QCD Physics with CMS detector
Olga Kodolova, SINP MSU(on behalf of CMS collaboration)

20th Lomonosov Conference on Elementary Particle Physics , 19-25 August, Moscow, Russian Federation1

Outline
Motivationl Soft physics
l Hard physicsl Summaryl2Motivation
QCD is the theory that explainsstrong interactions as part of theStandard Model

What is new at LHC:
Probing the new territory(x,Q2) range

Why we need to study:- Important background for new
territory in physics searches
enormous cross section: QCD canhide many possible signals of new
physics

What we need to study:- parton structure,- constrain the strong coupling- all other pQCD theory components- study non-perturbative effects- tune Monte-Carlo generators- QCD defines the hadronization
process of partons whateverinteraction mediator is in thehard production vertex

How do we proceed?

Collect puzzles!

3

QCD at hadron collidersµF – factorization scale separates longand short distance physics
aS (µR) – running coupling constantµR – renormalization scale
Q2 = -q2 – transferred momentum

Soft underlying event

h1

i

j

h2
X

F(Q)

p1=x1P1
p2=x2P2

Factorization theorem

Hard interaction: productionof the high-pT objects

σ (P h , P h )= ∑ i , j ∫ dx1 dx 2 f i/ h ( x1 , μ 2F ) f j / h (x 2 , μ 2F ) σ̂ ij ( p1 , p2 , α S (μ R ), Q 2 ; μ 2F , μ 2R )
1

2

1

2

Parton distributionfunction (PDF)
Soft interaction: production of
the low-pT hadrons

Partonic cross-section
computed in pQCDnασ̂ ij = α ∑ n ( πS ) σ nijkSFixed order pQCD

4

propagation
towards particles
levelparticles

How do we proceed
unfo
tow lding
ards
part
icl

Hard interaction cross-section
Parton Distribution Functions
Parton showering details

Reconstructedes l
eve particles,
l reconstructed jets
Measured
Cross-sections
Multiplicity
Rapidity
Momentum ofParticles andJets, missing ET

Theory approximations- Perturbative QCD (pQCD):
LO, NLO, NNLO calculations: ME + parton showering (PS),threshold resummation- non-pQCD: (Multi-parton interactions (MPI),
String/Cluster fragmentation models)5

Soft particle production

Charged particle multiplicity
Scaling, correlations
Underlying event

6Charged particles
new input to the dynamics of soft hadronic interactions: interplay between softand hard processes: no one MC describes data in all configurations
6(1/N

eventsch) dN /dη

54

CqpT>500 MeV, |h|<2.4

C4 CMS

20

3

5

2

4
1

3
0

CMS NSD(a)change of the slope at n~20

C4 UA5CMS Collaboration / Physics Letters
B 751 (2015) 143–163
147|η| < 2.4
Inclusive selection
C4 NA22
CMS 13 TeVPreliminary
40
C5 CMSCMS 7 TeV
C5 UA5
Nch ≥ 1 in |η| < 2.4
In addition, we gratefully acknowledge the computing centres and
CMS 0.9 TeV
pT > 0.5 GeVPYTHIA8 CUETM1
personnel of the Worldwide LHC Computing Grid for delivering so
PYTHIA8 MONASHPYTHIA8 4C MBR
effectively the computing infrastructure essential to our analyses.

