Transverse Energy-Energy Correlation on Hadron Collidertpcsf.ihep.ac.cn/english/reports/2012.12.27.pdf · Transverse EEC at Hadron collider parton level: not realistic results leading

Transverse Energy-Energy Correlation on Hadron Collider

Wei Wang (王伟) Deutsches Elektronen-Synchrotron

Work with Ahmed Ali, Fernando Barreiro, Javier Llorente

arXiv: 1205.1689, Phys.Rev. D86, 114017(2012)

Content §  Introduction §  Energy-Energy Correlation @e+e- collision §  Transverse EEC @ hadron collider

§  Results at LHC with √s=7TeV

§  Summary and outlook

§  Dependence on PDF, scale §  Impact on αs measurement

§  Transverse EEC §  jet algorithm §  trigger efficiency

QCD n Quantum Chromodynamics (QCD), the gauge field theory that describes the strong interactions of colored quarks and gluons, is the SU(3) component of the SU(3)×SU(2)×U(1) Standard Model of Particle Physics.

QCD n Quantum Chromodynamics (QCD), the gauge field theory that describes the strong interactions of colored quarks and gluons, is the SU(3) component of the SU(3)×SU(2)×U(1) Standard Model of Particle Physics.

QCD _ (S ) = 0.1184 ± 0.0007s Z

0.1

0.2

0.3

0.4

0.5

_s (Q)

1 10 100Q [GeV]

Heavy Quarkoniae+e– AnnihilationDeep Inelastic Scattering

July 2009

0.11 0.12 0.13_ (S )s Z

Quarkonia (lattice)

DIS F2 (N3LO)

o-decays (N3LO)

DIS jets (NLO)

e+e– jets & shps (NNLO)

electroweak fits (N3LO)

e+e– jets & shapes (NNLO)

[ decays (NLO)

Jet event shape n Event-shape variables are functions of the four momenta in the hadronic final state that characterize the topology of an event’s energy flow. They are sensitive to QCD radiation (and correspondingly to the strong coupling) insofar as gluon emission changes the shape of the energy flow.

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inclusive jet productionin hadron-induced processes

fastNLOhepforge.cedar.ac.uk/fastnlo

pp

DIS

pp-bar

3s = 200 GeV

3s = 300 GeV

3s = 318 GeV

3s = 546 GeV

3s = 630 GeV

3s = 1800 GeV

3s = 1960 GeV

STAR 0.2 < |y| < 0.8

H1 150 < Q2 < 200 GeV2

H1 200 < Q2 < 300 GeV2

H1 300 < Q2 < 600 GeV2

H1 600 < Q2 < 3000 GeV2

ZEUS 125 < Q2 < 250 GeV2

ZEUS 250 < Q2 < 500 GeV2

ZEUS 500 < Q2 < 1000 GeV2

ZEUS 1000 < Q2 < 2000 GeV2

ZEUS 2000 < Q2 < 5000 GeV2

CDF 0.1 < |y| < 0.7

DØ |y| < 0.5

CDF 0.1 < |y| < 0.7DØ 0.0 < |y| < 0.5DØ 0.5 < |y| < 1.0

CDF cone algorithmCDF kT algorithm

(× 400)

(× 100)

(× 35)

(× 16)

(× 6)

(× 3)

(× 1)

all pQCD calculations using NLOJET++ with fastNLO:_s(MZ)=0.118 | CTEQ6.1M PDFs | µr = µf = pT jetNLO plus non-perturbative corrections | pp, pp: incl. threshold corrections (2-loop)

pT (GeV/c)

data

/ theo

ry

PDG live

Jet event shape: energy-energy correlation n Event-shape variables are functions of the four momenta in the hadronic final state that characterize the topology of an event’s energy flow. They are sensitive to QCD radiation (and correspondingly to the strong coupling) insofar as gluon emission changes the shape of the energy flow.

