Jet Fragmentation Studies at CDFJet Fragmentation Studies at CDF
Sasha PronkoFermilab
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 1
Soft QCD Studies at CDFSoft QCD Studies at CDF
o In this talk – Jet Fragmentation
I l i p ti l m m t m di t ib ti• Inclusive particle momentum distribution• Particle multiplicities in Quark & Gluon jets• Two-particle momentum correlations
k di t ib ti f ti l
Data comparedto Theory & MC
• kT distribution of particles
o Not covered in this talko Not covered in this talk– Jet & Event Shapes
• Inclusive jet shapes• B-jet shapes Data compared to MC• Event shapes (coming soon)
– Underlying Event• Underlying event in dijets• Underlying event in Drell-Yan (coming soon)
Data compared to MCPythia tuning
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 2
Underlying event in Drell-Yan (coming soon)
Tevatron in Run IITevatron in Run II
o Proton-antiproton collisions at √√s=1.96 TeV
o 36×36 bunches o Collisions everyo Collisions every
396 nso Peak luminosity y
298*1030 cm-2s-1
o Two experiments: CDF & DØCDF & DØ
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Tevatron PerformanceTevatron Performance
o Delivered luminosity– Current: 3.7 fb-1 per experiment– Goal by 2009: 5-8 fb-1
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Goal by 2009: 5-8 fb
CDF Detector in Run IICDF Detector in Run II
o Multipurpose detector, classic design– Silicon Vertex Detector
ENDWALLHADCAL
CENTRAL HAD CALORIMETER = 1.0
MUON CHAMBERS
CENTRAL EM CALORIMETER
– Wire tracker– Solenoid– Pre-shower detector & TOF
EM C l i t
SOLENOID
= 2.0
CAL.
= 3.0
CENTRAL EM CALORIMETER
– EM Calorimeter– HAD Calorimeter– Muon chambers
o Broad Physics program CENTRAL OUTER TRACKER
CLC
PLUGHADCAL.LU
G E
M C
AL.
SiliconVertexDetecto
r
o Broad Physics program– QCD– EWK– Top
PL
p– B-physics– Higgs & New Physics searches
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Hadron Collider EnvironmentHadron Collider Environment
o Hahdron-hadron collisions is a complex environment for jet fragmentation studiesj g– Need to deal with underlying event
• Multiple parton interactions• Beam remnants
Initial state radiation
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• Initial state radiation
Partons, Hadrons, Jets…Partons, Hadrons, Jets…
o Jet identification– Jet clustering algorithms
o Hadronizationo Hadronization– Phenomenalogical models
o Soft final state radiationQCD i i i ll
Hadronic showers
EMshowers n – pQCD approximation in all
orderso Hard scattering: 2→X
showers
? et e
volu
tion
– pQCD exact matrix element at LO, sometimes NLO
o Pick two partons and their
?