CMS

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

η

CMS: pT>0 MeV, |h|<0.5
5.49

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Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by
the following funding agencies: BMWFW and FWF (Austria); FNRS
and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil);
MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIENCIASC2 CMS
MSES and CSF (Croatia); RPF (Cyprus); MoER, ERC IUT
C(Colombia);
NA22
2
Cand
UA5
ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland);2
C2 UA1CCEA
CMSand CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany);
3
CGSRT
NA22(Greece); OTKA and NIH (Hungary); DAE and DST (India);
3
C3 UA5
IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republicof Korea); LAS (Lithuania); MOE and UM (Malaysia); CINVESTAV,CONACYT, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC
(Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna);
3
102
104 (Serbia); SEIDI andMON, RosAtom,RAS and 10
RFBR (Russia); MESTD[GeV]CPAN (Spain); Swiss Funding s
Agencies(Switzerland); MST (Taipei);
ThEPCenter, IPST, STAR and NSTDA (Thailand); TUBITAK and TAEK
(Turkey); NASU and SFFR (Ukraine); STFC (United Kingdom); DOE
and NSF (USA).
Individuals have received support from the Marie-Curie programme and the European Research Council and EPLANET (European Union); the Leventis Foundation; the Alfred P. Sloan Foundaq the Alexander von Humboldt Foundation; the Belgian Fedtion;eral Science Policy Office; the Fonds pour la Formation à la
Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); theAgentschap voor Innovatie door Wetenschap en Technologie (IWTBelgium); the Ministry of Education, Youth and Sports (MEYS) of
the Czech Republic; the Council of Science and Industrial Research,
India; the HOMING PLUS programme of the Foundation for Polish
Science, cofinanced from European Union, Regional Development
Fund; the Compagnia di San Paolo (Torino); the Consorzio per laFisica (Trieste); MIUR project 20108T4XTM (Italy); the Thalis andAristeia programmes cofinanced by EU-ESF and the Greek NSRF;
the National Priorities Research Program by Qatar National Re-

KNO (Koba-Nielsen-Olesen)scaling assumes
the independenceof C on the collisionenergy: violation in therange |h|<2.4

Top) Distributions of the pseudorapidity density of charged hadrons in the

CMS-PAS-FSQ-15-008
Phys. Lett. B751 (2015) 143
JHEP 01 (2011) 079
EPJC 78 (2018) 697

7

Feynman’s s

pT & xT & limiting fragmentation
CMS PAS FSQ-15-006
Hard particles

Soft particles
The rise of the <pT> withmultiplicity Is energy
independent

The CMS results are consistent with Consistent with the
8/6/16xT=2pT/√s scaling (pQCD prediction)
hypothesisof limiting
with exponent N=4.9 +- 0.1

Sensitive to the interplay between soft,
semi-hard and hard particles production
JHEP 08 (2011) 086
JHEP 01 (2011) 079
EPJC 79 (2019) 391

fragmentation:
production of forward
particles is independent
on collision energy8Hard interactions

PDFs and aS measurementDPS
DGLAP vs BFKL
Multijet correlations

9Underlying events

Everything in event that is not “triggered”
interaction
Soft & semi-hard & hard
Beam remnants (BR): what remains after theinteracting partons left the hadron
Initial (ISR) and final (FSR) state radiation
Multiple Parton Interactions (MPI). If higher pt
interactions → Double Parton Scattering

UE activity is typicallystudied in the transverse
region in pp collisions as afunction of the hard scale ofthe event, and atdifferent centre-of-massenergies (√s):
Particle production in
MinBias events or eventswith high energy track or jet(hadronic events)
Drell-Yan events, Top events
(new)

10

Underlying events
ttbar events

Z+jetsTracker jetspp( p ) → Z + X → µ+µ- + X

Data

1.6

CMS

POWHEG + PYTHIA8POWHEG + HERWIG++

1.4

POWHEG + PYTHIA8, MPI OFFµµ1

p < 5 GeV
T
Charged particles
towards+transverse (|∆φ| < 120o)T

1.21/[∆η∆(∆φ)] 〈 Σp 〉 [GeV/rad]ch1/[∆η∆(∆φ)] 〈 N 〉 [rad-1]

pp( p ) → Z + X → µ+µ- + X

0.8
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T
Charged particles
towards+transverse (|∆φ| < 120o)

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µµ

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Data

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JHEP 07 (2018) 032
EPJC
79 (2019)
123
6
8
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JHEP 09 (2015)137
s [TeV]

Figure 10. Average particle density (left) and average ΣpT density (right) for Z events withpµµ < 5 GeV as a function of the center-of-mass energy, measured by CMS and CDF [9] in

11

A
B
Double Parton scattering(DPS)

T(b) is the overTwo and more hard interactions within the same production vertex can happen.
DPS is characterized by

