searches at the LHC: cross section predictions
σ(pp → H + X) [pb]√s = 14 TeV
NLO / 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 Kramer Page 14 Universitat Bielefeld, Mai 2005
Page 26
Higgs boson searches at the LHC: signal significance
1
10
10 2
100 120 140 160 180 200 mH (GeV/c2)
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/qq → ttH (H → bb, ττ)
qq → qqH (H → γγ,WW ∗, ττ)
qq′ →WH (H → γγ)
MH ∼> 2MZ →{
gg → H (H → ZZ,WW )
qq → qqH (H → ZZ,WW )
[ + diffractive Higgs production]
Michael Kramer Page 15 Universitat Bielefeld, Mai 2005
Page 27
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 Kramer Page 16 Universitat Bielefeld, Mai 2005
Page 28
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 Kramer Page 16 Universitat Bielefeld, Mai 2005
Page 29
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 Kramer Page 17 Universitat Bielefeld, Mai 2005
Page 30
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 Kramer Page 17 Universitat Bielefeld, Mai 2005
Page 31
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) fq(x2) σqq→l+l−
− fq,q(x) dx: probability to find (anti)quark with momentum fraction x
→ process independent, measured in DIS
− σqq→l+l− : hard scattering cross section
→ calculable in perturbation theory
Michael Kramer Page 18 Universitat Bielefeld, Mai 2005
Page 32
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) fq(x2) σqq→l+l−
− fq,q(x) dx: probability to find (anti)quark with momentum fraction x
→ process independent, measured in DIS
− σqq→l+l− : hard scattering cross section
→ calculable in perturbation theory
Michael Kramer Page 18 Universitat Bielefeld, Mai 2005
Page 33
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) fq(x2) σqq→l+l−
− fq,q(x) dx: probability to find (anti)quark with momentum fraction x
→ process independent, measured in DIS
− σqq→l+l− : hard scattering cross section
→ calculable in perturbation theory
Michael Kramer Page 18 Universitat Bielefeld, Mai 2005
Page 34
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) fq(x2) σqq→l+l−
− fq,q(x) dx: probability to find (anti)quark with momentum fraction x
→ process independent, measured in DIS
− σqq→l+l− : hard scattering cross section
→ calculable in perturbation theory
Michael Kramer Page 18 Universitat Bielefeld, Mai 2005
Page 35
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 Kramer Page 19 Universitat Bielefeld, Mai 2005
Page 36
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 Kramer Page 19 Universitat Bielefeld, Mai 2005
Page 37
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 Kramer Page 19 Universitat Bielefeld, Mai 2005
Page 38
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 Kramer Page 19 Universitat Bielefeld, Mai 2005
Page 39
Particle production at hadron colliders
Initial state collinear singularities,eg.
�
¡
¢£ ¤
− process independent divergence in∫
dk2T as k2
T → 0
→ absorb singularity in parton densities:
fq(x, µfac) = fq(x) +{
divergent part of∫ µ2
fac0 dk2
T
}
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 Kramer Page 20 Universitat Bielefeld, Mai 2005
Page 40
Particle production at hadron colliders
Initial state collinear singularities,eg.
¥
¦¦¦§
¨© ª
− process independent divergence in∫
dk2T as k2
T → 0
→ absorb singularity in parton densities:
fq(x, µfac) = fq(x) +{
divergent part of∫ µ2
fac0 dk2
T
}
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 Kramer Page 20 Universitat Bielefeld, Mai 2005
Page 41
Particle production at hadron colliders
Initial state collinear singularities,eg.
«
¬¬¬
®¯ °
− process independent divergence in∫
dk2T as k2
T → 0
→ absorb singularity in parton densities:
fq(x, µfac) = fq(x) +{
divergent part of∫ µ2
fac0 dk2
T
}
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 Kramer Page 20 Universitat Bielefeld, Mai 2005
Page 42
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 ∼ theoretical
uncertainty 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 Kramer Page 21 Universitat Bielefeld, Mai 2005
Page 43
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 ∼ theoretical
uncertainty 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 Kramer Page 21 Universitat Bielefeld, Mai 2005
Page 44
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 Kramer Page 22 Universitat Bielefeld, Mai 2005
Page 45
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 Kramer Page 23 Universitat Bielefeld, Mai 2005
Page 46
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 Kramer Page 24 Universitat Bielefeld, Mai 2005
Page 47
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 Kramer Page 24 Universitat Bielefeld, Mai 2005
Page 48
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 Kramer Page 24 Universitat Bielefeld, Mai 2005
Page 49
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 Kramer Page 24 Universitat Bielefeld, Mai 2005
Page 50
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 Kramer Page 24 Universitat Bielefeld, Mai 2005