ectio
n of
je
momenta– Parton distribution functions
(PDF’s)
Dire
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 7
Jet Fragmentation Analysis at CDFJet Fragmentation Analysis at CDFo Theoretical framework
– Partons: MLLA & extensions– Local Parton Hadron Duality (LPHD) hypothesis
• connects partons with hadrons:
Jet 2
• connects partons with hadrons: Nhadron=KLPHD*Nparton
• Naïve picture: parton~hadron (if p>mπ)o Select two well-balanced jets (or γ+jet)
– Need to know fraction of gluon jets
pθconep
– Need to know fraction of gluon jets• PDF+Pythia/Herwig
o Do analysis in dijet (or γ+jet) rest frame – Ejet=1/2Mjj (or 1/2Mγj)
Jet 1
o Do analysis for small opening angles– θC~0.3-0.5 rad– Theory is (strictly speaking) valid for soft and
collinear partonsp– Limits contribution from underlying event
o Energy scale is Q = 2Ejettan(θ/2) ≈ EjetθCo Subtract contribution from underlying event
and secondary interactions
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 8
and secondary interactions
Subtracting Underlying EventSubtracting Underlying Event
Jet 1
ular to dijet a
xis beam-line θ
θ
Jet 2plane perpendicu
la
o Dijet rest frameo Two complementary conesp y
– 90º away from dijet axis– Same polar angle θ as dijet axis with respect to beam line– Statistically collect same contribution from underlying event and
d i t ti d j t
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 9
secondary interactions as cones around jets
Inclusive Momentum DistributionInclusive Momentum Distribution
jetEpx
x
YDddN
==
=
),1ln(
),(/
ξ
ξξ
P i t
QCDcutoffeffcjeteff
QQEQQQY Λ=== ~,),ln( θ
o Previous measurements– Extensive studies at e+e- and e+p– Limited to quark jets only– Very good agreement with MLLA
o CDF– Never done in hadron-hadron
ll b fcollisions before…
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Inclusive Momentum Distribution at CDFInclusive Momentum Distribution at CDFo CDF analysis
– θc~0.3-0.5 rad– 9 Mjj bins
• 78 GeV/c2<|Mjj|<573 GeV/c2
– Fractions of gluon jets• From 65% (|Mjj|~70 (| jj|
GeV/c2) to ~20% (|Mjj|~600 GeV/c2)
o CDF results– Two parameter MLLA fit:– Two parameter MLLA fit:
• Qeff=230±40 MeV• KLPHD=0.56±0.10
– Works surprisingly well for wide range of dijet masses
– Evolution of peak position with Q agrees with e+e- and e+p very well
Fit range:1.6<ξ<ln(Q/Qeff)~ln(Q/0.25)
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e p very well 1.6 ξ ln(Q/Qeff) ln(Q/0.25)
Quark vs Gluon JetsQuark vs Gluon Jets
o Theory– From r=2.25 (LLA, Ejet→∞)– To r~1 3-1 8 (3NLLA)
History of measurements of the ratio of charged particle multiplicities in Gluon and Quark Jets
3
To r~1.3-1.8 (3NLLA)o Experiment (e+e-)
– 1991: r=1.02±0.07 (OPAL)2001: r=1 42±0 05 (OPAL)
2
LLA, r=CA/CF=2.25
– 2001: r=1.42±0.05 (OPAL)– Illustrates evolution of our
understanding of gluon jets• 3-jet events
r=N
g/N
q
1 3 jet events• choice of correct energy
scale is non-trivial o CDF0
Capella et al., 2000Lupia & Ochs, 1998Catani et al., 1991Mueller, 1984
CLEOHRSOPAL
DELPHIALEPHSLD
– Gluon jets are copiously produced
– Can we do it?
Q, GeV10 100
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Particle Multiplicities in Quark and Gluon JetsParticle Multiplicities in Quark and Gluon Jets
