Fluctuations and low transverse momentum correlation results from PHENIX

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by  J. T. Mitchell

Fluctuation and low transverse momentum
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Jeffery Mitchell†
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v BNL,USA
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E-mail: [email protected]
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ThePHENIXExperimentattheRelativisticHeavyIonColliderhasconductedasurveyoffluctu-
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7 ationsinchargedhadronmultiplicityinAu+AuandCu+Cucollisionsat√sNN =22,62,and200
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GeV.Auniversalpowerlawscalingformultiplicityfluctuationsexpressedass 2/m 2isobserved
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asafunctionofN forallspeciesstudiedthatisindependentofthetransversemomentumrange
e part
- of the measurement. PHENIX has also measuredtransversemomentumcorrelationamplitudes
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c
inp+p,d+Au,andAu+Aucollisions.Atlowtransversemomentum,significantdifferencesinthe
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n correlationsbetweenthebaselinep+pandd+AudataandtheAu+Audataarepresented.
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CorrelationsandFluctuationsinRelativisticNuclearCollisions
July7-92006
Florence,Italy
Speaker.
∗
†forthePHENIXCollaboration.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
FluctuationsandlowtransversemomentumcorrelationresultsfromPHENIX JefferyMitchell
1. A Survey ofChargedHadron MultiplicityFluctuations
The topic of event-by-event fluctuations of the inclusive charged particle multiplicity in rela-
tivistic heavy ioncollisions hasbeen revivedbytheobservation ofnon-monotonic behavior inthe
scaled variance asafunction ofsystem size atSPSenergies [1]. Thescaled variance isdefined as
s 2/m ,wheres 2representsthevarianceofthemultiplicitydistributioninagivencentralitybin,and
m isthemeanofthedistribution. Forreference,thescaledvarianceofaPoissondistribution is1.0,
independent of m . PHENIX has surveyed the behavior of inclusive charged particle multiplicity
fluctuations asafunctionofcentrality andtransverse momentumin√sNN =62GeVand200GeV
Au+Au and 22, 62, and 200 GeV Cu+Cu collisions in order to investigate if the non-monotonic
behavior persists atRHICenergies.
Details about thePHENIXexperimental configuration can befound elsewhere [2]. Allofthe
measurements described here utilize the PHENIXcentral arm detectors. The maximum PHENIX
acceptance of h <0.35 in pseudorapidity and 180o in azimuthal angle is considered small for
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event-by-eventmeasurements. However,theevent-by-eventmultiplicitiesarehighenoughinRHIC
heavyioncollisionsthatPHENIXhasacompetitivesensitivityforthedetectionofmanyfluctuation
signals. Forexample,adetailedexaminationofthePHENIXsensitivitytotemperaturefluctuations
derivedfromthemeasurement ofevent-by-event mean p fluctuations isdescribed in[3].
T
Ithasbeendemonstratedthatchargedparticlemultiplicity fluctuationdistributions inelemen-
taryandheavyioncollisionsarewelldescribedbynegativebinomialdistributions (NBD)[4]. The
NBDofanintegermisdefinedby
(m+k 1)! (m /k)m
P(m)= − (1.1)
m!(k 1)! (1+m /k)m+k
−
whereP(m)isnormalizedfor0 m ¥ ,m <m>. TheNBDcontains anadditional parameter,
≤ ≤ ≡
k, whencompared toaPoisson distribution. TheNBDbecomes aPoisson distribution inthelimit
k ¥ . ThevarianceandthemeanoftheNBDisrelatedtokby1/k=s 2/m 2 1/m . ThePHENIX
→ −
multiplicity distributions arewelldescribedbyNBDfitsforallspecies,centralities, andtransverse
momentumranges. ThedatapresentedhereareresultsofNBDfitsofthemultiplicitydistributions,
anexampleofwhichisshowninFig. 1.
Each 5% wide centrality bin selects a range of impact parameters. This introduces a com-
ponent to the multiplicity fluctuations that can be attributed to fluctuations in the geometry of the
collision. Itisdesireabletoestimateandremovethisknownsourceoffluctuationssothatonlyfluc-
tuations due tothe dynamics ofthe collision remain. The contribution of geometrical fluctuations
isestimatedusingtheHIJINGeventgenerator[5],whichwellreproduces themeanmultiplicityof
RHICcollisions[6]. Theestimateisperformedbycomparingfluctuationsfromeventswithafixed
impactparametertofluctuationsfromeventswitharangeofimpactparameterscoveringthewidth
of each centrality bin, as determined from Glauber model simulations. TheHIJING estimates are
confirmedbycomparingtheHIJINGfixed/ranged fluctuationratiostomeasured1%/5%binwidth
fluctuation ratios. The magnitude of the scaled variance is reduced by this correction. A 15%
systematic errorforthisestimateisincluded intheerrorsshown.
