Date post: | 19-Dec-2015 |
Category: |
Documents |
View: | 218 times |
Download: | 2 times |
Peter Uwer*)
Universität Karlsruhe
*) Financed through Heisenberg fellowship and SFB-TR09
Graduiertenkolleg “Physik an Hadronbeschleunigern”, Freiburg 07.11.07
ppttj and ppWWj at next-to-leading order in QCD
Work in collaboration with S.Dittmaier, S. Kallweit and S.Weinzierl
3
Preliminaries
Technicalities Physics
Experts Non-Experts
Outline of the main problems/issues/challenges with only brief description of methods used
5
Residual scale dependence
Quantum corrections lead to scale dependence of the coupling constants, i.e:
Large residual scale dependence of the Born approximation
In particular, if we have high powers of s:
6
Scale dependence
For ≈ mt and a variation of a factor 2 up and down:
1 2 3 4 n
20 %
40 %
30 %
10 %
22QCD
23QCD
24QCD
In addition we have also the factorization scale...
Need loop corrections to make quantitative predictions
Born approximation gives only crude estimate!
7
Corrections are not small...
Top-quark pair production at LHC:
~30-40%
/mt
[Dawson, Ellis, Nason ’89, Beenakker et al ’89,’91,Bernreuther, Brandenburg, Si, P.U. ‘04]
Scale independent corrections are also important !
8
...and difficult to estimate
WW production via gluon fusion:
tot = no cuts, std = standard LHC cuts, bkg = Higgs search cuts
30 % enhancement due to an “NNLO” effect (s2)
[Duhrssen, Jakobs, van der Bij, Marquard 05Binoth, Ciccolini,Kauer Krämer 05,06]
9
To summarize:
NLO corrections are needed because
● Large scale dependence of LO predictions…
● New channels/new kinematics in higher orders can have important impact in particular in the presence of cuts
● Impact of NLO corrections very difficult to predict without actually doing the calculation
11
WW + 1 Jet ― Motivation
● For 155 GeV < mh < 185 GeV, H WW is important channel
● In mass range 130 ―190 GeV, VBF dominates over ggH
NLO corrections for VBF known [Han, Valencia, Willenbrock 92Figy, Oleari, Zeppenfeld 03,Berger,Campbell 04, …]
Signal:
Background reactions:
WW + 2 Jets, WW + 1 Jet
If only leptonic decay of W´s and 1 Jet is demanded(improved signal significance)
Higgs search:
two forward tagging jets + Higgs
NLO corrections unknown
Top of the Les Houches list 07
12
t t + 1 Jet ― Motivation
Important signal process
- Top quark physics plays important role at LHC
- Large fraction of inclusive tt are due to tt+jet
- Search for anomalous couplings
- Forward-backward charge asymmetry (Tevatron)
- Top quark pair production at NNLO ?
- New physics ?
- Also important as background (H via VBF)
LHC is as top quark factory
14
Next-to leading order corrections
Experimentally soft and collinear partons cannot be resolved due to finite detector resolution
Real corrections have to be included
The inclusion of real corrections also solves the problemof soft and collinear singularities*)
Regularization needed dimensional regularisation
1
n
1
n
* 1
n+1
*) For hadronic initial state additional term from factorization…
*)
15
Ingredients for NLO
1
n
1
n
*
1
n+1
1
n+1
1
n
1
n
+
Many diagrams, complicated structure,
Loop integrals (scalar and tonsorial)divergent (soft and mass sing.)
Many diagrams,divergent (after phase space integ.)
Combination procedure to addvirtual and real corrections
16
How to do the cancellation in practice
Consider toy example:
Phase space slicing method:
Subtraction method [Frixione,Kunszt,Signer ´95, Catani,Seymour ´96, Nason,Oleari 98, Phaf, Weinzierl, Catani,Dittmaier,Seymour, Trocsanyi ´02]
[Giele,Glover,Kosower]
17
Dipole subtraction method (1)
How it works in practise:
Requirements:
in all single-unresolved regions
Due to universality of soft and collinear factorization,general algorithms to construct subtractions exist
[Frixione,Kunszt,Signer ´95, Catani,Seymour ´96, Nason,Oleari 98, Phaf, Weinzierl, Catani,Dittmaier,Seymour, Trocsanyi ´02]
Recently: NNLO algorithm [Daleo, Gehrmann, Gehrmann-de Ridder, Glover, Heinrich, Maitre]
18
Dipole subtraction method (2)
Universal structure:
Generic form of individual dipol:Leading-order amplitudes
Vector in color space
Color charge operators,induce color correlation
Spin dependent part,induces spin correlation
universal
Example ggttgg: 6 different colorstructures in LO,
36 (singular) dipoles
! !
Universality of soft and coll. Limits!
