Precision calculations for LHC physicsweb.physik.rwth-aachen.de/~mkraemer/mkraemer_dpg.pdf ·...
Transcript of Precision calculations for LHC physicsweb.physik.rwth-aachen.de/~mkraemer/mkraemer_dpg.pdf ·...
DPG Fruhjahrstagung, February 2008
Precision calculations for LHC physics
Michael Kramer (RWTH Aachen)
Sponsored by:
SFB/TR 9 “Computational Particle Physics”, Helmholtz Alliance “Physics at the Terascale”, BMBF-
Theorie-Verbund, Marie Curie Research Training Network “Heptools”, Graduiertenkolleg “Elemen-
tarteilchenphysik an der TeV-Skala”
Michael Kramer page 1 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
We do not need theory input for LHC discoveries
8000
6000
4000
2000
080 100 120 140
mγγ (GeV)
Higgs signal
Eve
nts
/ 500
MeV
for
105
pb-
1
HSM γγ
Simulated 2γ mass plotfor 105 pb-1 mH =130 GeV
in the lead tungstate calorimeter
D_D
_105
5c
CMS, 105 pb-1
but only if we see a resonance. . .
Michael Kramer page 2 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
We do not need theory input for LHC discoveries
8000
6000
4000
2000
080 100 120 140
mγγ (GeV)
Higgs signal
Eve
nts
/ 500
MeV
for
105
pb-
1
HSM γγ
Simulated 2γ mass plotfor 105 pb-1 mH =130 GeV
in the lead tungstate calorimeter
D_D
_105
5c
CMS, 105 pb-1
but only if we see a resonance. . .
Michael Kramer page 2 DPG Fruhjahrstagung 2008
Contents
Why precision calculations for discoveries?
– lessons from the past
– prospects: Higgs physics & BSM searches at the LHC
Theoretical tools for LHC phenomenology
– (N)NLO multi-leg calculations
– matching with parton showers & hadronization
Michael Kramer page 3 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Tevatron jet cross section at large ET
Et (GeV)-0.5
0
0.5
1(D
ata
- The
ory)
/ The
ory
200 300 40010050
CTEQ3MCDF (Preliminary) * 1.03D0 (Preliminary) * 1.01
Michael Kramer page 4 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Tevatron jet cross section at large ET
Et (GeV)-0.5
0
0.5
1(D
ata
- The
ory)
/ The
ory
200 300 40010050
CTEQ3MCDF (Preliminary) * 1.03D0 (Preliminary) * 1.01
⇒ new physics? + ?
Michael Kramer page 5 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Tevatron jet cross section at large ET
Et (GeV)-0.5
0
0.5
1(D
ata
- The
ory)
/ The
ory
200 300 40010050
CTEQ3MCDF (Preliminary) * 1.03D0 (Preliminary) * 1.01
LBSM ⊇g2
M2ψγµψ ψγµψ ⇒
data − theory
theory∝ g2 E
2T
M2
Michael Kramer page 6 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Tevatron jet cross section at large ET
(GeV)TInclusive Jet E0 100 200 300 400 500 600
(nb/
GeV
)η
d T /
dEσ2
d
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-11
10
102
CDF Run II PreliminaryIntegrated L = 85 pb-1
0.1 < |ηDet| < 0.7JetClu Cone R = 0.7
Run II DataCTEQ 6.1 Uncertainty+/- 5% Energy Scale Uncertainty
⇒ just QCD. . . (uncertainty in gluon pdf at large x)
Michael Kramer page 7 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Tevatron bottom quark cross section
[D0, PLB 487 (2000)]
⇒ new physics?
Michael Kramer page 8 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Tevatron bottom quark cross section
[Berger et al., PRL 86 (2001)]
10-1
1
10
10 2
10 3
10 4
10 5
10 102
SumQCDg → b~
D0 Data
CDF Data
√S = 1.8 TeV
mg = 14 GeV
mb = 3.5 GeV
mb = 4.75 GeV
~
~
pT (GeV)min
σ b(p T
≥ p
T )
(nb
)m
in
⇒ light gluino/sbottom production?
Michael Kramer page 9 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Tevatron bottom quark cross section
[Mangano, AIP Conf.Proc, 2005]
⇒ just QCD. . . (αs, low-x gluon pdf, b→ B fragmentation & exp. analyses)
Michael Kramer page 10 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Signals of discovery include
– mass peaks
– anomalous shapes of kinematic distributions
e.g. jet production at large ET
– excess of events after kinematic selection
e.g. bottom cross section
Michael Kramer page 11 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Signals of discovery include
– mass peaks
– anomalous shapes of kinematic distributionse.g. jet production at large ET
– excess of events after kinematic selectione.g. bottom cross section
Michael Kramer page 11 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Signals of discovery include
– mass peakse.g. Higgs searches in H → γγ/ZZ∗ final states
– anomalous shapes of kinematic distributionse.g. SUSY searches in multijet + ET,miss final states
– excess of events after kinematic selectione.g. Higgs searches in H → WW ∗ final states
Experiments measure multi-parton final states in restricted phase space region
→ Need flexible and realistic precision calculations
– precise → including loops & many legs
– flexible → allowing for exclusive cross sections & phase space cuts
– realistic → matched with parton showers and hadronization
Michael Kramer page 12 DPG Fruhjahrstagung 2008
Why precision calculations for discoveries?