Jet event shape: energy-energy correlation n Event-shape variables are functions of the four momenta in the hadronic final state that characterize the topology of an event’s energy flow. They are sensitive to QCD radiation (and correspondingly to the strong coupling) insofar as gluon emission changes the shape of the energy flow.

n Energy-energy correlation (EEC): energy-weighted angular distributions

EEC@e+e-: state of the art

DELPHI dataDipole ShowerDipole Shower + NLO

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Energy-energy correlation, EEC

EE

C

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cos!

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When two jets are parallel, large logarithms will be generated. S. Platzer, S. Gieseke, NLO/NLL matching in matchbox method 1109.6256

Transverse EEC at Hadron collider

Normalized Transverse EEC:

v  boost invariant v  Almost

independent of structure functions


parton level: not realistic results

leading order in αs

collision energy at 540 GeV

Ali, Pietarinen, Stirling Phys. Lett. B 141, 447 (1984).

We will use the state-of-the-art PDFs, include the next-to-leading order corrections and compute the transverse EEC at hadron collider (LHC and Tevatron)!

Jet algorithm

Jet algorithm: definition of jet

Jet algorithm

anti-kT algorithm first handle energetic particles and then soft

anti-kT algorithm is more “cone-like”

Cacciari,Salam,Soyez, 0802.1189

ATLAS detector efficiency

Detector efficiency is very high.

But most events will be rejected.

ATLAS note:

ATL-COM-PHYS-2011-534

Monte Carlo simulation

Event generators: PYTHIA, Herwig++, WHIZARD, Sherpa

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incl

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HERWIG++ UE-7000-EE-3

HEJ + ARIADNE

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dijets > 35 GeV

Tp

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PYTHIA6 Z2

PYTHIA8 4C


HEJ + ARIADNE

CASCADE

= 7 TeVsCMS, pp,

dijets > 35 GeV

Tp

|y| < 4.7

Figure 1: Ratios of the inclusive to exclusive dijet cross sections as a function of the rapidityseparation |Dy| between the two jets, Rincl (left panel) and RMN (right panel), compared to thepredictions of the DGLAP-based MC generators PYTHIA6, PYTHIA8 and HERWIG++, as well asof CASCADE and HEJ+ARIADNE which incorporate elements of the BFKL approach. The shadedband indicates the size of the total systematic uncertainty of the data. Statistical uncertaintiesare smaller than the symbol sizes. Because of limitations in the CASCADE generator it was notpossible to obtain a reliable prediction for |Dy| > 8.

y|!|0 1 2 3 4 5 6 7 8 9

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1.5dataPYTHIA6 Z2PYTHIA8 4CHERWIG++

= 7 TeVsCMS, pp,

incldijets, R > 35 GeV

Tp

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= 7 TeVsCMS, pp,

MNdijets, R > 35 GeV

Tp

|y| < 4.7

Figure 2: Predictions for Rincl (left) and RMN (right) from DGLAP-based MC generators pre-sented as ratio to data corrected for detector effects. Both BFKL-motivated generators CASCADEand HEJ+ARIADNE (not shown) lead to a MC/data ratio well above unity. The shaded bandindicates the size of the total systematic uncertainty of the data while statistical uncertaintiesare shown as bars.

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incl

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52010 data

PYTHIA6 Z2

PYTHIA8 4C


HEJ + ARIADNE

CASCADE

= 7 TeVsCMS, pp,

dijets > 35 GeV

Tp

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y|!|0 1 2 3 4 5 6 7 8 9

MN

R

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52010 data

PYTHIA6 Z2

PYTHIA8 4C


HEJ + ARIADNE

CASCADE

= 7 TeVsCMS, pp,

dijets > 35 GeV

Tp

|y| < 4.7

Figure 1: Ratios of the inclusive to exclusive dijet cross sections as a function of the rapidityseparation |Dy| between the two jets, Rincl (left panel) and RMN (right panel), compared to thepredictions of the DGLAP-based MC generators PYTHIA6, PYTHIA8 and HERWIG++, as well asof CASCADE and HEJ+ARIADNE which incorporate elements of the BFKL approach. The shadedband indicates the size of the total systematic uncertainty of the data. Statistical uncertaintiesare smaller than the symbol sizes. Because of limitations in the CASCADE generator it was notpossible to obtain a reliable prediction for |Dy| > 8.