Page 51
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 Kramer Page 25 Universitat Bielefeld, Mai 2005
Page 52
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 Kramer Page 25 Universitat Bielefeld, Mai 2005
Page 53
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 Kramer Page 26 Universitat Bielefeld, Mai 2005
Page 54
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
ÕÕ
Ö×Ö
Ø
− σ(ttH) ∼< 1 pb (LHC, MH > 115 GeV)
but: distinctive final state:
pp→ t(→W+b) t(→W−b) H(→ bb)
→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH
⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Muller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeV
MH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ0
0.2 0.5 1 2 5200
400
600
800
1000
1200
1400
1
Michael Kramer Page 27 Universitat Bielefeld, Mai 2005
Page 55
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
ÙÙ
ÚÛÚ
Ü
− σ(ttH) ∼< 1 pb (LHC, MH > 115 GeV)
but: distinctive final state:
pp→ t(→W+b) t(→W−b) H(→ bb)
→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH
⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Muller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeV
MH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ0
0.2 0.5 1 2 5200
400
600
800
1000
1200
1400
1
Michael Kramer Page 27 Universitat Bielefeld, Mai 2005
Page 56
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
ÝÝ
ÞßÞ
à
− σ(ttH) ∼< 1 pb (LHC, MH > 115 GeV)
but: distinctive final state:
pp→ t(→W+b) t(→W−b) H(→ bb)
→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH
⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Muller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeV
MH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ0
0.2 0.5 1 2 5200
400
600
800
1000
1200
1400
1
Michael Kramer Page 27 Universitat Bielefeld, Mai 2005
Page 57
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
áá
âãâ
ä
− σ(ttH) ∼< 1 pb (LHC, MH > 115 GeV)
but: distinctive final state:
pp→ t(→W+b) t(→W−b) H(→ bb)
→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH
⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Muller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeV
MH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ0
0.2 0.5 1 2 5200
400
600
800
1000
1200
1400
1
Michael Kramer Page 27 Universitat Bielefeld, Mai 2005
Page 58
Higgs production cross sections: theoretical status
Higgs production in association with top quarks
åå
æçæ
è
− σ(ttH) ∼< 1 pb (LHC, MH > 115 GeV)
but: distinctive final state:
pp→ t(→W+b) t(→W−b) H(→ bb)
→ important contribution to 5σ discovery
for MH ∼< 130 GeV
− cross section ∝ g2ttH
⇒ direct measurement of top Yukawa coupling
δgttH/gttH ≈ 15% (exp.)[Drollinger, Muller, Denegri]
− NLO scale dependence ∼< 15%[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas ’01;
Dawson, Jackson, Orr, Reina, Wackeroth ’01-’03]
[Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas]
σ(pp → tt_ H + X) [fb]
√s = 14 TeV
MH = 120 GeV
µ0 = mt + MH/2
NLO
LO
µ/µ0
0.2 0.5 1 2 5200
400
600
800
1000
1200
1400
1
Michael Kramer Page 27 Universitat Bielefeld, Mai 2005
Page 59
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;Blumlein, Ravindran; . . . (02-05)]
– NNLO QCD calculations for pp → HZ, HW[Brein, Djouadi, Harlander (04)]
– (N)NLO QCD calculations for pp → QQH[Beenakker, Dittmaier, MK, Plumper, 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 Kramer Page 28 Universitat Bielefeld, Mai 2005
Page 60
Higgs production in the MSSM: associated bbh production
Associated bbh/H production is crucial for MSSM Higgs searches at large tan β
Bottom-Higgs Yukawa coupling:
gMSSMbbh = − sin α
cos βgSM
bbH
gMSSMbbH = cos α
cos βgSM
bbH
}
tan β � 1-
{
tan β gSMbbH (Mh'MA'MZ)
tan β gSMbbH (MH'MA�MZ)
At tanβ � 1 associated bbh/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 Kramer Page 29 Universitat Bielefeld, Mai 2005
Page 61
Higgs production in the MSSM: associated bbh production
Associated bbh/H production is crucial for MSSM Higgs searches at large tan β
Bottom-Higgs Yukawa coupling:
gMSSMbbh = − sin α
cos βgSM
bbH
gMSSMbbH = cos α
cos βgSM
bbH
}
tan β � 1-
{
tan β gSMbbH (Mh'MA'MZ)
tan β gSMbbH (MH'MA�MZ)
At tanβ � 1 associated bbh/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 Kramer Page 29 Universitat Bielefeld, Mai 2005
Page 62
Associated bbh production mechanism
At leading order
︸ ︷︷ ︸ ︸ ︷︷ ︸ ︸ ︷︷ ︸
MQ � MH : ∼ α2s ln2(MH/MQ) ∼ α2
s 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 Kramer Page 30 Universitat Bielefeld, Mai 2005
Page 63
Associated bbh production mechanism
At leading order
︸ ︷︷ ︸ ︸ ︷︷ ︸ ︸ ︷︷ ︸
MQ � MH : ∼ α2s ln2(MH/MQ) ∼ α2
s 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 Kramer Page 30 Universitat Bielefeld, Mai 2005
Page 64
Associated bbh production mechanism
At leading order
︸ ︷︷ ︸ ︸ ︷︷ ︸ ︸ ︷︷ ︸
MQ � MH : ∼ α2s ln2(MH/MQ) ∼ α2