Signals of discovery include
– mass peakse.g. Higgs searches in H → γγ/ZZ∗ final states
– anomalous shapes of kinematic distributionse.g. SUSY searches in multijet + ET,miss final states
– excess of events after kinematic selectione.g. Higgs searches in H → WW ∗ final states
Experiments measure multi-parton final states in restricted phase space region
→ Need flexible and realistic precision calculations
– precise → including loops & many legs
– flexible → allowing for exclusive cross sections & phase space cuts
– realistic → matched with parton showers and hadronization
Michael Kramer page 12 DPG Fruhjahrstagung 2008
Searches at the LHC: outline
Examples from Higgs physics
– discovery from excess of events: pp→ H → WW ∗ → l+νl−ν
– backgrounds: beware of cuts
– beyond discovery: measuring Higgs couplings
Examples from beyond the standard model physics
– anomalous shapes: SUSY searches with multi-jets + ET,miss signatures
– backgrounds: multi-leg calculations needed
Theoretical tools for LHC physics
– LO and NLO multi-leg calculations
– matching with parton showers and hadronization
Michael Kramer page 13 DPG Fruhjahrstagung 2008
Searches at the LHC: outline
Examples from Higgs physics
– discovery from excess of events: pp→ H → WW ∗ → l+νl−ν
– backgrounds: beware of cuts
– beyond discovery: measuring Higgs couplings
• Examples from beyond the standard model physics
– anomalous shapes: SUSY searches with multi-jets + ET,miss signatures
– backgrounds: multi-leg calculations needed
• Theoretical tools for LHC physics
– LO and NLO multi-leg calculations
– matching with parton showers and hadronization
Michael Kramer page 14 DPG Fruhjahrstagung 2008
Searches at the LHC: pp → H → WW ∗→ l+νl−ν
g
g
H
W−
W+
ν
l−
l+
ν
– neutrinos in final state
→ no invariant Higgs mass peak
– large background from QCD
process qq → WW
– exploit lepton rapidity distributions
and angular correlations to sup-
press background(Dittmar, Dreiner) 0
100
200
300
0 50 100 150 200 250
mT (GeV)
Eve
nts
/ 5 G
eV
⇒ a precise theoretical description of the background is crucial
Michael Kramer page 15 DPG Fruhjahrstagung 2008
Searches at the LHC: pp → H → WW ∗→ l+νl−ν
g
g
H
W−
W+
ν
l−
l+
ν
– neutrinos in final state
→ no invariant Higgs mass peak
– large background from QCD
process qq → WW
– exploit lepton rapidity distributions
and angular correlations to sup-
press background(Dittmar, Dreiner) 0
100
200
300
0 50 100 150 200 250
mT (GeV)
Eve
nts
/ 5 G
eV
⇒ a precise theoretical description of the background is crucial
Michael Kramer page 15 DPG Fruhjahrstagung 2008
Searches at the LHC: pp → H → WW ∗→ l+νl−ν
g
g
H
W−
W+
ν
l−
l+
ν
– neutrinos in final state
→ no invariant Higgs mass peak
– large background from QCD
process qq → WW
– exploit lepton rapidity distributions
and angular correlations to sup-
press background(Dittmar, Dreiner) 0
100
200
300
0 50 100 150 200 250
mT (GeV)
Eve
nts
/ 5 G
eV
⇒ a precise theoretical description of the background is crucial
Michael Kramer page 15 DPG Fruhjahrstagung 2008
Searches at the LHC: pp → H → WW ∗→ l+νl−ν
LO background from qq scattering
������
���
���
� � ��
� �
�����
���
���
� � ��
experimental selection cuts may enhance the importance of higher-order
corrections for background processes: gg → WW → lνl′ν′
[Binoth, Ciccolini, Kauer, MK; Duhrssen, Jakobs, van der Bij, Marquard]
W−
W+
γ, Z
ν
`
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
gd
d u
W−d
W+
ν ′
¯′
`
ν
`
ν
ν ′
¯′
ν ′
¯′
→ 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 16 DPG Fruhjahrstagung 2008
Searches at the LHC: pp → H → WW ∗→ l+νl−ν
LO background from qq scattering
������
���
��� �
� � ���
���
�����
���
��� �
� � ���
experimental selection cuts may enhance the importance of higher-order
corrections for background processes: gg → WW → lνl′ν′
[Binoth, Ciccolini, Kauer, MK; Duhrssen, Jakobs, van der Bij, Marquard]
W−
W+
γ, Z
ν
`
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
gd
d u
W−d
W+
ν ′
¯′
`
ν
`
ν
ν ′
¯′
ν ′
¯′
→ 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 16 DPG Fruhjahrstagung 2008
Searches at the LHC: pp → H → WW ∗→ l+νl−ν
LO background from qq scattering
������
!