y|!|0 1 2 3 4 5 6 7 8 9

MC

/ da

ta

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= 7 TeVsCMS, pp,

MNdijets, R > 35 GeV

Tp

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Figure 2: Predictions for Rincl (left) and RMN (right) from DGLAP-based MC generators pre-sented as ratio to data corrected for detector effects. Both BFKL-motivated generators CASCADEand HEJ+ARIADNE (not shown) lead to a MC/data ratio well above unity. The shaded bandindicates the size of the total systematic uncertainty of the data while statistical uncertaintiesare shown as bars.

Ratios of the inclusive to exclusive dijet cross sections as a function of the rapidity separation of the two jets: PYTHIA can well describe the data.

CMS:1204.0696

Monte Carlo simulation: ET distribution

sumEtEntries 156667Mean 258.5RMS 79.25

0 100 200 300 400 500 600 700 800 900 10001

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sumEtEntries 156667Mean 258.5RMS 79.25

sumEt

Monte Carlo simulation: Jet multiplicity

jetNEntries 156667Mean 2.928RMS 0.9671

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510jetN

Entries 156667Mean 2.928RMS 0.9671

jetN

Processes with more than four jets in the final state are suppressed.

Small angle vs large angle region

EEC

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10

In endpoint region, large logarithms are produced, and have to be resummed. The small angle region is also correlated with the jet algorithm size R The NLO results are valid only in the intermediate region, |Cos(phi)|<0.8

Red: R=0.6 Blue: R=0.4

Small angle vs large angle region

EEC

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

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Asymmetry

NLOJET++

NLOJET++ is a C++ code for calculating LO and NLO order cross section on at e+e-, DIS and hadron collider, written by Zoltan Nagyz a bug in 6q interaction is fixed We modify NLOJET++ and use anti-kT algorithm. Two PDFs: MSTW and CT10 pT> 25 GeV pT1+pT2>500 GeV |y|<2.5 R=0.4 default scale choice For NLO results, we have generated 1010 events

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inclusive jet productionin hadron-induced processes

fastNLOhepforge.cedar.ac.uk/fastnlo

pp

DIS

pp-bar

3s = 200 GeV

3s = 300 GeV

3s = 318 GeV

3s = 546 GeV

3s = 630 GeV

3s = 1800 GeV

3s = 1960 GeV

STAR 0.2 < |y| < 0.8

H1 150 < Q2 < 200 GeV2

H1 200 < Q2 < 300 GeV2

H1 300 < Q2 < 600 GeV2

H1 600 < Q2 < 3000 GeV2

ZEUS 125 < Q2 < 250 GeV2

ZEUS 250 < Q2 < 500 GeV2

ZEUS 500 < Q2 < 1000 GeV2

ZEUS 1000 < Q2 < 2000 GeV2

ZEUS 2000 < Q2 < 5000 GeV2

CDF 0.1 < |y| < 0.7

DØ |y| < 0.5

CDF 0.1 < |y| < 0.7DØ 0.0 < |y| < 0.5DØ 0.5 < |y| < 1.0

CDF cone algorithmCDF kT algorithm

(× 400)

(× 100)

(× 35)

(× 16)

(× 6)

(× 3)

(× 1)

all pQCD calculations using NLOJET++ with fastNLO:_s(MZ)=0.118 | CTEQ6.1M PDFs | µr = µf = pT jetNLO plus non-perturbative corrections | pp, pp: incl. threshold corrections (2-loop)

pT (GeV/c)

data

/ theo

ry


!cos

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)!

/d(c

os

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d#

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LO Prediction, MSTW2008 PDF

LO Prediction, CT10 PDF

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NLO Prediction, MSTW2008 PDF

NLO Prediction, CT10 PDF

PDF dependence: the PDF-related differences on the transverse EEC are negligible, with the largest difference found in some bins amounting to 3%.