o How can we do that CDF?– Compare di-jet and γ+jet– Extract properties of Q & G jets
• Two equations & two unknowns• Obtain fraction of gluon jets from PDF+MC
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Particle Multiplicities in Quark and Gluon JetsParticle Multiplicities in Quark and Gluon Jets
DF d ll h N & EP ( d l d do CDF data agree well with 3NLLA & LEP (model-independent results)– r=1.64±0.17 at Q=19 GeV
Confirms Q E θ scaling:– Confirms Q≈EjetθC scaling:• Ejet1≠Ejet2 and θ1≠ θ2, but Ejet1θ1=Ejet2θ2 ⇒N1(Ejet1θ1)=N2(Ejet2θ2)
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 14
Particle Multiplicity Gluon JetsParticle Multiplicity Gluon Jets
o CDF data for gluon jets agree with model-dependent results from OPAL
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Ratio of Inclusive Momentum DistributionsRatio of Inclusive Momentum Distributions
o r(ξ)~1.8 for soft particles (large ξ)– Expected from p
theoryo Data vs MC
– MC qualitatively q yreproduces data
/E 1 0 5 0 1 0 05
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x = p/Ejet = 1 0.5 0.1 0.05
TwoTwo--particle Momentum Correlationsparticle Momentum Correlations
o Theory– Fong & Webber, Phys.Lett. B241:255 (1990)– R.Perez-Ramos, JHEP 0606, 019 (2006), , ( )
),(),()(),( 212211021
2
21 ξξξξξξξξ Δ−Δ+Δ+Δ+=∗
= YRYRYRdNdNddNd
R)ln()ln(
θ==
eff
cjet
eff QE
QQY
– R(ξ1,ξ2) mixes together momentum correlations and multiplicity fluctuations
21 ξξ∗
dd 0ξξξ −=Δ
∫(dN/dξ)dξ=N
– To de-couple momentum correlations and multiplicity fluctuations we use distributions normalized to unity (F is taken from theory):
∫(dN/dξ)dξ=N∫d2N/(dξ1dξ2)dξ1dξ2=N(N-1)
use distributions normalized to unity (F is taken from theory):
),(),()(),()1(
),(),( 2122110
21212
21
2
21 ξξξξξξξξξξξξ Δ−Δ+Δ+Δ+==−
=∗
= YCYCYCF
RNNRN
dndnddnd
C
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 17
)1(21 ξξ
∗ FNNdd
TwoTwo--particle Momentum Correlationsparticle Momentum Correlations2d
),(),()(),( 2122110
21
21
2
21 ξξξξ
ξξ
ξξξξ Δ−Δ+Δ+Δ+=∗
= YCYCYC
ddn
ddn
ddnd
C
o Ridge-like structure– Particles with like momenta correlate
C l ti i t f ft ti l
21 ξξ
– Correlation is stronger for soft particleso OPAL measurement (Phys.Lett.B287,401)
– Only quark jets– Trends with energy not studied– Large angles considered (θC=π/2)– OPAL data can’t be described by NLLA
ith bl h i f Qwith reasonable choice of Qeff
o CDF measurement– θC=0.5, 66 GeV/c2<Mjj<563 GeV/c2
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 18
ξ0ξ0-1 ξ0+1
TwoTwo--particle Momentum Correlationsparticle Momentum Correlations
o Hadron correlations follow pattern predicted by Fong/Webber
),(),()(),( 212211021 ξξξξξξ Δ−Δ+Δ+Δ+= YCYCYCC
) 2ξΔ 1 5
1.6CDF Run IIfit to CDF data, 1ξΔ
C(
1 2
1.3
1.4
1.5 uncertainty of the fit=180 MeVeffFong/Webber Q
=230 MeVeffR.Perez-Ramos Q
=100*0.5=50 GeVcθjetQ=E
0.9
1
1.1
1.2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 20.6
0.7
0.8
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
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2ξΔ-1ξΔ2 1.5 1 0.5 0 0.5 1 1.5 2
2ξΔ-1ξΔ2 1.5 1 0.5 0 0.5 1 1.5 2
TwoTwo--particle Momentum Correlationsparticle Momentum Correlations
o Hadron correlations follow pattern predicted by Fong/Webber