"�# $
! # %&�
'()
�����
!
"�# $
! # %&�
experimental selection cuts may enhance the importance of higher-order
corrections for background processes: gg → WW → lνl′ν′
[Binoth, Ciccolini, Kauer, MK; Duhrssen, Jakobs, van der Bij, Marquard]
W−
W+
γ, Z
ν
`
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
gd
d u
W−d
W+
ν ′
¯′
`
ν
`
ν
ν ′
¯′
ν ′
¯′
→ 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 16 DPG Fruhjahrstagung 2008
Searches at the LHC: pp → H → WW ∗→ l+νl−ν
LO background from qq scattering
*�+*�,
-.-
/+0 1
. 0 23,
456
*+*�,
-.-
/+0 1
. 0 23,
experimental selection cuts may enhance the importance of higher-order
corrections for background processes: gg → WW → lνl′ν′
[Binoth, Ciccolini, Kauer, MK; Duhrssen, Jakobs, van der Bij, Marquard]
W−
W+
γ, Z
ν
`
W+γ, Z, H
g
gq
q
q
g
gq
q
q
g
gd
d u
W−d
W+
ν ′
¯′
`
ν
`
ν
ν ′
¯′
ν ′
¯′
→ 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 16 DPG Fruhjahrstagung 2008
Searches at the LHC: outline
• Examples from Higgs physics
– discovery from excess of events: pp→ H → WW ∗ → l+νl−ν
– backgrounds: beware of cuts
– beyond discovery: measuring Higgs couplings
Examples from beyond the standard model physics
– anomalous shapes: SUSY searches with multi-jets + ET,miss signatures
– backgrounds: multi-leg calculations needed
• Theoretical tools for LHC physics
– LO and NLO multi-leg calculations
– matching with parton showers and hadronization
Michael Kramer page 17 DPG Fruhjahrstagung 2008
Searches at the LHC: BSM physics
Many model for new physics are addressing two problems:
– the hierarchy/naturalness problem
– the origin of dark matter
→ spectrum of new particles at the TeV-scale with weakly interacting & stable particle
→ generic BSM signature at the LHC involves cascade decays with missing energy,
eg. supersymmetry
D_D
_204
7.c.
1
q
q
q
q
q~
~
~
~
—
—
—b
b
l+
l+
g
~g
W— W+t
t
t1
ν
χ1
~χ10
~χ20
Gluino/squark production event topology al lowing sparticle mass reconstruction
3 isolated leptons+ 2 b-jets+ 4 jets
+ Etmiss
~l
+
l-
Such cascade decays allow to reconstructsleptons, neutralinos, squarks, gluinos...in favorable cases with %level mass resolutions
Michael Kramer page 18 DPG Fruhjahrstagung 2008
Searches at the LHC: BSM physics
Many model for new physics are addressing two problems:
– the hierarchy/naturalness problem
– the origin of dark matter
→ spectrum of new particles at the TeV-scale with weakly interacting & stable particle
→ generic BSM signature at the LHC involves cascade decays with missing energy,
eg. supersymmetry
D_D
_204
7.c.
1
q
q
q
q
q~
~
~
~
—
—
—b
b
l+
l+
g
~g
W— W+t
t
t1
ν
χ1
~χ10
~χ20
Gluino/squark production event topology al lowing sparticle mass reconstruction
3 isolated leptons+ 2 b-jets+ 4 jets
+ Etmiss
~l
+
l-
Such cascade decays allow to reconstructsleptons, neutralinos, squarks, gluinos...in favorable cases with %level mass resolutions
Michael Kramer page 18 DPG Fruhjahrstagung 2008
Searches at the LHC: BSM physics
• simple discriminant for SUSY
searches: effective mass
Meff = ET,miss +∑4
i=1 pjetT
• excess of events with large Meff
→ initial discovery of SUSY
LHC Point 5
10-13
10-12
10-11
10-10
10-9
10-8
10-7
0 1000 2000 3000 4000Meff (GeV)
dσ/d
Mef
f (m
b/40
0 G
eV)
Michael Kramer page 19 DPG Fruhjahrstagung 2008
Searches at the LHC: BSM physics
• simple discriminant for SUSY
searches: effective mass
Meff = ET,miss +∑4
i=1 pjetT
• excess of events with large Meff
→ initial discovery of SUSY
Modern LO Monte Carlo tools predict much larger multi-jet background
What will disagreement between Monte Carlo and data mean?
→ Need precision NLO calculations to tell!