The smaller theT(b) is the overlap function that charact
occupied by the interactiseff differs from 10 to 20 mb
The smaller the σeff the largerStrong
the Interactio
probabT(b) is the8/6/16
overlap function of two
partons
interacting hadrons
8/6/16

WW at 13 TeV(77 fb-1):
sDPS=1.41+-0.28+--0.28 pb
Significance = 3.9
seff = 12 +5 -2.9 mb
JHEP 02 (2018) 032
CMS-PAS-FSQ-16-009
CMS-PAS-SMP-18-015
JHEP 11 (2016) 110
Phys. Lett. 790 (2019) 595
CMS-PAS-SMP-20-009 subm to JHEP
CMS-PAS-SMP-20-007

Why it is important:increase of SM background forStrong Interactions, HA, TAU
the searches.
Question:is seff independent on the process
and interaction energy?

4 jets events at 13 TeV:A strong dependence of the extracted values of σeffon the model used to the describe the SPS contribution
is observed.
ME NLO 2->2 or 2->3 gives 10 mb
ME LO 2->4 gives 15 mb
ME LO 2->2 gives 20 mb

12PDFs and aS
For the fixed pQCD order and definite PDF evolution (DGLAP, BFKL, CCFM,..):A) Define PDFs at fixed aSB) Define aS for the particulary PDF set which gives the best approximationof the Data by TheoryC) Combined PDFs and aS fit

Process

Sensitivity

W mass measurement

Valence quarks

W,Z production

Quark flavor
separation

W+c production

Strange quark

Drell-Yan, high mass

Sea quark, high-x,
photon PDF

Drell-Yan low mass

Low-x, resummation

W,Z+jets

Gluon medium-x

Inclusive jets, multijets

Gluon and aS(MZ)

Direct photon

Gluon medium, high-x

ttbar, single top

Gluon, aS(MZ)

Differential production(single, double, triple),correlations, ratios,
assymmetry13W+-, Z production and aS
Sensitive to aS(mZ) due-to ISR, virtual gluon exchange, gq scattering (NLO, NNLO, …).
Calculate V-production cross-section at NNLO level for varying aS(mZ) and compare
theoretical predictions to experimental data (12 samples with different decay modes).

Cross-sections with CT14 and MMHT14 sets are the most sensitive to the underlying αS value.
Robust and stable with respect to variations in the data and theoretical cross sections.
The result derived combining the CT14 and MMHT14 extractions:αS(mZ)= 0.1175+0.0025−0.0028, has a ≈2.3%
This extracted value is fully compatible with the current αS(mZ) world average.
JHEP 06 (2020) 018

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Summary on aS

15

W+c: strange quark PDF

PHYSICAL REVIEW D 90, 032004 (2014)
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HERA I DIS + CMS W production
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exp. unc.
model unc.
parametrization unc.

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PDFs are probed at< x >≈ 0.007
at the scale of W mass

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model unc.
parametrization unc.

x⋅s

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FIG. 13 (color online). Antistrange-quark distribution s̄ðx; QÞand the ratio Rs ðx; QÞ, obtained in the QCD analysis of HERA
and CMS data, shown as functions of x at the scale Q2 ¼
1.9 GeV2 (top) and Q2 ¼ m2W (bottom). The full band represents

EPJC 77 (2017) 367
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Z+c/Z+b: towards c- and b-quarks PDFs
Page 11 of 34 751

Data

j

MadGraph 5FS + Pythia6

10-1

MadGraph 4FS + Pythia6

10

T

19.8 fb-1 (8 TeV)

[dσ(Z+b) / dpb ] / [dσ(Z+j) / dp ] (%)

CMS

Tdσ / dpb (pb/GeV)

Eur. Phys. J. C (2017) 77:751

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CMS: Eur. Phys. J.C. (2017) 77:751
MadGraph-aMC@NLO + Pythia8

10-2

10-3

Z/ γ *(→ ll) + at least 1 b jet-410

anti-kT (R = 0.5) jets
jet

jet

p > 30 GeV, |η | < 2.4

Theory / Data

T

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MadGraph 5FS + Pythia6, normalized to σ NNLO, stat. uncertaintyy only

Phys. J.C. (2017) 77:751
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MadGraph 4FS + Pythia6, normalized to σ NLO, stat. uncertainty only