),(),()(),( 212211021 ξξξξξξ Δ−Δ+Δ+Δ+= YCYCYCC
) 2ξΔ, 1ξΔ
1.5
1.6CDF Run IIfit to CDF datauncertainty of the fit
ΔC
(
1.2
1.3
1.4=180 MeVeffFong/Webber Q
=230 MeVeffR.Perez-Ramos Q
=100*0.5=50 GeVcθjetQ=E
0.9
1
1.1
-2 -1 5 -1 -0 5 0 0 5 1 1 5 20.6
0.7
0.8
-2 -1 5 -1 -0 5 0 0 5 1 1 5 2
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2ξΔ+1ξΔ2 1.5 1 0.5 0 0.5 1 1.5 2
2ξΔ+1ξΔ2 1.5 1 0.5 0 0.5 1 1.5 2
TwoTwo--particle Momentum Correlationsparticle Momentum Correlationso Fong/Webber and MLLA/NMLLA predictions by Perez-Ramos
have different range of applicabilityo NMLLA predictions agree with data better than MLLA
) 2ξΔ, 1ξΔC
( 1.4
1.5
1.6CDF Run IIfit to CDF datauncertainty of the fit
=230MeVeffFong/Webber Q
) 2ξΔ, 1ξΔC
( 1.4
1.5
1.6 CDF Run IIfit to CDF datauncertainty of the fit
=230MeVeffFong/Webber Q230M VMLLA QC
1 1
1.2
1.3
1.4 eff=230MeVeffMLLA Q
=230MeVeffNMLLA Q
=238*0.5=119GeVcθjetQ=E
C
1.2
1.3
1.4 e=230MeVeffMLLA Q
=230MeVeffNMLLA Q
=238*0.5=119GeVcθjetQ=E
0.9
1
1.1
0.9
1
1.1
-2 -1 5 -1 -0 5 0 0 5 1 1 5 20.6
0.7
0.8
-2 -1 5 -1 -0 5 0 0 5 1 1 5 2 2 1 5 1 0 5 0 0 5 1 1 5 20.6
0.7
0.8
2 1 5 1 0 5 0 0 5 1 1 5 2
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2ξΔ-1ξΔ-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
2ξΔ-1ξΔ-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
2ξΔ+1ξΔ-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
2ξΔ+1ξΔ-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
TwoTwo--particle Momentum Correlationsparticle Momentum Correlations
o Pythia and Herwig predictions agree with data in entire jet energy range
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TwoTwo--particle Momentum Correlationsparticle Momentum Correlations
o Evolution of parameters with energy allows to extract value of Qeff
o Theory reproduces trends in datao Resultso Results
– From fit to C1 and C2 give consistent results– Combined: Qeff=137+85
-69 MeV
1C
0.12
0.14 CDF Run II
=145 MeVeffCDF data fit to Fong/Webber Q
2C
-0.02
0
0.06
0.08
0.1
=145 MeVeffFong/Webber quark jet Q
=145 MeVeffFong/Webber gluon jet Q
-0.08
-0.06
-0.04
CDF Run II
0
0.02
0.04
0.06
-0.14
-0.12
-0.1=129 MeVeffCDF data fit to Fong/Webber Q
=129 MeVeffFong/Webber quark jet Q
=129 MeVeffFong/Webber gluon jet Q
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Q (GeV)0 20 40 60 80 100 120
0
Q (GeV)0 20 40 60 80 100 120
TwoTwo--particle Momentum Correlationsparticle Momentum Correlationso C0 is too small compared to theoryo Almost no energy dependence, as expected
o From theoretical point of view C has some issueso From theoretical point of view, C0 has some issues…
0C
1 3
1.35CDF Run II
=0.1 MeVffCDF data fit to Fong/Webber Q
1.2
1.25
1.3 =0.1 MeVeffCDF data fit to Fong/Webber Q
=137 MeVeffFong/Webber Q
=137 MeVeffFong/Webber quark jet Q
=137 MeVeffFong/Webber gluon jet Q
1.1
1.15
Constant off-set
0 20 40 60 80 100 1201
1.05
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Q (GeV)0 20 40 60 80 100 120
TwoTwo--particle Momentum Correlationsparticle Momentum Correlations
o We measure correlations around peak position, ξ0– True peak position: ξ0=1/2Y+a*Y1/2+O(1), Y=ln(Q/Qeff)– Peak position in Fong/Webber: ξ0=1/2Y+a*Y1/2+O(1), Y=ln(Q/Qeff)p g ξ0 ( ), (Q Qeff)