Michael Kramer page 20 DPG Fruhjahrstagung 2008
Searches at the LHC: BSM physics
• simple discriminant for SUSY
searches: effective mass
Meff = ET,miss +∑4
i=1 pjetT
• excess of events with large Meff
→ initial discovery of SUSY
Modern LO Monte Carlo tools predict much larger multi-jet background
What will disagreement between Monte Carlo and data mean?
→ Need precision NLO calculations to tell!
Michael Kramer page 20 DPG Fruhjahrstagung 2008
Searches at the LHC: outline
• Examples from Higgs physics
– discovery from excess of events: pp→ H → WW ∗ → l+νl−ν
– backgrounds: beware of cuts
– beyond discovery: measuring Higgs couplings
• Examples from beyond the standard model physics
– anomalous shapes: SUSY searches with multi-jets + ET,miss signatures
– backgrounds: multi-leg calculations needed
Theoretical tools for LHC physics
– LO and NLO multi-leg calculations
– matching with parton showers and hadronization
Michael Kramer page 21 DPG Fruhjahrstagung 2008
Theoretical tools for LHC physics
Need flexible and realistic precision calculations
– precise → including loops & many legs
– flexible → allowing for exclusive cross sections & phase space cuts
– realistic → matched with parton showers and hadronization
Mini review of current status for LHC QCD multi-leg
– LO calculations
– LO calculations & parton showers
– NLO calculations
– NLO calculations & parton showers
Note: focus on QCD tools for LHC cross section predictions. Do not cover important QCD and elec-
troweak precision calculations for masses, couplings, decays and renormalization group evolutions in
the SM and beyond. . .
Michael Kramer page 22 DPG Fruhjahrstagung 2008
LO calculations
Automation of LO calculations: several program packages exist for the automatic calcu-
lation of generic 2 → N cross sections (N ≤ 8) including integration over phase space:
HELAC/PHEGAS, MADGRAPH/MADEVENT, COMPHEP, GRACE, SHERPA/AMEGIC,
O’MEGA/WHIZARD, ALPGEN, ...
→ Non-trivial achievement:
consider number of Feynman graphs e.g. for gg → N gluons:
N jets 2 3 4 5 6 7 8
# diag’s 4 25 220 2485 34300 5 × 105 107
Michael Kramer page 23 DPG Fruhjahrstagung 2008
LO calculations
Automation of LO calculations: several program packages exist for the automatic calcu-
lation of generic 2 → N cross sections (N ≤ 8) including integration over phase space:
HELAC/PHEGAS, MADGRAPH/MADEVENT, COMPHEP, GRACE, SHERPA/AMEGIC,
O’MEGA/WHIZARD, ALPGEN, ...
→ Non-trivial achievement:
consider number of Feynman graphs e.g. for gg → N gluons:
N jets 2 3 4 5 6 7 8
# diag’s 4 25 220 2485 34300 5 × 105 107
Michael Kramer page 23 DPG Fruhjahrstagung 2008
LO calculations
Automation of LO calculations: several program packages exist for the automatic calcu-
lation of generic 2 → N cross sections (N ≤ 8) including integration over phase space:
HELAC/PHEGAS, MADGRAPH/MADEVENT, COMPHEP, GRACE, SHERPA/AMEGIC,
O’MEGA/WHIZARD, ALPGEN, ...
→ matrix element calculations crucial for the description of multi-leg processes:
(Mangano)
11
Exact, LO matrix
element estimate
Shower MC result
N.B . R eliability/system atics of M C tools: Shower M C vs M atrix elem ent results
Michael Kramer page 24 DPG Fruhjahrstagung 2008
LO calculations with parton showers & hadronization
Include parton showers and hadronization to sum soft/collinear parton emission
and predict realistic final states
→ Beware of double counting: N -jet cross section from 2 → N parton process or from 2 →
N − (1, 2, . . .) parton process plus parton shower
→ Construct matching schemes: CKKW-L (Catani, Kuhn, Krauss, Webber; Lonnblad), MLM (Mangano), SCET (Bauer,
Schwarz), implemented in HELAC, MADGRAPH, SHERPA, ARIADNE, ALPGEN
(Alwell et al.)
dσ/d
E⊥
1 (p
b/G
eV)
(a)Alpgen
AriadneHelac
MadEventSherpa
10-2
10-1
100
101
102
E⊥1 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200 250 300 350 400 450 500
dσ/d
E⊥
2 (p
b/G
eV)
(b)
10-2
10-1
100
101
102
E⊥2 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200 250 300 350 400
dσ/d
E⊥
3 (p
b/G
eV)
(c)
10-3
10-2
10-1
100
101
E⊥3 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200 250 300
dσ/d
E⊥
4 (p
b/G
eV)
(d)
10-3
10-2
10-1
100
101
E⊥4 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200
Validation, systematic comparison & tuning of MC tools crucial
Michael Kramer page 25 DPG Fruhjahrstagung 2008
LO calculations with parton showers & hadronization
Include parton showers and hadronization to sum soft/collinear parton emission
and predict realistic final states
→ Beware of double counting: N -jet cross section from 2 → N parton process or from 2 →
N − (1, 2, . . .) parton process plus parton shower
→ Construct matching schemes: CKKW-L (Catani, Kuhn, Krauss, Webber; Lonnblad), MLM (Mangano), SCET (Bauer,
Schwarz), implemented in HELAC, MADGRAPH, SHERPA, ARIADNE, ALPGEN
(Alwell et al.)