, 4F and 5F schemes tested
1

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MadGraph-aMC@NLO + Pythia8, normalized to σ NLO, stat. + syst. uncertainties only

Theory / Data

T

Powheg MINLO + Pythia8

1.5

Data

Z/ γ *(→ ll) + at least 1 b jet

MadGraph 5FS + Pythia6

anti-kT (R = 0.5) jets

MadGraph 4FS + Pythia6

jet

jet

p > 30 GeV, |η | < 2.4
6

Powheg MINLO + Pythia8

4

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MadGraph 5FS + Pythia6, normalized to σ NNLO, stat. uncertainty onlyy
MadGraph 4FS + Pythia6, normalized to σ NLO, stat. uncertainty only1
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Powheg MINLO + Pythia8, normalized to σ NLO , stat. +syst. uncertainties only
100

150

200

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Leading (b/j) jet p (GeV)

Fig. 4 Differential fiducial cross section for Z(1b) production as afunction of the leading b jet pT (left), and the cross section ratio forZ(1b) and Z+jets production as a function of the leading b/inclusive (j)jet pT (right), compared with the MadGraph 5FS, MadGraph 4FS,
MadGraph5_aMC@NLO, and powheg minlo theoretical predictions(shaded bands), normalized to the theoretical cross sections describedin the text. For each data point the statistical and the total (sum inquadrature of statistical and systematic) uncertainties are represented
by the double error bar. The width of the shaded bands represents theuncertainty in the theoretical predictions, and, for NLO calculations,the inner darker area represents the statistical component only

T

MadGraph 5FS + Pythia6

10

MadGraph 4FS + Pythia6
MadGraph-aMC@NLO + Pythia8bPowheg MINLO + Pythia81Z/ γ *(→ ll) + at least 1 b jet

For Z+>=1b 4F schema fails
to describe bjet vs pT
anti-kT (R = 0.5) jets
jet

jet

p > 30 GeV, |η | < 2.4

1

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1.5

MadGraph 5FS + Pythia6, normalized to σ NNLO, stat. uncertainty only
MadGraph 4FS + Pythia6, normalized to σ NLO, stat. uncertainty only1
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MadGraph-aMC@NLO + Pythia8, normalized to σ NLO, stat. + syst. uncertainties only

Theory / Data

Theory / Data

T

1.5

12

CMS

19.8 fb-1 (8 TeV)
Data

j

Data

b

dσ / d|η | (pb)19.8 fb-1 (8 TeV)

[dσ(Z+b) / d|η |] / [dσ(Z+j) / d|η |] (%)

T

CMS

10

Z/ γ *(→ ll) + at least 1 b jet

MadGraph 5FS + Pythia6

anti-kT (R = 0.5) jets

MadGraph 4FS + Pythia6

jet

8Inclusive Z+c cross-section:
405.4 ± 5.6 (stat)± 24.3 (exp)± 3.7 (theo) pb
MadGraph5+MCatNLO:
524.9 ± 11.7 (theo) pb

Powheg MINLO + Pythia8, normalized to σ NLO , stat. +syst. uncertainties only

Leading b jet p (GeV)

4-flavour vs 5 flavour?
hemes tested
uud vs uudQQbar

One step before c-quark PDF
extraction

MadGraph-aMC@NLO + Pythia8

T

1

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1.5

s-section vs M bb
0.5

CMS

jet

p > 30 GeV, |η | < 2.4
T

MCatNLO and Sherpa
overestimate Z+c cross-section
at NLO andMCatNLO agreed with data
at LO.