Scale dependence is significantly reduced when NLO corrections are taken into account.

!cos

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maxT = E

Rµ =

FµLO Prediction,

/2maxT = E

Rµ =

FµLO Prediction,

maxT = 2E

Rµ =

FµLO Prediction,

!cos

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

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maxT = E

Rµ =

FµNLO Prediction,

/2maxT = E

Rµ =

FµNLO Prediction,

maxT = 2E

Rµ =

FµNLO Prediction,


!cos

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d#

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(a)LO Prediction

NLO PredictionPythia Prediction

!cos

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

K-F

act

or

0.9

1

1.1

1.2

1.3NLO / LONLO / Pythia

(c)

Effects of the NLO corrections are discernible, both compared to the LO and PYTHIA8. The NLO corrections distort the shape of the transverse EEC.

EEC K-factor


!cos

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(b)LO Prediction

NLO PredictionPythia Prediction

Transverse EEC asymmetry is defined as

2

The first sum on the right-hand side in the second of the

above equations is over the events A with total transverse

energy EAT =

⇤a ET

Aa ⇤ Emin

T , with the EminT set by the

experimental setup. The second sum is over the pairs of

partons (a, b) whose transverse momenta have relative

azimuthal angle ⇧ to ⇧+�⇧.In leading order QCD, the transverse energy spectrum

d⌅/dET is a convolution of the parton distribution func-

tions (PDFs) with the 2 ⇧ 2 hard scattering partonic

subprocesses. Away from the end-points, i.e., for ⇧ ⌃= 0⇥

and ⇧ ⌃= 180⇥, in the leading order in �s, the energy-

weighted cross section d2⇥/dET d⇧ involves the convolu-

tion of the PDFs with the 2 ⇧ 3 subprocesses, such as

gg ⇧ ggg. Thus, schematically, the leading contribution

for the transverse EEC function is calculated from the

following expression:

1

⌅⌅d⇥⌅

d⇧=

⇥ai,bifa1/p(x1)fa2/p(x2) ⌃ ⇥̂a1a2⇤b1b2b3

⇥ai,bifa1/p(x1)fa2/p(x2) ⌃ ⌅̂a1a2⇤b1b2, (2)

where ⇥̂a1a2⇤b1b2b3 is the transverse energy-energy

weighted partonic cross section, xi (i = 1, 2) are the

fractional longitudinal momenta carried by the partons,

fa1/p(x1) and fa2/p(x2) are the PDFs, the ⌃ denotes a

convolution over the appropriate variables. The function

defined in Eq. (2) depends not only on ⇧, but also on

the ratio EminT /

⌥s and the rapidity variable ⇥. In gen-

eral, the numerator and the denominator in Eq. (2) have

a di⇤erent dependence on these variables, as the PDFs

are weighted di⇤erently. Hence, this function in hadronic

collisions is an “average” angular function, weighted ac-

cording to the di⇤erent PDFs, as opposed to its e+e�

counterpart, in which case there is no initial state QCD

radiation involved. However, as already observed in [16],

certain normalized distributions for the various subpro-

cesses contributing to the 2 ⇧ 3 hard scatterings are

similar, and the same combination of PDFs enters in the

2 ⇧ 2 and 2 ⇧ 3 cross sections, hence the transverse

EEC cross section is to a good approximation indepen-dent of the PDFs (see, Fig. 1 in [16]). Thus, for a fixed

rapidity range |⇥| < ⇥c and the variable ET/⌥s, one has

an approximate factorized result, which in the LO in �s

reads as

1

⌅⌅d⇥⌅

d⇧⌅ �s(µ)

⇤F (⇧) , (3)

where µ is a factorization scale. The function F (⇧) andthe corresponding tranverse EEC asymmetry defined as