dσ/d
E⊥
1 (p
b/G
eV)
(a)Alpgen
AriadneHelac
MadEventSherpa
10-2
10-1
100
101
102
E⊥1 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200 250 300 350 400 450 500
dσ/d
E⊥
2 (p
b/G
eV)
(b)
10-2
10-1
100
101
102
E⊥2 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200 250 300 350 400
dσ/d
E⊥
3 (p
b/G
eV)
(c)
10-3
10-2
10-1
100
101
E⊥3 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200 250 300
dσ/d
E⊥
4 (p
b/G
eV)
(d)
10-3
10-2
10-1
100
101
E⊥4 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200
Validation, systematic comparison & tuning of MC tools crucial
Michael Kramer page 25 DPG Fruhjahrstagung 2008
LO calculations with parton showers & hadronization
Include parton showers and hadronization to sum soft/collinear parton emission
and predict realistic final states
→ Beware of double counting: N -jet cross section from 2 → N parton process or from 2 →
N − (1, 2, . . .) parton process plus parton shower
→ Construct matching schemes: CKKW-L (Catani, Kuhn, Krauss, Webber; Lonnblad), MLM (Mangano), SCET (Bauer,
Schwarz), implemented in HELAC, MADGRAPH, SHERPA, ARIADNE, ALPGEN
(Alwell et al.)
dσ/d
E⊥
1 (p
b/G
eV)
(a)Alpgen
AriadneHelac
MadEventSherpa
10-2
10-1
100
101
102
E⊥1 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200 250 300 350 400 450 500
dσ/d
E⊥
2 (p
b/G
eV)
(b)
10-2
10-1
100
101
102
E⊥2 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200 250 300 350 400
dσ/d
E⊥
3 (p
b/G
eV)
(c)
10-3
10-2
10-1
100
101
E⊥3 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200 250 300
dσ/d
E⊥
4 (p
b/G
eV)
(d)
10-3
10-2
10-1
100
101
E⊥4 (GeV)
-1-0.5
0 0.5
1
0 50 100 150 200
Validation, systematic comparison & tuning of MC tools crucial
Michael Kramer page 25 DPG Fruhjahrstagung 2008
NLO calculations
Want to test & explore models, eg. measure Higgs couplings
[Duhrssen et al.]
→ ratios of Higgs couplings can be measured with an accuracy of 10-30%
→ must be matched by theoretical accuracy in cross section and BR predictions
Michael Kramer page 26 DPG Fruhjahrstagung 2008
NLO calculations
An accuracy δσ/σ ∼< 20% is only possible at NLO or beyond!
for example σ(pp→ ttH) ∝ g2ttH
[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
⇒ δσ/σ ≈
{
100% LO
15% NLO
Michael Kramer page 27 DPG Fruhjahrstagung 2008
NLO calculations
cross sections are obtained from counting events after selection cuts
→ need acceptance and efficiency
→ need flexible (N)NLO calculations
modern (N)NLO calculations are set up as parton-level Monte Carlo programs
– e.g. at NLO using (dipole) subtraction [Catani, Seymour, Dittmaier, Trocsanyi, . . . ]
σNLO
=
Z
dPSm+1
»
dσreal
−dσsub
–
| {z }
finite
+
Z
dPSm
»
dσvirtual
+dσsub1
–
| {z }
finite
⇒ parton-level events (4-momenta) with positive or negative weights
– recent progress at NNLO, e.g. for Higgs production [Anastasiou, Melnikov, Petriello; Grazzini]
Note: (N)NLO parton-level Monte Carlo programs are not parton shower event generators
– they do not include parton showers and hadronization
– they do not generate unweighted events
Michael Kramer page 28 DPG Fruhjahrstagung 2008
NLO calculations
cross sections are obtained from counting events after selection cuts
→ need acceptance and efficiency
→ need flexible (N)NLO calculations
modern (N)NLO calculations are set up as parton-level Monte Carlo programs
– e.g. at NLO using (dipole) subtraction [Catani, Seymour, Dittmaier, Trocsanyi, . . . ]
σNLO
=
Z
dPSm+1
»
dσreal
−dσsub
–
| {z }
finite
+
Z
dPSm
»
dσvirtual
+dσsub1
–
| {z }
finite
⇒ parton-level events (4-momenta) with positive or negative weights
– recent progress at NNLO, e.g. for Higgs production [Anastasiou, Melnikov, Petriello; Grazzini]
Note: (N)NLO parton-level Monte Carlo programs are not parton shower event generators
– they do not include parton showers and hadronization