MadGraph-aMC@NLO + Pythia8

For Z+jets, NLO calculations has better agreementwith data then L0 -> PDF overestimate c-content?
Powheg MINLO + Pythia8

6
4
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1
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MadGraph 5FS + Pythia6, normalized to σ NNLO, stat. uncertainty only
MadGraph 4FS + Pythia6, normalized to σ NLO, stat. uncertainty only1
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MadGraph-aMC@NLO + Pythia8, normalized to σ NLO, stat. + syst. uncertainties only

EPJC 77 (2017) 751
EPJC 78 (2018) 287
JHEP04 (2021) 109

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Summary
CMS measures both hard and soft QCD processes in various phase space
regions and compare them with a wide range of LO , NLO and NNLO
calculations
l CMS measurements are used for the combinations with other experiments inglobal fits and in Monte-Carlo Models tuning. Validation of the QCD
predictions (scaling properties, particles spectra, strong coupling behavior,
PDFs, evolution, etc) allows to further constrain and tune existing models.
More results can be found in CMS public web page:
http://cms-results.web.cern.ch/cms-results/publicresults/publications/SMP/index.html
lhttp://cms-results.web.cern.ch/cms-results/publicresults/publications/FSQ/index.html

Presentation is supported by the Journal Symmetry:18

SS symmetry

IMPACT
FACTOR

2.713

CITESCORE

3.4

SCOPUSan Open Access Journal by MDPI

Section Physics and Symmetry/Asymmetry
Section Editor-in-Chief

Message from the Section Editor-in-ChiefProf. Dr. Stefano Profumo
Department of Physics,
University of California,
Berkeley, CA, USA

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original research, and peer-reviewed articles related to thelatest research and developments in any field of physics
where symmetry plays a key role. This is a vast, highlyinterdisciplinary area, which runs the gamut from classicalsymmetries, to space-time symmetries, gauge symmetries,
symmetry breaking, the origin of symmetry, etc. Areasof physics relevant to this section include mathematicalphysics, classical and quantum gravity, particles and fields,
condensed matter systems, dynamical, disordered, and nonequilibrium systems, and biophysics.

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Contact Us
Symmetry
MDPI, St. Alban-Anlage 664052 Basel, Switzerland& )Tel: +41 61 683 77 34
Fax: +41 61 302 89 18▶ www.mdpi.com▶

mdpi.com/journal/symmetry
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20

Multi-jet correlations
Theoretical predictions are based on

 Matrix element expansion and parton shower Multi-parton interactions and hadronization

21

11

References

Azimuthal decorrelations
Back-to-back region of dijetcorrelations-sensitive probeof soft gluon radiation

Dfjj in bins of pT1 for pT>100 GeV,
pT1>200GeV, |y1|<2.5,|y2|<2.5

multijets
4 jet LO

Ratio to Data

3-jet NLO

CMS
Preliminary
1.3
1.2
1.1
1
0.9
1.3
1.2
1.1
1
0.9
1.3
1.2
1.1
1
0.9
1.3
1.2
1.1
1
0.9
1.3
1.2
1.1
1
0.9

anti−k t R=0.4

PH-2J + P8CUETM1

Inclusive 3-jets
Total Exp. Unc.

PH-3J + P8CUETM1
MadGraph + P8CUETM1
35.9 fb-1 (13TeV)

200 < pmax

400 < pmax

600 < pmax

800 < p

T

T

T

max
T

< 300 GeV

<∆500
φ GeV
[deg]
1,2

<∆700
φ GeV
[deg]
1,2

<∆
1000
φ GeV
[deg]
1,2

pmax > ∆
1200
φ GeV
[deg]
T

1,2

1.3
1.2
1.1
1
0.9
1.3
1.2
1.1
1
0.9
1.3
1.2
1.1
1
0.9
1.3
1.2
1.1
1
0.9

300 < pmax

500 < pmax

700 < pmax

1000 < p

T

T

T

max
T

< 400 GeV

<∆600
φ GeV
[deg]
1,2

<∆800
φ GeV
[deg]
1,2

< 1200∆φ GeV[deg]
1,2

170 171 172 173 174 175 176 177 178 179 180

∆φ

1,2

[deg]

170 171 172 173 174 175 176 177 178 179 180

∆φ

1,2

Comparison is donewith fixed-order
pQCD (NLO)
and with LO ME+PS[deg]

Deviations (~10%) are observed for
all tested generators

Figure 6: Ratios of PH -2 J + PYTHIA 8, PH -3 J + PYTHIA 8 and M AD G RAPH + PYTHIA 8 predictions
to data, of the normalized inclusive 3-jet distributions as a function of the azimuthal differenceof the two leading jets Df1,2 , for all pmax
regions. The solid band indicates the total experimental
T
uncertainty and the error bars on the MC points represent the statistical uncertainties of thesimulated data.

