-- AlexanderFedotov - 09-Sep-2010

Looking for long-range two-particle angular correlations in Pythia6

Introduction

Considering the process of QCD high-pt jet production in a string fragmentation model a la pythia, the jet is a fragmentation product of a string stretched between

• a hard (high-pt) final state parton (or its close descendant in a parton shower), and
• another parton, which has typically a much lower pt.

The high-pt jet is formed near (in terms of ) the high-pt end of the string, while the other end may give rise to a much-lower-pt jet. If the distance between the end partons of the string is large enough, one can suppose, that

• there may be a trail of relatively hight-pt particles extending from the high-pt end of the string towards (along ) the low-pt end
• it would not be surprising if particles in the trail/tail would "remember" also the value of the high-pt end parton.

Aim of the exercise

To test these naive expectations with Pythia6 dijet events on generator level.

Method

In a loop over events and strings, a suitable string is selected, then considered are stable particles (status=1, including undecayed particles with "lifetime" > 1cm), descending from the string. For those particle, made are

1. a two-particle correlation plot in the plane where 's are the corresponding differences between the two particles
   (a 2-d histo is filled with particle pairs from a selected string in a double loop over strings and events) ,
2. a similar particle - high-pt-end parton correlation plot .

If the above expectations are correct, an enhancement near in the distribution at a constant might be observed which would be a possible manifestation of the expected correlation (particles "remembering" the value of the high-pt end parton).
While a flat distribution would mean an absence of correlations.

Actually, a correlation in the first plot would not prove the physics picture in question, for there is no association of a particle pair with the high-pt end parton in such a plot. The second plot provides, in principle, a much more direct test.

For simplicity, the range is limited by a high-enough max value of 4 .

Event sample

The Pythia6 dijet dataset
/QCDDiJet_Pt80to120/Summer10-START36_V9_S09-v1/GEN-SIM-RECO
was used:

• D6T tune
• 7 TeV
• pthat: 80-120 GeV
• cross section: 6.358e+06 pb
• More... Close
  Its parent
  /QCDDiJet_Pt80to120/Summer10-START36_V9_S09-v1/GEN-SIM-RAW ,
  according to ProductionReProcessingSummer10 (see request id 1004060), was a repro of the following Summer09 dataset:
  /QCDDiJet_Pt80to120/Summer09-MC_31X_V3_7TeV-v1/GEN-SIM-RAW
  An info on the latter:
  • its cfg contains
    

process.configurationMetadata = cms.untracked.PSet(
    version = cms.untracked.string('$Revision: 1.2 $'),
    annotation = cms.untracked.string('Summer09: Pythia6 generation of QCD events, 7TeV, D6T tune, pthat = 80 .. 120 GeV'),
    name = cms.untracked.string('$Source: /cvs_server/repositories/CMSSW/CMSSW/Configuration/GenProduction/python/PYTHIA6_QCDpt_80_120_7TeV_cff.py,v $')
)
        

• • the cross section can be found in ProductionSummer2009at7TeV, under request id = 1004060

Statistics: 184k evs corresponding to luminosity = 0.0289 pb-1 were truncated to a GenParticleCollection format and then analysed. More... Close
The original dataset contains 607k evs, the reduction is due to a CRAB failure to deliver the output files to CASTOR in 7 jobs out of 11. The 4 successful files are

/castor/cern.ch/user/f/fedotov/crab/ridge/QCDDiJet_Pt80to120.Summer10-START36_V9_S09-v1.GEN-SIM-RECO.SW363_genParticles/SW363.genParticles_1_1_YjX.root
/castor/cern.ch/user/f/fedotov/crab/ridge/QCDDiJet_Pt80to120.Summer10-START36_V9_S09-v1.GEN-SIM-RECO.SW363_genParticles/SW363.genParticles_2_1_N9o.root
/castor/cern.ch/user/f/fedotov/crab/ridge/QCDDiJet_Pt80to120.Summer10-START36_V9_S09-v1.GEN-SIM-RECO.SW363_genParticles/SW363.genParticles_6_1_ZkW.root
/castor/cern.ch/user/f/fedotov/crab/ridge/QCDDiJet_Pt80to120.Summer10-START36_V9_S09-v1.GEN-SIM-RECO.SW363_genParticles/SW363.genParticles_7_1_1hp.root

The files contain the GenParticleCollection and GenEventInfoProduct products only selected in the CRAB task with

process.out = cms.OutputModule("PoolOutputModule",
    fileName = cms.untracked.string( 'SW363.genParticles.root' ),
    outputCommands = cms.untracked.vstring("drop *",
                                           "keep GenEventInfoProduct_*_*_*",
                                           "keep *_genParticles_*_*"
                                           )
)

The CRAB stage: done under CMSSW_3_6_3.
The final analysis: CMSSW_3_7_0.

Selection of strings

The strings are selected with three cutoffs applied to the parameters of end partons:

selection label	cut #	cut
	1	pt(high-pt-end parton) > 50 GeV
A = 1*2	2	pt(low-pt-end parton) < 5 GeV
B = 1*2*3	3	> 8 for the distance between the high- and low-pt-end partons

The motivation for cuts A is a desire to have

• a "hard" string, and
• an asymmetry in pt between the end partons.

The motivation for the (two partons) > 8 is that

• for particle-parton correlations (see Method) for particles with (particle-parton) < 4 to be studied, the cut selects the particles which are closer to the high-pt parton,
• while for the two-particle correlation it provides a phase space (may be excessively) for two particles to reach (two particles) = 4 .