o Agreement improves if O(1)=-0.6 inserted by hand– O(1)=-0.6 obtained from fits of CDF data for dN/dξ
Fong/Webber: c0’=c0-2c1O(1)=c0+1.2c1
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KKTT distributiondistributiono kT studies probe softer particle spectra than dN/dξ and C(ξ1,ξ2)
studieso First study of kT distributions at hadron collider
– θC=0.5, 66 GeV/c2<Mjj<737 GeV/c2
o Compare with recent theoretical results – MLLA calculations by Perez-Ramos & Machet, JHEP 04, 043 (2006)
NMLL l l i b l P R & M h– NMLLA calculations by Arleo, Perez-Ramos & Machetjet axis
kT
p
kT
θ
kT=p*sin(θ)
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KKTT distributiondistributiono NMLLA agrees better with data compared to MLLA
– Indicates importance of higher level corrections– MLLA: agreement with data becomes better at large Q
NMLLA: agreement with data is good at all Q’s– NMLLA: agreement with data is good at all Q s
)T
N/d
ln(k
1
=100*0.5=50 GeVcθjet
Q=E
)<0.0 (N’)TNormalized to bin:-0.2<ln(k
)T
dN
/dln
(k
1
CDF Run II
Total Uncertainty
MLLA (Machet/Perez-Ramos)
NMLLA (Arleo/Machet/Perez-Ramos)
)<0.0 (N’)TNormalized to bin:-0.2<ln(k )T
N/d
ln(k
1
=310*0.5=155 GeVcθjet
Q=E
)<0.0 (N’)TNormalized to bin:-0.2<ln(k
1/N
’ dN
-110
1
1/N
’ d
-110
1 NMLLA (Arleo/Machet/Perez-Ramos)
1/N
’ dN
-110
1
-310
-210CDF Run II
Total Uncertainty
MLLA (Machet/Perez-Ramos)
NMLLA (Arleo/Machet/Perez-Ramos)
0 5 0 0 5 1 1 5 2 2 5-310
-210
=38*0.5=19 GeVcθjet
Q=E
-310
-210CDF Run II
Total Uncertainty
MLLA (Machet/Perez-Ramos)
NMLLA (Arleo/Machet/Perez-Ramos)
/1GeV/c)Tln(k-0.5 0 0.5 1 1.5 2 2.5
10/1GeV/c)Tln(k
-0.5 0 0.5 1 1.5 2 2.5
MLLA
NMLLA
/1GeV/c)Tln(k-0.5 0 0.5 1 1.5 2 2.5 3
10
MLLA
NMLLARange of validity:MLLA works for y=ln(kT/Qeff)<Y-2.5NMLLA k f l (k /Q )<Y 1 6
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 27
NMLLA works for y=ln(kT/Qeff)<Y-1.6
KKTT distributiondistribution
o Both Herwig and Pythia agree with data in entire range of jet energiesenergies
02/27/08 Sasha Pronko, ECT workshop, Trento, Italy 2008 28
Summary and CoclusionSummary and Coclusion
o Studies of jet fragmentation at CDF confirm that pQCD calculations can be successfully applied to describe most aspects of jet formationof jet formation– Further support to LPHD– dN/dξ distribution: Phys.Rev.D 068:012003 (2003)
• Q ff=230±40 MeV; KLPHD=0 56±0 10Qeff 230±40 MeV; KLPHD 0.56±0.10– Multiplicity in gluon & quark jets, NG & NQ: PRL94:171802 (2005)
• r=NG/NQ=1.64±0.17 at Q=19 GeV– Two-particle momentum correlations: submitted to PRDTwo particle momentum correlations: submitted to PRD
• Qeff=137+85-69 MeV
– kT distribution: to be submitted to PRL soon• Data agree with NMLLA at all Q’s g Q
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BackupBackup
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TwoTwo--particle Momentum Correlationsparticle Momentum Correlations
o Consider all pairs of particles with ξ0-1<ξ<ξ0+1 in cone θc<0.5 around jet axis
2nd
),(),()(),( 2122110
21
2121 ξξξξ
ξξ
ξξξξ Δ−Δ+Δ+Δ+=∗
= YCYCYC
ddn
ddn
ddC
ξξ0-1 ξ0+1
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ξ0ξ0-1 ξ0+1
KKTT distributiondistribution
o MLLA seem to agree with kT distribution of partons in Pythia
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