– they do not generate unweighted events
Michael Kramer page 28 DPG Fruhjahrstagung 2008
NLO calculations
cross sections are obtained from counting events after selection cuts
→ need acceptance and efficiency
→ need flexible (N)NLO calculations
modern (N)NLO calculations are set up as parton-level Monte Carlo programs
– e.g. at NLO using (dipole) subtraction [Catani, Seymour, Dittmaier, Trocsanyi, . . . ]
σNLO
=
Z
dPSm+1
»
dσreal
−dσsub
–
| {z }
finite
+
Z
dPSm
»
dσvirtual
+dσsub1
–
| {z }
finite
⇒ parton-level events (4-momenta) with positive or negative weights
– recent progress at NNLO, e.g. for Higgs production [Anastasiou, Melnikov, Petriello; Grazzini]
Note: (N)NLO parton-level Monte Carlo programs are not parton shower event generators
– they do not include parton showers and hadronization
– they do not generate unweighted events
Michael Kramer page 28 DPG Fruhjahrstagung 2008
(QCD-) NLO calculations at the LHC: status
2 → 2: anything you want. . . (cf. MCFM (Campbell, Ellis, . . . ))
2 → 3: pp → jjj (Bern, Dixon, Kosower; Kunszt, Signer, Troscanyi; Giele, Kilgore, Nagy)
pp → V jj (Campbell, Glover, Miller)
pp → Hjj[GF] (Campbell, Ellis, Zanderighi)
pp → Htt (Beenakker, Dittmaier, MK, Plumper, Spira, Zerwas; Dason, Reina, Wackeroth, Orr, Jackson;)
pp → γγj (de Florian, Kunszt; Del Duca, Maltoni, Nagy, Troscani, Binoth, Guillet, Mahmoudi)
pp → Hjj(j)[WBF] (Figy, Hankele, Oleari, Zeppenfeld)
pp → HHH (Plehn, Rauch; Binoth, Karg, Kauer, Ruckl)
pp → V V jj[WBF] (Jager, Oleary, Zeppenfeld)
pp → ZZZ (Lazopoulos, Melnikov, Petriello)
pp → WWZ (Hankele, Zeppenfeld)
pp → ttj (Dittmaier, Uwer, Weinzierl)
pp → V V j (Dittmaier, Kallweit, Uwer; Campbell, Ellis, Zanderighi; Binoth, Guillet, Karg, Kauer, Sanguinetti)
2 → 4: no LHC process yet. . .
Michael Kramer page 29 DPG Fruhjahrstagung 2008
An experimenters wishlist. . .
Theorists reply: In your dreams. . .
Michael Kramer page 30 DPG Fruhjahrstagung 2008
An experimenters wishlist. . .
Theorists reply: In your dreams. . .
Michael Kramer page 30 DPG Fruhjahrstagung 2008
An experimenters wishlist. . .
Main bottleneck for multi-leg NLO calculations:
tensor-reduction of Pentagon/Hexagon/Heptagon loop integrals, e.g.
77
89
:8
;:;
89
:8
<=> ?
With current techniques
pp→ 3 partons @ NLO is “straightforward but tedious”
pp→ 4 partons @ NLO is possible
Need breakthrough in technology for pp→ 4 partons @ NLO
spinors & twistors, on-shell methods. . . ?
⇒ NLO (parton-level) Monte Carlo programs will not be available for all potentially
relevant (background) processes in the near future
Michael Kramer page 31 DPG Fruhjahrstagung 2008
An experimenters wishlist. . .
Main bottleneck for multi-leg NLO calculations:
tensor-reduction of Pentagon/Hexagon/Heptagon loop integrals, e.g.
@@
AB
CA
DCD
AB
CA
EFG H
With current techniques
pp→ 3 partons @ NLO is “straightforward but tedious”
pp→ 4 partons @ NLO is possible
Need breakthrough in technology for pp→ 4 partons @ NLO
spinors & twistors, on-shell methods. . . ?
⇒ NLO (parton-level) Monte Carlo programs will not be available for all potentially
relevant (background) processes in the near future
Michael Kramer page 31 DPG Fruhjahrstagung 2008
An experimenters wishlist. . .
Main bottleneck for multi-leg NLO calculations:
tensor-reduction of Pentagon/Hexagon/Heptagon loop integrals, e.g.
II
JK
LJ
MLM
JK
LJ
NOP Q
With current techniques
pp→ 3 partons @ NLO is “straightforward but tedious”
pp→ 4 partons @ NLO is possible
Need breakthrough in technology for pp→ 4 partons @ NLO
spinors & twistors, on-shell methods. . . ?
⇒ NLO (parton-level) Monte Carlo programs will not be available for all potentially
relevant (background) processes in the near future
Michael Kramer page 31 DPG Fruhjahrstagung 2008
Need for NNLO at the LHC?