EPJC 76 (2016) 536
CMS-PAS-SMP-17-009

22

Jet clustering technique
Fixed cone algorithms:
Iterative Cone (CMS) / JetClu (ATLAS)
Midpoint algorithm (CDF/D0)
Seedless Infrared Safe Cone (SISCone)

Iterative cone

SisconeSuccessive recombination algorithms:2

2p 2p δ ij
d ij = min (kti ,ktj ) 2R2p
diB =k ti

p=1

p=0

if(dij < diB) add i to j
and recalculate pj
p=1 ->kT jet algorithm
p=0 ->CA jet algorithm
p=-1 ->“Anti-kT” jet algorithm
CMS uses R=0.5,0.7 in Run1
R=0.4,0.6 in Run2ATLAS uses R=0.4,0.6 in Run1,2

p=-1

JHEP 1009 (2010) 091

23

QCD Evolution equation
Connection between various scales in QCD (for instance, between PDF and thehigh-momentum scattering) is performed via evolution differential equations.

In small-x region standard
approach to NLO QCD
perturbative calculations.
DGLAP (expansion in termsof power of aS ln(Q2)) is predicted to
be not sufficient.
Need to develop alternative approaches:
BFKL (expansion in terms of ln(1/x)).
CCFM angular and energy ordering
LDC (Linked dipole chain)…
Non perturbative effects,
Multi Parton Interaction(MPI) etc. models have tobe tuned to data.

DGLAP

BFKL?

24

Angular correlations of jets
11

1

41 pb-1 (7 TeV)

CMS

C2/C1

C2/C1

• Events with at least two jets passing cuts: pT>35 GeV in |η|<4.7• For a pair of jets with the largest Δη (CMS) the angular distance iscalculated: Δφ = φ1 – φ2
DATA
PYTHIA 6 Z2PYTHIA 8 4C
HERWIG++ 2.5
POWHEG+PYTHIA 6
POWHEG+PYTHIA 8

0.9

0.8

1

DATA
SHERPA 1.4

0.9

NLL BFKL
HEJ+ARIADNE

0.8

0.7

DGLAP generators
start to be worse inhigh Dy description

0.7

0.6

0.6
Mueller-Navelet dijets

0.5

PT > 35 GeV, |y| < 4.7

0.4
0

1

1

2

3

4

Mueller-Navelet dijets

5

6

7

8

9

∆y

0.5

PT > 35 GeV, |y| < 4.7

0.4
0

1

41 pb-1 (7 TeV)

CMS

C3/C2

C3/C2

41 pb-1 (7 TeV)

CMS

DATA
PYTHIA 6 Z2PYTHIA 8 4C
HERWIG++ 2.5
POWHEG+PYTHIA 6
POWHEG+PYTHIA 8

0.9

0.8

1

2

3

4

5

6

7

8

9

∆y

41 pb-1 (7 TeV)

CMS
DATA
SHERPA 1.4

0.9

NLL BFKL
HEJ+ARIADNE

0.8

0.7

0.7

0.6

0.6
Mueller-Navelet dijets

0.5

PT > 35 GeV, |y| < 4.7

0.4
0

1

2

3

4

Mueller-Navelet dijets

5

6

7

8

9

∆y

0.5

PT > 35 GeV, |y| < 4.7

0.4
0

1

2

3

4

5

6

7

8

9

∆y

Figure 3: Left: The measured ratios C2 /C1 (top row) and C3 /C2 (bottom row) as a function of
rapidity difference Dy are compared to LL DGLAP parton shower generators and to the NLOnPOWHEG interfaced
Tmin with PYTHIA 6 and PYTHIA 8. Right: Comparison of the ratios togenerator
the MC generator SHERPA with parton matrix element matched to a LL DGLAP parton shower,
to the LL BFKL-inspired generator HEJ with hadronisation by ARIADNE, and to analytical NLL
BFKL calculations at the parton level.