Some statistics:

     class    No. of   class
        ID   entries   comment

         1    183759  input evs
        10    183759  genParticles handle got
        20    654990  a string found
        30    654990  nMothers >= 2
        40    654990  all particles between the string ends are gluons
        50    100501  pt(highPtEnd) >        50
        60     75347     && pt(lowPtEnd) <         5
        70     75347  selected strings A (cuts on pt's of high-/low-pt ends) 
       100     75347  strings A with single-mother descendants
       200     29985  selected strings B (= A && eta-long strings)
       220     29985  strings B with single-mother descendants
       500    183759  evs with strings
       510     67327  evs with SELECTED strings A
       520     29150  evs with SELECTED strings B

• the initial inclusive string multiplicity = 3.6
• 41% and 16% of strings survive the cuts A and B respectively
• the multiplicity of the selected strings is 0.58 (or 1.03 for events where they are present)

The pt distributions of end partons for all the stings before selections :

Fig: Inclusive strings before selections

and their correlation:

Fig: Inclusive strings before selections

• the initial strings are quite asymmetric in terms of pt of end partons:
  < pt(high) > / < pt(low) > = ~8 .
• cuts A enlarge this asymmetry

The distribution of strings after the selection A in the distance between the high- and low-pt-end partons where the region > 8 is selected finally:

correlation between end partons of a string

• no significant deviation from a flat behaviour is seen

Multiplicities of stable particles

Multiplicities of stable particles in strings

The distribution of strings in the number of stable particles which are the string descendants, for selections A,B :

Fraction of stable string descendants in the total number of stable particles in event

The distribution of strings for selections A,B :

Event distribution in total number of stable particles

The events distributions are shown below for the three event samples:

1. all input events,
2. events with strings satisfying the selection A ,
3. events with strings satisfying the selection B .

Two particle correlations

The analysis is done in a set of particle-pt bins for stable particles - descendants of strings satisfying the selection B .

Total (over strings) numbers
of particles and particle pairs
in pt bins:

pt bin (GeV)	particles	pairs
all	3583929	255279573
0 - 0.5	2002457	79971668
.5 - 1	697580	10079592
1 - 2	440778	4335538
2 - 3	146175	479095
3 - 4	70187	110297
>4	226752	976802

Shown below for each bin (a subsection per bin) are

1. a 2-d pair distribution in
2. one or two zoomed versions of 1,
3. and a 1-d distribution in for 3.75 < < 4

Two particles : all pt

• There is a "ridge" at = 0 clearly extending to = 4 -- the effect we looked for.
  • the relative height of the bump at 3.75 < < 4 (0 degree / 110 degree - 1) is 5.8 %
• There is another ridge/bump at = 180 which is completely unexpected in a string fragmentation picture if there is no back-to-back correlation between end partons , and we did not see such a correlation in the corresponding plot

Two particles : 0 < pt < 0.5 GeV

• The enhancement towards = 0 is available, though its size is smaller than that in the all-pt case:
  ((0 deg / 170 deg) - 1) = 3.0 % at =3.75 - 4
• no back-to-back enhancement

Two particles : 0.5 < pt < 1 GeV

• the "parallel" enhancement gets larger:
  9.0% at = 3.75-4
• the back-to-back one appears

Two particles : 1 < pt < 2 GeV

• the "parallel" enhancement grows further:
  23% at = 3.75-4
• the back-to-back one does too

Two particles : 2 < pt < 3 GeV

• for the "parallel" enhancement, a decreased statistics does not allow to tell the trend; the size is
  10-30% at = 3.75-4
• the back-to-back enhancement continues to grow (up to 50% ?)

Two particles : 3 < pt < 4 GeV

• the "parallel" enhancement: statistics is low,
  the size in the interval 0-30% ( = 3.75-4)
• the back-to-back one: gets very high to about 200% ( = 3.75-4)

Two particles : pt > 4 GeV

• the "parallel" enhancement: disappears completely (in the tail of the back-to-back one?)
• the back-to-back enhancement: reached maximum size of ~700%

A summary for two particles correlations

• a "parallel" enhancement is observed at = 3.75-4 in the interval of pt 0 to 4 GeV. Its size grows from 3% at pt < .5 GeV to 23% at 1 < pt < 2 GeV, the further trend is unclear with the used statistics.
• the "parallel" enhancement is what was expected to be observed in a string fragmentation picture. However, its nature is not revealed in the current observation. E.g. the reason may be correlations between decay products of resonances and other unstable particles (even the photons from -decays may play a role; by the way, these photons may constitute up to 50% of the studied stable particle sample)
• a huge back-to-back enhancement is observed, which was not expected at all in the naive string fragmentation picture.

Particle - high-pt-parton correlations

particle-parton : all pt

• "parallel" and "back-to-back" enhancements are present

particle-parton : 0 < pt < 0.5 GeV

• "parallel" and "back-to-back" enhancements are present

particle-parton : 0.5 < pt < 1 GeV

• "parallel" and "back-to-back" enhancements are present

particle-parton : 1 < pt < 2 GeV

• "parallel" and "back-to-back" enhancements are present

particle-parton : 2 < pt < 3 GeV

• the "back-to-back" enhancement remains only

particle-parton : 3 < pt < 4 GeV

• the "back-to-back" enhancement is available only

particle-parton : pt > 4 GeV

• the "back-to-back" enhancement available only

A summary for particle-parton correlations

• a "parallel" enhancement is observed at = 3.75-4 in the interval of pt 0 to 2 GeV.
• a "parallel" enhancement is what was expected to be observed in a string fragmentation picture. Unlike to a similar enhancement in two-particle distribution, this one supports the naive string fragmentation picture, because this case ia a direct study of correlation between the particle and string variables.
• a back-to-back enhancement is also observed. Why does pythia produce it? A correlated appearence of gluons within a parton shower? The fragmentation of a string proceeding not independently of the fragmentation of other strings in an event?