Phenomenological studies of top-pair production at NLO

Phenomenological studies of 

top-pair production at NLO 

Malgorzata Worek 

Wuppertal University 

XXXV International Conference of Theoretical Physics, Ustron’11 

12-18 September 20011, Ustron, Poland 1

Outline 

General motivation for NLO QCD calculations 

HELAC-NLO in a nutshell 

ttbb, ttjj, Htt, WWbb 

Applications: WWbb & ttjj @ TeVatron and LHC 

Summary & Outlook 

2

HELAC-NLO Group 

G. Bevilacqua (RWTH Aachen) 

M. Czakon (RWTH Aachen) 

M.V. Garzelli (Debrecen Uni.) 

A. van Hameren (INP Krakow) 

I. Malamos (Nijmegen Uni.) 

C. G. Papadopoulos (INP Athens) 

R. Pittau (Granada Uni.) 

M. Worek (Wuppertal Uni.) 

 

 

 

 

 

 

Contributors: 

A. Kanaki 

A. Cafarella 

P. Draggiotis (Valencia Uni.) 

G. Ossola (New York Uni.) 

3

Introduction 

8-10 partons in the final state @ LO, well separated to avoid divergences 

Standard Model and beyond tools @ tree level (just few examples) 

ALPGEN, AMEGIC++/SHERPA, CARLOMAT, COMIX/SHERPA, 

COMPHEP, HELAC-PHEGAS, MADGRAPH/MADEVENT, 

O'MEGA/WHIZARD, ... 

General purpose Monte Carlo programs (parton shower, hadronization, 

multiple interactions, hadrons decays, etc.) 

HERWIG, HERWIG++, PYTHIA 6.4, PYTHIA 8.1, SHERPA, ... 

High sensitivity to unphysical input scales 

Higher order calculations are needed to improve accuracy of prediction 

4

Motivation for NLO 

Stabilizing the scale in the QCD input parameters: 

Strong coupling constant and PDFs 

More reliable theoretical error related to the scale dependence 

Normalization and shape of distributions first known at NLO 

Many scale processes: V+ jets, ttH, tt + jets, bb + jets, njets ... 

How do we know which scale to choose ? 

Improved description of jets 

Jets: LO NLO Parton Hadron 

Shower 

Level 

5

Structure of NLO 

Calculations 

 

σ NLO = 

 

= 

m 

m 

 

dσ B + 

 

dσ B + 

m+1 

m+1 

 

dσ R − 

m+1 

 

dσ A + 

 

dσ R − dσ D 

+ 

m 

m+1 

 

dσ A + 

m 

dσ V 

 

dσ V + dσ I + dσ KP 

Catani-Seymour subtraction scheme 

At NLO: dσ R with m+1 partons and dσ V with m partons in the final 

Separately divergent although their sum is finite 

dσ A is a proper approximation of dσ R 

i. same singular behavior point-by-point 

ii. integrable over extra parton degrees of freedom 

Individual contributions finite. MC integration can be performed !



 


 

= 

m 

m 

 

dσ B + 

 

dσ B + 

m+1 

m+1 

 

dσ R − 

m+1 

 

dσ A + 

 


+ 

m 

m+1 

 

dσ A + 

m 

dσ V 

 


Three main building blocks are needed 

Evaluation of one-loop amplitude - HELAC-1LOOP 

Determination of coefficients via reduction method 

Reduction at integrand level - OPP method - CUTTOOLS 

Evaluation of scalar functions - ONELOOP 

Ossola, Papadopoulos, Pittau ‘07, ’08 

Draggiotis, Garzelli, Papadopoulos, Pittau ’09 

Garzelli, Malamos, Pittau ’09 

van Hameren, Papadopoulos, Pittau ’09 

van Hameren, ’10 

7



 


 

= 

m 

m 

 

dσ B + 

 

dσ B + 

m+1 

m+1 

 

dσ R − 

m+1 

 

dσ A + 

 


+ 

m 

m+1 

 

dσ A + 

m 

dσ V 

 


HELAC-DIPOLES - complete, public and automatic Catani-Seymour dipoles 

Extended for arbitrary polarizations 

Monte Carlo over polarization states of external particles 

Monte Carlo over color 

Phase space restriction on the dipoles phase space 

Less dipole subtraction terms per event 

Increased numerical stability 

Reduced missed binning problem 

Czakon, Papadopoulos, Worek '09 

8

One-loop amplitude 

and rational part 

Reduction of tensor integrals 

OPP coefficients and rational part 

HELAC-1LOOP 

CUTTOOLS 

pp → t¯tjj 

HELAC-NLO 

HELAC- 

DIPOLES 

ONELOOP 

Catani-Seymour dipole subtraction 

for massless and massive cases 

Scalar integrals 

9

Top Quark 

Produced in hadron-hadron collisions through strong interactions 

Decays without forming hadrons through the single mode tW b 

Distinguished by its large mass, close to EW symmetry breaking scale 

Unique property raises questions: 

Is the top quark mass generated by the Higgs mechanism ? 

Does it play more fundamental role ? 

Are there new particles lighter than the top quark ? 

Does the top quark decay into them ? 

Could non-SM physics manifest itself in non-standard couplings of top 

quark which show up as anomalies in top quark production and decays? 