C (Dy,pAnalytical BFKL
calculations at NLL
accuracy with an optimized
renormalization schemaprovide reasonable
description ofdata for the measured jet
variables at Dy>4

) = <cos(n(p-Df))>

JHEP08(2016)139

25

Perturbative QCD (pQCD)
pQCD prediction at fixed order calculation
Singularities (soft andthecollinear)are:proton are almost
free, and are sampled essentially
one
at
a
time
in
hard
collisions.
q partially cancelled between realand This picture leads to
the QCD-improved parton model, in which the hadronic
virtual contributions,cross section for production of a final state X factorizes in
into PDFs
products ofand
pdfs facoupling
and partonic cross sections
q partially absorbed
σ̂ab→X ,renormalizations
σpp→X (s; α , µ , µ )
s

!" 1

F

R

=
dx1 dx2 fa (x1 , αs , µF )fb (x2 , αs , µF )Finally, fixed order QCD calculations
are matcheda,b 0with parton showers (PYTHIA or HERWIG)
×σ̂ab→X (sx1 x2 ; αs , µF , µR ). (2.1)
Monte-Carlomodelswhich
represent
soft andThe PS corrections derived
with powheg + pythia6
HereareµF andµR are the factorization
and renormalizapresented in Fig. 3. They are significant at large p , partiction
scales,
which
are
in
principle
arbitrary.
In practice,ularly at high rapidity,
where the factors approach−20 %.
collinearradiation
patterns
However, the combination of powheg + pythia6 has
nevertruncating
the cross section at a given order in perturbabeen tuned
and the Z2* tune strictly isapproach
only valid for aOR
into dataalternative
non-perturbativetion theory induces
dependence on µF and µandR.
LO + PS tune with pythia6, but not with showers matched to
Althoughpartondistributionsarenonperturbative
powheg. Moreover, powheg employs the CT10-NLO PDF,
Electroweak
corrections
arewhich
appliedas weights
while the Z2* tune requires the CTEQ6L1-LO PDF
to bequantities
must be measured experimentally at
288 Page 8 of 42

_
q

Z

LO

e−
e+

q

_
q
_
q

g

NLO

Z

Z

q
_
q

g

g

_
q

q

Z

NP correction

Eur. Phys. J. C (2015) 75:288

T

1.20

(7 TeV)CMS Simulation

anti-kT R = 0.7

1.15|y| < 0.5
0.5 ≤ |y| < 1.0
1.0 ≤ |y| < 1.5
1.5 ≤ |y| < 2.0
2.0 ≤ |y| < 2.5

1.05

PS correction

PS corr

Nonperturbative correction factor

Nonperturbative correction factor

NP corr
T

NNLO

1.10

used for the showering part. Therefore, such PS corrections
someinshort-distancescale µ, their evolution with µ is gov1.00
can be considered as only an illustrative test, as reported
746 Page 6 of 292
2×10
2×103
Sect. 4.3.
erned
by
the
DGLAP
equation[8], 10753 :288p (GeV)
288 Page 6 of 42
Eur. Phys. J. C (2015) Jet
T
The maximum parton virtuality allowed in the parton"1
2 , is varied by factors of 0.5 and 1.5 by(7 TeV)CMS Simulation
shower evolution, µ1.20
CMS Simulation(7 TeV)(7 TeV)
1.20
PS CMS Simulation∂fdξαs (µ)
1.20
a (x, µ)|y| < 0.5changing the corresponding parameter PARP(67) in pythia6
P
=
(x/ξ,
α
(µ))f
1.15
0.5 ≤s|y| < 1.0b (ξ, µ), (2.2)
R =ab
0.7
anti-k
Herwig++Herwig++ (2.3)|y| < 0.5
0.5 ≤ |y| < 1.0
1.0 ≤ |y| < 1.5∂ ln µ21.15 anti-k
2π
ξ (Z2)(2.3)
from its default value1.15
of 4–2anti-k
andR =6,0.7respectively.
resulting
1.10
Pythia6 The(Z2)
x Pythia6
1.5 ≤ |y| < 2.0
R = 0.7(Z2*, P11)
Powheg+Pythia6 (Z2*, P11) 2.0 ≤ |y| < 2.5changes in the PS factors are shown in Fig.Powheg+Pythia6
3. The powheg
1.05
whose kernel
is1.00known through NNLO [9],+ pythia6 PS factors
1.10 employed in an illustrative test later
1.10
are determined as the average of the predictions from the0.95# α $2αs (1)
two extreme scale limits.
Again, a parameterization using a
s
(0)
(2)
1.05
P
Pab (x, αs )1.05= P0.90
(x)+
(x)+
Pab (x)+O(α3s ).
functional form of a0 + a1 / pTa2 is employed to smoothen
ab
ab
0.85
2π
2π
statistical fluctuations.
1.00
1.00
0.80
(2.3)
2
2×10
103 PS, and
2×103
2×102 3×102
103
Finally, Fig. 4 presents an
overviewof the NP,
0.75
p (GeV)Jet p (GeV) 103
32×102
2×10similarly
TT
partonic crosssectioncanbeexpandedincombined corrections for all five ranges in |y|. JetThepQCD X