NNLO calculations are needed
– for high-precision measurements (αs, MW , pdf’s,. . . )
– if there are large corrections & scale dependence at NLO, eg. for gg → H
– if NLO accuracy is reduced after cuts:
Ht
g
g
g
is
{
NLO for σinclusive
LO for dσ/dpT
Michael Kramer page 32 DPG Fruhjahrstagung 2008
Need for NNLO at the LHC?
NNLO calculations are needed
– for high-precision measurements (αs, MW , pdf’s,. . . )
– if there are large corrections & scale dependence at NLO, eg. for gg → H
– if NLO accuracy is reduced after cuts:
Ht
g
g
g
is
{
NLO for σinclusive
LO for dσ/dpT
Michael Kramer page 32 DPG Fruhjahrstagung 2008
Need for NNLO at the LHC?
NNLO calculations are needed
– for high-precision measurements (αs, MW , pdf’s,. . . )
– if there are large NLO corrections & scale dependence, eg. for gg → H
– if NLO accuracy is reduced after cuts:
(Anastasiou, Dissertori, Stockli)
Michael Kramer page 33 DPG Fruhjahrstagung 2008
NLO calculations with parton showers & hadronization
Michael Kramer page 34 DPG Fruhjahrstagung 2008
NLO calculations with parton showers & hadronization
Fixed-oder calculations have limitations
– they do not predict realistic final states
experimentally theoretically at LO
Michael Kramer page 35 DPG Fruhjahrstagung 2008
NLO calculations with parton showers & hadronization
Fixed-oder calculations have limitations
– they do not predict realistic final states
experimentally theoretically at NLO
Michael Kramer page 36 DPG Fruhjahrstagung 2008
NLO calculations with parton showers & hadronization
Fixed-oder calculations have limitations
– they break down for certain kinematic configurations
[MK, Mrenna, Soper]
-0.1
0
0.1
0 5 10 15 20
e+e– → 3 jets: jet-mass distribution df3/dM [GeV-1]
NLO
(√s = MZ; µ = √s/6, kT algorithm, ycut = 0.05)
M [GeV]
⇒ wrong jet structure for M → 0
Michael Kramer page 37 DPG Fruhjahrstagung 2008
NLO calculations with parton showers & hadronization
Fixed-oder calculations have limitations
⇒ add parton showers → summation of multi-parton emission
[MK, Mrenna, Soper]
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20
e+e– → 3 jets: jet-mass distribution f -13 df3/dM [GeV-1]
NLO+Pythia
NLO
(√s = MZ; µ = √s/6, kT algorithm, ycut = 0.05)
M [GeV]
⇒ realistic jet structure and accurate (NLO) prediction for rate
Michael Kramer page 38 DPG Fruhjahrstagung 2008
NLO calculations with parton showers & hadronization
NLO⊕PS matching formalism
– avoid double counting: parton showers include part of the short-distance physics already
included in the NLO calculation
– various schemes have been proposed (Frixione, Webber, Nason, Oleari, Collins, Zu, Soper,MK, Nagy, Weinzierl, Giele, Kosower, Skands, Bauer, Schwarz,. . . )
MC@NLO (Frixione, Webber, . . . ) is still top of the class
– well tested and supported
– includes many processes: pp → V, H, ll, lν, QQ, HV, single top, V V
(Near?) future: variety of general NLO⊕PS matching formalisms
– independent of specific shower algorithm → combine NLO with any MC
– in terms of commonly used dipole subtraction formalism→ easy to use for NLO practitioner
Note: There are also new development in parton showers designed for NLO matching and showersincluding quantum interference (Gieseke, Stephens, Webber, Seymour, Siodmok,. . . ; Sjostrand, Skands,. . . ; Nagy, Soper; Dinsdale,
Ternick, Weinzierl, Schumann, Krauss; Giele, Kosower)
Michael Kramer page 39 DPG Fruhjahrstagung 2008
NLO calculations with parton showers & hadronization
NLO⊕PS matching formalism
– avoid double counting: parton showers include part of the short-distance physics already
included in the NLO calculation
– various schemes have been proposed (Frixione, Webber, Nason, Oleari, Collins, Zu, Soper,MK, Nagy, Weinzierl, Giele, Kosower, Skands, Bauer, Schwarz,. . . )
MC@NLO (Frixione, Webber, . . . ) is still top of the class
– well tested and supported
– includes many processes: pp → V, H, ll, lν, QQ, HV, single top, V V
(Near?) future: variety of general NLO⊕PS matching formalisms
– independent of specific shower algorithm → combine NLO with any MC
– in terms of commonly used dipole subtraction formalism→ easy to use for NLO practitioner
Note: There are also new development in parton showers designed for NLO matching and showersincluding quantum interference (Gieseke, Stephens, Webber, Seymour, Siodmok,. . . ; Sjostrand, Skands,. . . ; Nagy, Soper; Dinsdale,
Ternick, Weinzierl, Schumann, Krauss; Giele, Kosower)
Michael Kramer page 39 DPG Fruhjahrstagung 2008
NLO calculations with parton showers & hadronization
NLO⊕PS matching formalism