Bymeasuringthescaledvarianceinsuccessivelywiderazimuthalranges,alineardependence
on azimuthal acceptance is observed, with the scaled variance increasing with azimuthal accep-
tance. Inordertofacilitatedirectcomparisonswithotherexperiments,themultiplicityfluctuations
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FluctuationsandlowtransversemomentumcorrelationresultsfromPHENIX JefferyMitchell
N
d
/Nevents
d104
103
102
0 20 40 60 80 100
N
Figure1: PHENIXPreliminary. Theevent-by-eventinclusivechargedhadronmultiplicitydistributionfor
0-5% central200 GeV Au+Au collisions with transverse momentumin the range 0.2< p <2.0 GeV/c.
T
ThedashedlineisaNegativeBinomialDistributionfittothedata.
quoted here have been linearly extrapolated to 2p acceptance by fitting the azimuthal dependance
within the detector acceptance. Systematic errors due to the extrapolation have been included in
thetotalerrorsshown. TheresultsofthesurveyareshowninFig. 2through5,wherethecorrected
scaledvariance isplottedasafunction ofcentrality andtransverse momentumrange.
In the Grand Canonical Ensemble, the variance and the mean of the particle number can be
directly related to the compressibility: s 2/m 2 =k (T/V)k , where k is Boltzmann’s constant,
B T B
T is the system temperature, and V is its volume [7]. The multiplicity fluctuations in terms of
s 2/m 2=1/k +1/m areshowninFig. 6asafunctionofcentralityforAu+Aucollisionsat200
NBD
and 62 GeV and Cu+Cu collisions at 200, 62, and 22 GeV. In order to demonstrate their scaling
propertiesasafunctionofcentrality,eachcurvehasbeenscaledtothe200GeVAu+Aucurve. All
fourdatasetscanbedescribed byapower-lawfunction asfollows: s 2/m 2(cid:181) N 1.40 0.03.
p−art ±
Itisexpectedthatthecompressibilitydivergesasoneapproachesthecriticalpoint,andtherate
g
of divergence is described by a power law, k =A((T T )/T ) , where T is the value of the
T C C − C
−
temperature at the critical point, and g is the critical exponent for isothermal compressibility [7].
However,itisnotprudenttointerprettheobservedscalingascriticalbehaviorsinceithasnotbeen
established that the temperature varies significantly as a function of N . A more robust critical
part
exponentstudycouldbeperformedwithaRHICscanatlowenergywherethefreeze-outtempera-
turecould beestimated from identified particle spectra andHanbury-Brown Twisscorrelations, as
outlined in[9].
Figures 6 and 7 show the multiplicity fluctuations as a function of centrality for different
p ranges. In each case, the exponent of the power law function describing the data remains
T
unchanged. Hence, theinfluence of p -dependent processes athigher p ,such ashard scattering,
T T
have little effect on the scaling properties. The scaling also applies to the low energy 22 GeV
Cu+Cudata.
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FluctuationsandlowtransversemomentumcorrelationresultsfromPHENIX JefferyMitchell
2. Low Transverse Momentum Correlations
Thetechnique oftwo-particle correlations has demonstrated itseffectiveness inextracting in-
formation about jet production in reference (p+p and d+Au) and heavy-ion collisions at RHIC.
Some features of the correlations are dependent on the p of the trigger and associated particles.
T
It is important to examine and understand the evolution of correlation functions from high to low
p in heavy ion collisions with comparisons to reference collisions. Examining the p evolution
T T
ofthecorrelations mayprovide information thatcanaidintheinterpretation ofsuchfeatures such
asexcessjetproduction atlow p oreventually theobserveddisplaced awaysidepeaks.
T
Interpreting correlation functions at low p (in this context, with both the trigger and associ-
T
ated particle below 1 GeV/c) is complicated by several factors: a) the hard scattering correlation
becomesreducedinamplitudeanddilutedinazimuthalseparation,b)correlationsduetocollective
flow are present, although the magnitude of elliptic flow is much reduced at low p , c) Hanbury-
T
Brown Twiss correlations are also present, and d) correlations due to resonance production are
present. Inordertohelpdisentangle thelattertwocontributions, allcorrelations areseparated into
only like-sign or only unlike-sign pairs. Here, only the like-sign results, which should not have a
significant resonance contribution, arepresented.