19
Dipole subtraction method — implementation
LO – amplitude, with colour information,
i.e. correlations
List of dipoles we want to calculate
0
1234
5
reduced kinematics,“tilde momenta” + Vij,k
Dipole di
21
Leading order amplitudes ― techniques
Many different methods to calculate LO amplitudes exist
We used:
● Berends-Giele recurrence relations
● Feynman-diagramatic approach
● Madgraph based code
Issues:
Speed and numerical stability
Helicity bases
(Tools: Alpgen [MLM et al], Madgraph [Maltoni, Stelzer], O’mega/Whizard [Kilian,Ohl,Reuter],…)
23
Virtual corrections
Issues:
● Scalar integrals
● How to derive the decomposition?
Traditional approach: Passarino-Veltman reduction
Scalar integrals
Large expressions numerical implementation
Numerical stability and speed are important
25
Reduction of tensor integrals — what we did…
Reduction à la Passarino-Veltman,with special reduction formulae in singular regions, two complete independent implementations !
Five-point tensor integrals:
Four and lower-point tensor integrals:
● Apply 4-dimensional reduction scheme, 5-point tensor
integrals are reduced to 4-point tensor integrals
Based on the fact that in 4 dimension 5-point integrals can be reduced to 4 point integrals
No dangerous Gram determinants!
[Melrose ´65, v. Neerven, Vermaseren 84]
[Denner, Dittmaier 02]
● Reduction à la Giele and Glover [Duplancic, Nizic 03, Giele, Glover 04]
Use integration-by-parts identities to reduce loop-integralsnice feature: algorithm provides diagnostics and rescue system
26
What about twistor inspired techniques ?
● For tree amplitudes no advantage compared to Berends-Giele like techniques (numerical solution!)
● In one-loop many open questions
– Spurious poles
– exceptional momentum configurations
– speed
My opinion:
● For tree amplitudes tune Berends-Giele for stability and speed taking into account the CPU architecture of the LHC periode: x86_64
● For one-loop amplitudes have a look at cut inspired methods
28
tt + 1-Jet production
Sample diagrams (LO):
Partonic processes:
related by crossing
One-loop diagrams (~ 350 (100) for gg (qq)):
Most complicated 1-loop diagrams pentagons of the type:
29
Leading-order results — some features
Observable: ● Assume top quarks as always tagged
● To resolve additional jet demand minimum kt of 20 GeV
Note:● Strong scale dependence of LO result
● No dependence on jet algorithm
● Cross section is NOT small
LHCTevatron
30
Checks of the NLO calculation
● Leading-order amplitudes checked with Madgraph
● Subtractions checked in singular regions
● Structure of UV singularities checked
● Structure of IR singularities checked
Most important:
● Two complete independent programs using a complete different tool chain and different algorithms, complete numerics done twice !
Virtual corrections:
QGraf — Form3 — C,C++
Feynarts 1.0 — Mathematica — Fortran77
31
Top-quark pair + 1 Jet Production at NLO[Dittmaier, P.U., Weinzierl PRL 98:262002, ’07]
● Scale dependence is improved
● Sensitivity to the jet algorithm
● Corrections are moderate in size
● Arbitrary (IR-safe) obserables calculable
Tevtron LHC
work in progress
32
Forward-backward charge asymmetry (Tevatron)
● Numerics more involved due to cancellations, easy to improve
● Large corrections, LO asymmetry almost washed out● Refined definition (larger cut, different jet algorithm…) ?
Effect appears already in top quark pair production
[Kühn, Rodrigo]
[Dittmaier, P.U., Weinzierl PRL 98:262002, ’07]
33
Differential distributions
Preliminary *)
*) Virtual correction cross checked, real corrections underway
34
pT distribution of the additional jet
Corrections of the oder of 10-20 %,again scale dependence is improved
LHCTevtron
36
Top quark pt distribution
The K-factor is nota constant!
Phase space dependence, dependence on the observable
Tevtron
37
WW + 1 Jet
Leading-order – sample diagrams
Next-to-leading order – sample diagramsNext-to-leading order – sample diagrams
Many different channels!
38
Checks
Similar to those made in tt + 1 Jet
Main difference:
Virtual corrections were cross checked using LoopTools[T.Hahn]
39
Scale dependence WW+1jet
Cross section defined as in tt + 1 Jet
[Dittmaier, Kallweit, Uwer 07]
[NLO corrections have been calculated also by Ellis,Campbell, Zanderighi t0+1d]
40
Cut dependence[Dittmaier, Kallweit, Uwer 07]
Note: shown results independent from the decay of the W´s
41
Conclusions
● NLO calculations are important for the success of LHC
● After more than 30 years (QCD) they are still difficult
● Active field, many new methods proposed recently!
● Many new results
General lesson:
42
Conclusions
Top quark pair + 1-Jet production at NLO:
● Two complete independent calculations
● Methods used work very well
● Cross section corrections are under control
● Further investigations for the FB-charge
asymmetry necessary (Tevatron)
● Preliminary results for distributions
43
Conclusions
WW + 1-Jet production at NLO:
● Two complete independent calculations
● Scale dependence is improved (LHC jet-veto)
● Corrections are important
[Gudrun Heinrich ]
44
Outlook
● Proper definition of FB-charge asymmetry
● Further improvements possible
(remove redundancy, further tuning, except. momenta,…)
● Distributions
● Include decay
● Apply tools to other processes