s 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 Kramer Page 30 Universitat Bielefeld, Mai 2005
Page 65
Associated bbh production: two calculational schemes
4-flavour scheme
+ exact g → bb splitting & mass effects
− no summation of ln(MH/Mb) terms
5-flavour scheme
+ summation of ln(MH/Mb) terms
− LL approximation to g → bb 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 Kramer Page 31 Universitat Bielefeld, Mai 2005
Page 66
Associated bbh production: two calculational schemes
4-flavour scheme
+ exact g → bb splitting & mass effects
− no summation of ln(MH/Mb) terms
5-flavour scheme
+ summation of ln(MH/Mb) terms
− LL approximation to g → bb 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 Kramer Page 31 Universitat Bielefeld, Mai 2005
Page 67
Associated bbh production: two calculational schemes
4-flavour scheme
+ exact g → bb splitting & mass effects
− no summation of ln(MH/Mb) terms
5-flavour scheme
+ summation of ln(MH/Mb) terms
− LL approximation to g → bb 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 Kramer Page 31 Universitat Bielefeld, Mai 2005
Page 68
Associated bbh production: two calculational schemes
4-flavour scheme
+ exact g → bb splitting & mass effects
− no summation of ln(MH/Mb) terms
5-flavour scheme
+ summation of ln(MH/Mb) terms
− LL approximation to g → bb 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 Kramer Page 31 Universitat Bielefeld, Mai 2005
Page 69
Associated bbh production: two calculational schemes
Comparison at leading order
→ strong scale dependence
→ σ(bb→ H) � σ(gg → bbH) at µ = MH
→ discrepancy reduced at µF = MH/4 (→ Harlander, Kilgore)
[see also Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn]
Michael Kramer Page 32 Universitat Bielefeld, Mai 2005
Page 70
Associated bbh production: two calculational schemes
Comparison at leading order
→ strong scale dependence
→ σ(bb→ H) � σ(gg → bbH) at µ = MH
→ discrepancy reduced at µF = MH/4 (→ Harlander, Kilgore)
[see also Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn]
Michael Kramer Page 32 Universitat Bielefeld, Mai 2005
Page 71
Associated bbh production: two calculational schemes
Comparison at leading order
→ strong scale dependence
→ σ(bb→ H) � σ(gg → bbH) at µ = MH
→ discrepancy reduced at µF = MH/4 (→ Harlander, Kilgore)
[see also Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn]
Michael Kramer Page 32 Universitat Bielefeld, Mai 2005
Page 72
Associated bbh 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 TeV
µ = (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 Kramer Page 33 Universitat Bielefeld, Mai 2005
Page 73
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]
– tt backgrounds including finite width effects [Kauer, Zeppenfeld]
– NLO parton level MC program pp→W/Z + bb [Campbell, Ellis, Veseli]
– gluon-gluon induced contributions to pp→WW → lνlν [Binoth, Ciccolini, Kauer, MK ’05]
Michael Kramer Page 34 Universitat Bielefeld, Mai 2005
Page 74
WW production: a background to Higgs searches
pp → H → WW → lν l′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 → lν l′ν′ [Binoth, Ciccolini, Kauer, MK (05)]
W−
νµ
µ+
W+
e−
νe γ, Z
νe
e−
νµ
µ+
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
g W+
νµ
µ+
e−
νe
d
d u
W−d
→ formally NNLO
→ but enhanced by Higgs search cuts
gg qq (NLO) corr.
σtot 54 fb 1373 fb 4%
σbkg 1.39 fb 4.8 fb 30%
Michael Kramer Page 35 Universitat Bielefeld, Mai 2005
Page 75
WW production: a background to Higgs searches
pp → H → WW → lν l′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 → lν l′ν′ [Binoth, Ciccolini, Kauer, MK (05)]
W−
νµ
µ+
W+
e−
νe γ, Z
νe
e−
νµ
µ+
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
g W+
νµ
µ+
e−
νe
d
d u
W−d
→ formally NNLO
→ but enhanced by Higgs search cuts
gg qq (NLO) corr.
σtot 54 fb 1373 fb 4%
σbkg 1.39 fb 4.8 fb 30%
Michael Kramer Page 35 Universitat Bielefeld, Mai 2005
Page 76
WW production: a background to Higgs searches
pp → H → WW → lν l′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 → lν l′ν′ [Binoth, Ciccolini, Kauer, MK (05)]
W−
νµ
µ+
W+
e−
νe γ, Z
νe
e−
νµ
µ+
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
g W+
νµ
µ+
e−
νe
d
d u
W−d
→ formally NNLO
→ but enhanced by Higgs search cuts
gg qq (NLO) corr.
σtot 54 fb 1373 fb 4%
σbkg 1.39 fb 4.8 fb 30%
Michael Kramer Page 35 Universitat Bielefeld, Mai 2005
Page 77
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 Kramer Page 36 Universitat Bielefeld, Mai 2005
Page 78
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 Kramer Page 36 Universitat Bielefeld, Mai 2005
Page 79
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 Kramer Page 36 Universitat Bielefeld, Mai 2005
Page 80
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 Kramer Page 36 Universitat Bielefeld, Mai 2005
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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 Kramer Page 36 Universitat Bielefeld, Mai 2005