– avoid double counting: parton showers include part of the short-distance physics already
included in the NLO calculation
– various schemes have been proposed (Frixione, Webber, Nason, Oleari, Collins, Zu, Soper,MK, Nagy, Weinzierl, Giele, Kosower, Skands, Bauer, Schwarz,. . . )
MC@NLO (Frixione, Webber, . . . ) is still top of the class
– well tested and supported
– includes many processes: pp → V, H, ll, lν, QQ, HV, single top, V V
(Near?) future: variety of general NLO⊕PS matching formalisms
– independent of specific shower algorithm → combine NLO with any MC
– in terms of commonly used dipole subtraction formalism→ easy to use for NLO practitioner
Note: There are also new development in parton showers designed for NLO matching and showersincluding quantum interference (Gieseke, Stephens, Webber, Seymour, Siodmok,. . . ; Sjostrand, Skands,. . . ; Nagy, Soper; Dinsdale,
Ternick, Weinzierl, Schumann, Krauss; Giele, Kosower)
Michael Kramer page 39 DPG Fruhjahrstagung 2008
NLO calculations with parton showers & hadronization
NLO⊕PS matching formalism
– avoid double counting: parton showers include part of the short-distance physics already
included in the NLO calculation
– various schemes have been proposed (Frixione, Webber, Nason, Oleari, Collins, Zu, Soper,MK, Nagy, Weinzierl, Giele, Kosower, Skands, Bauer, Schwarz,. . . )
MC@NLO (Frixione, Webber, . . . ) is still top of the class
– well tested and supported
– includes many processes: pp → V, H, ll, lν, QQ, HV, single top, V V
(Near?) future: variety of general NLO⊕PS matching formalisms
– independent of specific shower algorithm → combine NLO with any MC
– in terms of commonly used dipole subtraction formalism→ easy to use for NLO practitioner
Note: There are also new development in parton showers designed for NLO matching and showersincluding quantum interference (Gieseke, Stephens, Webber, Seymour, Siodmok,. . . ; Sjostrand, Skands,. . . ; Nagy, Soper; Dinsdale,
Ternick, Weinzierl, Schumann, Krauss; Giele, Kosower)
Michael Kramer page 39 DPG Fruhjahrstagung 2008
Conclusions & outlook . . .
Signal cross sections in the SM and MSSM are (or will rather soon be) known at
NLO accuracy
– theoretical uncertainty ≈ 15% for inclusive cross sections
– larger uncertainty for exclusive observables
– can predict distributions and observables with cuts
– in general no parton showers/hadronization
Progress in matching (N)LO calculations with parton showers and hadronization
Many backgrounds (multi-leg processes) are only know at LO
(Need breakthrough in techniques to do pp→> 4 partons at NLO)
First LHC data will allow us to focus on the relevant processes. . .
Michael Kramer page 40 DPG Fruhjahrstagung 2008
Conclusions & outlook . . .
Signal cross sections in the SM and MSSM are (or will rather soon be) known at
NLO accuracy
– theoretical uncertainty ≈ 15% for inclusive cross sections
– larger uncertainty for exclusive observables
– can predict distributions and observables with cuts
– in general no parton showers/hadronization
Progress in matching (N)LO calculations with parton showers and hadronization
Many backgrounds (multi-leg processes) are only know at LO
(Need breakthrough in techniques to do pp→> 4 partons at NLO)
First LHC data will allow us to focus on the relevant processes. . .
Michael Kramer page 40 DPG Fruhjahrstagung 2008
Conclusions & outlook . . .
Signal cross sections in the SM and MSSM are (or will rather soon be) known at
NLO accuracy
– theoretical uncertainty ≈ 15% for inclusive cross sections
– larger uncertainty for exclusive observables
– can predict distributions and observables with cuts
– in general no parton showers/hadronization
Progress in matching (N)LO calculations with parton showers and hadronization
Many backgrounds (multi-leg processes) are only know at LO
(Need breakthrough in techniques to do pp→> 4 partons at NLO)
First LHC data will allow us to focus on the relevant processes. . .
Michael Kramer page 40 DPG Fruhjahrstagung 2008
Conclusions & outlook . . .
Signal cross sections in the SM and MSSM are (or will rather soon be) known at
NLO accuracy
– theoretical uncertainty ≈ 15% for inclusive cross sections
– larger uncertainty for exclusive observables
– can predict distributions and observables with cuts
– in general no parton showers/hadronization
Progress in matching (N)LO calculations with parton showers and hadronization
Many backgrounds (multi-leg processes) are only know at LO
(Need breakthrough in techniques to do pp→> 4 partons at NLO)
First LHC data will allow us to focus on the relevant processes. . .
Michael Kramer page 40 DPG Fruhjahrstagung 2008