1

⇥⌅d⇥⌅asy

d⇧⇥ 1

⇥⌅d⇥⌅

d⇧|⇥ � 1

⇥⌅d⇥⌅

d⇧|��⇥ , (4)

were worked out in [16] in the leading order of �s for the

CERN SPS pp̄ collider at⌥s = 540 GeV. In particular,

it was shown that the transverse EEC functions for the

gg-, gq- and qq̄-scatterings had very similar shapes, and

their relative contributions were found consistent to a

good approximation with the ratio of the corresponding

color factors 1:4/9:16/81 for the gg, gq(= gq̄) and qq̄initial states over a large range of ⇧. The relative cross

sections get closer to this ratio of the color factors for the

backward angles (⇧ ⌅ 180⇥), as expected in the leading

log approximation. However, the ratios hold also in the

angular region where the sub-leading contributions are

not expected to follow the color factor ratio.

We have used the existing program NLOJET++ [9],

which has been checked in a number of independent

NLO jet calculations [21], to compute the transverse EEC

and its asymmetry AEEC in the NLO accuracy for the

LHC proton-proton center-of-mass energy⌥s = 7 TeV.

Schematically, this entails the calculations of the 2 ⇧ 3

partonic subprocesses in the NLO accuracy and of the

2 ⇧ 4 partonic processes in the leading order in �s(µ),which contribute to the numerator on the r.h.s. of Eq. (2).

We have restricted the azimuthal angle range by cutting

out regions near ⇧ = 0⇥ and ⇧ = 180⇥. This would,

in particular, remove the self-correlations (a = b) and

frees us from calculating the O(�2s) (or two-loop) virtual

corrections to the 2 ⇧ 2 processes. Thus, with the az-

imuthal angle cut, the numerator in Eq. (2) is calculated

from the 2 ⇧ 3 and 2 ⇧ 4 processes to O(�4s). The

denominator in Eq. (2) includes the 2 ⇧ 2 and 2 ⇧ 3

processes, which are calculated up to and including the

O(�3s) corrections.

In the NLO accuracy, one can express the EEC cross

section as

1

⌅⌅d⇥⌅

d⇧⌅ �s(µ)

⇤F (⇧)

�1 +

�s(µ)

⇤G(⇧)

⇥. (5)

It is customary to lump the NLO corrections in a so-

called K-factor (which, in general, is a non-trivial func-

tion of ⇧), defined as

K(⇧) ⇥ 1 +�s(µ)

⇤G(⇧) . (6)

The principal result of this Letter is the calculation of

the NLO function K(⇧) and in demonstrating the insen-

sitivity of the EEC and the AEEC functions, calculated

to NLO accuracy, to the various intrinsic parametric and

underlying event uncertainties.

We now give details of the computations: In tran-

scribing the NLOJET++ [9] program, we have replaced

the default structure functions therein by the state of

the art PDFs, for which we use the MSTW [22] and

the CT10 [23] sets, and have also replaced the kT jet


!cos

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(a)

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(b)


Integrated transverse EEC asymmetry with the dependence on αs

where we have symmetrized the dominant uncertainty from the scale-variance.

B. Malaescu, P. Starovoitov arXiv:1203.5416

§  Jets and event shapes are useful tools to test QCD §  We explored the transverse EEC at hadron collider

v  boost invariant v  Almost independent of structure functions v  Show low sensitivity to scale v  Do not depend on modeling underlying events v  Preserve sensitivity to αs

Summary

These measurements will prove to be powerful techniques for the quantitative tests of perturbative QCD using event shape variables and in the measurement of αs in hadron colliders.

OutLook

Collisions with various choices of inputs

Comparison with the available data

Njet: S. Badger, B. Biedermann, P. Uwer, V. Yundin

Back-to-back and collinear region: have to deal with large logarithms

resummation effects in collaboration with Eduard Kuraev

Matchbox within Herwig++:Judith Katzy, Jan Kotanski and Simon Plaetzer

Thank you for your attention!

Current results for αs at hadron collider

B. Malaescu and P. Starovoitov

Documents

Transverse Energy-Energy Correlation on Hadron Collidertpcsf.ihep.ac.cn/english/reports/2012.12.27.pdf · Transverse EEC at Hadron collider parton level: not realistic results leading