2

FIG. 1: Sample Feynman diagrams contributing to Z boson
production at a hadron collider, at LO, NLO, and NNLO.
J. C (2017) 77:746
Only one diagramEur.isPhys.
shown
for each contributing amplitude,
and some amplitudes are omitted.

EWK corrTTX

1.0 ≤ |y| < 1.5

anti-kT R = 0.7(7 TeV)

Herwig++ (2.3)
Pythia6 (Z2)

Powheg+Pythia6 (Z2*, P11)

CMS Simulation

CMS Simulation

1.5 ≤ |y| < 2.0

correction

CMS Simulation

ative correction factor

ative correction factor

scattering amplitudes are required. These amplitudes areillustrated in fig. 1 for one of the simplest processes, theinclusive production of a Z boson at a hadron collider,followed by Z decay to an electron-positron pair. At LO,
only tree amplitudes are needed. In this example, a single Feynman diagram contributes to qq̄ → Z → e+ e− .
Jet p (GeV)
powers of1.20αs ,1.20This diagram just needs to be squared, and convoluted
http://www.slac.stanford.edu/
ab→X1.20
4 Determination of1.15
the strong coupling constantσ̂1.15(αs , µF , µR )with the pdfs, while incorporating any experimental cuts
1.15%
cgi-wrap/getdoc/slac-pub-13054.pdf
1.10
on the final state leptons.
The measurement of
1.10the inclusive jet cross section [1], as1.10
αs (µR ) (1)1.05
described in Sect. 2, can be used to determine α S (MZ ), whereσ̂ (µ , µ )= [α (µ )]nα σ̂(0) +At NLO, one-loop amplitudes contribute to virtual cor-X

anti-kT R = 0.7(7 TeV)

Herwig++ (2.3)

T|y| < 0.5
Pythia6 (Z2)
0.5 ≤ |y| < 1.0
anti-kT R = 0.7 (Z2*, P11)
Powheg+Pythia6
1.0 ≤ |y| < 1.5
1.5 ≤ |y| < 2.0
2.0 ≤ |y| < 2.5(7 TeV)26

Jet reconstruction in detector
Calorimeter jets (CaloJets):
Jet clustered from
Calorimeter
Towers (CMS,ATLAS)
Or TopoClusters(ATLAS)
CaloMET
ParticleFlow jets (PFJets):
Jet clustered from Particle
Flow objects (a la generator
level particles) which arereconstructed based oncluster separation.
Subdetectors:
ECAL,HCAL,
Tracker, Muon
PFMET

CMS

Anti-Kt clustering Tracker jets (TrackJets):algorithm is applied Jet clustered from Tracks
to the different
Subdetectors:
objects
Tracker(ATLAS,CMS)

All subdetectors
participate inreconstruction
The residual
jet energy
corrections isapplied on topof all algorithms

JetPlusTrack jets (JPTJets):
Starting from calorimeterjets tracking information isadded via subtracting
average response andreplacing with tracker
measurements.
Subdetectors:
ECAL,HCAL,
Tracker, Muon
TcMET
CMS

27