Theminimumbiasdatasetsanalyzedherecontain10millioneventsfromtheRHICRun-3p+p
run,10millioneventsfromtheRun-3d+Aurun,2millioneventsfromtheRun-4200GeVAu+Au
run, and 750,000 events from the Run-4 62 GeV Au+Au run. All correlation functions are con-
structed using astrict mixedevent procedure withall cuts, including track proximity cuts, applied
identically tothe data andmixed event samples. Mixed events areconstructed from identical data
classes (distinguished by centralities within 5% and event vertex z coordinates within 10 cm) by
directlysamplingthedatachargedparticlemultiplicitydistributionafterallcutshavebeenapplied.
Since every event contains multiple particles at low p , the correlations are constructed by
T
considering every particle in the event as a trigger particle in succession and associating it with
everyotherparticleintheevent. Correlationsconstructedinthismannerareauto-correlations [10].
Thecorrelationamplitudesreportedherearenormalizedbin-by-binasfollows:C= Ndata/Nevents,data ,
Nmixed/Nevents,mixed
where N and N are the number of pair counts in a given p and/or D f bin. Correlations
data mixed T
shown for the near-side are defined as the integrated correlation amplitude over the range D f <
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60o.
Correlationamplitudesplottedasafunctionofthetransverserapidity,y =ln((m +p )/m )
T T T 0
with the pion mass assumed for m , for like-sign pairs on the near-side, are shown in Fig. 8 for
0
minimumbias200GeVd+AucollisionsandinFig. 9for0-5%central200GeVAu+Aucollisions.
They variableischoseninordertoemphasizethedistributionatlow p withrespecttothatathigh
T T
p andtofacilitate comparisons tomeasurements bytheSTARCollaboration [10]. Forreference,
T
y =1.5corresponds to p =300MeV/candy =2.7corresponds to p =1.0GeV/cforpions.
T T T T
There are two primary features observed in these correlations. First, there is the expected large
correlation amplitude primarily due to hard scattering processes when either particle in the pair
has a large p along with a small fractional contribution due to elliptic flow. Second, there is a
T
peak when both pairs have low p . This peak is dominated by HBTcorrelations, which has been
T
confirmed by observing a sharp reduction in the amplitude of the peak for unlike-sign pairs and
by simultaneously observing a peak in the Q distribution in this region for like-sign pairs.
invariant
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FluctuationsandlowtransversemomentumcorrelationresultsfromPHENIX JefferyMitchell
Closer xamination of the low p peak reveals that there is a difference in the location of the peak
T
iny between d+AuandAu+Aucollisions. Ind+Aucollisions, thepeakamplitude risesuptothe
T
low p edge of the PHENIXacceptance. This holds for p+p collisions, also. However, there is a
T
maximuminthepeakaty 1.4(p 250MeV/c)inAu+Aucollisionsatboth200and62GeV.
T T
≈ ≈
Fig. 10showsthepeaktakenalong the p = p diagonal fornear-side like-sign pairs. Possible
T,1 T,2
explanations forthesedifferences requirefurtherstudy.
Tofacilitate amore detailed direct comparison of the d+Auand Au+Au correlations over the
entire p range, it is necessary to subtract the flow component from the Au+Au azimuthal corre-
T
lation distributions. This is done by fitting the near-side region (D f <90o) of these distributions
with a function containing a harmonic cos(2D f ) term and a Gaussian distribution with a mean of
D f =0. Forp+p andd+Au collisions, the Gaussian fitisperformed, but theharmonic term isnot
included.
Fig. 11showsthecorrelation amplitudefromthenear-sideGaussianfitforlike-signpairsasa
functionofcentrality. Forthisplot,allpairshavea p between200and500MeV/c. Inordertobest
T
isolate the HBT contribution to the peak, all pairs are required to be within D h <0.1. For both
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200 and 62 GeV Au+Au collisions, the amplitude drops exponentially as a function N .
participants
Only asmall fraction of the decrease in the amplitude isdue to random dilution ofthe correlation
amplitude [11].
Fig. 12 shows the standard deviation of the near-side Gaussian fit for like-sign pairs as a
functionofcentrality. Again,bothparticlesinallpairshavea p between200and500MeV/cand
T
D h <0.1. Theerror bars are dominated by systematic errors due to the fitting procedure. There
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isalargedifferenceobservedinthewidthbetweenp+pandd+Aucollisions. InAu+Aucollisions,
particularly forthe higher statistics 200 GeVAu+Audataset, asignificant increase inthe width is
seeninthemostcentralcollisions.