Top quark physics tries to answer all these questions 

Properties of the top quark have already been examined at the Tevatron 

LHC is a top factory, producing about 8 million tt pairs per 

experiment per year at low luminosity (10 fb 1 /year) 

10

Top Pair Production 

Complete off-shell effects @ NLO 

Double-, single- and non-resonant 

top contributions of the order O( s3 4 ) 

Complex-mass scheme for unstable top 

W gauge bosons are treated off-shell 

pp(p¯p) → e + ν e µ − ν µ b¯b + X 

Sum over helicities and color via MC 

LO + V obtained by reweighting of tree 

level unweighted events 

Dipole channels for subtracted real part 

Check of Ward identity for virtual part 

Cancellation of divergences 

max independence test for real part 

Bevilacqua, Czakon, van Hameren, Papadopoulos, Worek ’11 

11


TeVatron 

LO & NLO scale dependence 

σ LO = 34.922 +40% 

−26% fb 

σ NLO = 35.727 −4% 

−8% fb 

K = 1.023 

LHC 

σ LO = 550.538 +37% 

−25% fb 

σ NLO = 808.665 +4% 

−9% fb 

K = 1.47 


12



Differential cross section 

Fixed scale m t 

Not rescale LO shapes 

Distortions 15% - 80% 

For angular distributions 

corrections 5% - 10% 


13


LHC 

Differential cross section 

Fixed scale m t 

Corrections 50% - 60 % 

Relatively constant 

H T distorted up to 80% 


14



A t FB =0.051 

A b FB =0.033 

A + 

FB =0.034 

top quarks are emitted in the 

direction of incoming protons 

 

A t y>0 

FB = 

N t(y) − y0 N t(y)+ y

Top Pair + 2 Jets 

Important background for Higgs searches @ Tevatron and @ LHC 

H WW ∗ produced via weak boson fusion 

For m H ~ 130 GeV, i.e. when BR(H WW ∗ ) is large enough 

Higgs boson mass peak cannot be directly reconstructed 

Background processes can not be measured from the side bands 

H bb produced via associated production with a tt pair 

Process useful only in the low mass range m H < 135 GeV 

Unique access to the top and bottom Yukawa couplings 

Reconstruction of the H bb mass peak difficult 

The bb pair can be chosen incorrectly 

b-tagging efficiency, two b-jets can arise from mistagged light jets 

Very precise knowledge of QCD backgrounds 

ttjj, ttbb, WWjj is necessary ! 

16


Partonic subprocesses 

Number of Feynman diagrams 

Number of dipoles 

As a measure of complexity 

dσ R − dσ D 

dσ V 

Bevilacqua, Czakon, Papadopoulos, Worek ’10 ‘11 

17



σ LO =0.3584 +94% 

−45% pb 

σ NLO =0.2709 +0.5% 

−21% pb 

94% 21% 

K = 0.76 -24% 

Total cross sections 

with different jets 

separation cuts R jj 

and the jet resolution 

parameters R 

K = 0.86 -14% 


18



Corrections to p T and m tt 

are substantial 

Do not simply rescale the 

LO shapes 

Induce distortions 40% 

For H T even 50% 60% 

deformations 


19



Angular distributions 

Negative and moderate 

corrections 

15% 30% 

Relatively constant 


20


A t FB,LO = −0.103 +0.003 

−0.004 

A t FB,NLO = −0.046 +0.005 

−0.006 

anti-top quarks are emitted in the 

direction of incoming protons 

(forward direction by definition) 

with a consistent expansion in s 

A t FB,NLO = −0.058 +0.014 

−0.042 

unexpanded ratio of the NLO cross sections 


21


LHC 

σ LO = 13.398 +87% 

−43% pb 

σ NLO =9.82 −15% 

−15% pb 

87% 15% 

K = 0.73 -27% 

Total cross sections 

with different jets 

separation cuts R jj 

and the jet resolution 

parameters R 

K = 0.86 -14% 


22

LHC 


m tt 20% 30% corrections 

p T up to 60% distortions 

H T even 80% deformations 

Corrections are substantial 

and do not simply rescale 

LO shapes 

Bevilacqua, Czakon, Papadopoulos, Worek ‘10 ’11 

23

LHC 


NLO QCD corrections 

are negative and 

relatively constant 

Angular distributions 

20% 30% corrections 

Bevilacqua, Czakon, Papadopoulos, Worek ’1o ‘11 

24

Summary & Outlook 

Already calculated by HELAC-NLO: ttbb, ttjj, Htt, WWbb 

ttbb, WWbb completed by two groups 

Permille level agreement in both cases! 

Much wider study for ttjj: variation of the center of mass energy, jet 

algorithms, cone size in jet algorithm, transverse momentum cuts 

HELAC-NLO 

Complete tool at NLO built around HELAC‐PHEGAS: 

HELAC‐1LOOP, CUTTOOLS, ONELOOP, HELAC‐DIPOLES 

Other processes from NLO Wishlist under attack 

Constant improvements in speed and functionality 

Interfaced to PYTHIA and HERWIG showers via POWHEG-BOX: ttj, ttH 

Decays of massive particles, showering and hadronization 

Final results at the hadron level 

http://helac-phegas.web.cern.ch/helac-phegas/ 

25

Phenomenological studies of top-pair production at NLO

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