Fig. 13 shows the correlation amplitude for the near-side Gaussian fit for like-sign pairs as
a function of transverse momentum. Here, p < p < p and p < p < p (p
T,min T,1 T,max T,min T,2 T,max T
withinthelimitsofthebin, p and p )and D h <0.1. Thepointsareplottedinthegeomet-
T,min T,max
| |
ric center of the bin. The bins are exponentially distributed in order to nullify any variations due
torandomdilutionofthecorrelation amplitudeswithineachcollisionspecies. Inboththep+pand
d+Audatasets,theamplitudesarerelativelyflatasafunctionof p uptoabout1-1.5GeV/c,where
T
theamplitudesbegintorisesignificantly. Thisriseislikelyduetotheinfluenceofcorrelations due
to jets, which has been confirmed by the appearance of an away-side component in the azimuthal
correlations. A rise in the correlation amplitudes for Au+Au collisions is also seen starting at the
same p . However, unlike the p+p and d+Au datasets, the Au+Au data exhibit an exponential
T
decreaseintheamplitudeasafunctionof p below1GeV/c. Thisdecreaseiscontrarytothetrend
T
inthereferencedatasets, andcontrarytotheansatzofsignificantcontributions fromjetproduction
atlow p [10]. Moredetailed studiesofthecauseofthiseffectareunderway.
T
3. Summary
PHENIX has completed a comprehensive survey of charged hadron multiplicity fluctuations
forseveraldifferentcollisionspeciesandenergies, allofwhichdemonstrateauniversalpower-law
scaling as a function of N . Also presented is a survey of two-particle correlations for several
part
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FluctuationsandlowtransversemomentumcorrelationresultsfromPHENIX JefferyMitchell
collision species at 62 and 200 GeV focusing on the behavior of the near-side peak for like-sign
pairs, which is dominated by HBT correlations. Examination of spatial HBT correlations shows
severalstatistically significantdifferencesbetweenp+pandd+AucollisionsandAu+Aucollisions
thatwillwarrantfurtherstudy.
References
[1] RybczynskiMetal(NA49Collaboration)2004Preprintnucl-ex/0409009.
[2] AdcoxKetal(PHENIXCollaboration)2003Nucl.Instrum.Meth.A499469.
[3] AdcoxKetal(PHENIXCollaboration)2002Phys.Rev.C66024901.
[4] AbbottTetal(E-802Collaboration)1995Phys.Rev.C522663.
[5] WangXandGyulassyM1991Phys.Rev.D443501.
[6] AdlerSetal(PHENIXCollaboration)2005Phys.Rev.C71034908.
[7] StanleyH1971OxfordUniversityPress,Inc..
[8] StephanovMetal1999Phys.Rev.D60114028.
[9] S.Adleretal.(PHENIXCollaboration),Phys.Rev.C72(2005)014903.
[10] AdamsJetal(STARCollaboration)Pre-printnucl-ex/0509030.
[11] VoloshinS.Pre-printnucl-th/0410024.
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FluctuationsandlowtransversemomentumcorrelationresultsfromPHENIX JefferyMitchell
200 GeV Au+Au
62 GeV Au+Au
e e
c c
n2.2 n2.2
a a
ari 2 ari 2
V V
ed 1.8 ed 1.8
al al
c1.6 c1.6
S S
1.4 1.4
100 100
1.2 150 1.2 150
200 200
10.5 1 1.5 2 2.5 3 353002N050participants 10.5 1 1.5 2 2.5 3 302N050participants
pT,max [GeV/c] pT,max [GeV/c]
Figure2: PHENIXPreliminarymultiplicityfluctua- Figure3: PHENIXpreliminarymultiplicityfluctua-
tionsfor inclusivechargedhadronsin termsof s 2/m tionsforinclusivechargedhadronsin termsof s 2/m
as a function of N and the transverse mo- as a function of N and the transverse mo-
participants participants
mentumrange0.2<p <p GeV/cfor200GeV mentum range 0.2< p < p GeV/c for 62 GeV
T T,max T T,max
Au+Au collisions. The data have been corrected to Au+Au collisions. The data have been corrected to
remove impact parameter fluctuations and have been remove impact parameter fluctuations and have been
extrapolatedto2p azimuthalacceptance. extrapolatedto2p azimuthalacceptance.
200 GeV Cu+Cu 62 GeV Cu+Cu
e e2.8
c c
an2.2 an2.6
ari 2 ari2.4
V V
d 1.8 d 2.2
e e
cal1.6 50 cal 2 50
S 60 S1.8 60
1.4
70 1.6 70
1.2 80 1.4 80
10.5 1 1.5 2 pT,ma2x. 5[GeV/c]3 10900Nparticipants 1.20.5 1 1.5 2 pT,ma2x .[5GeV/c]3 10900Nparticipants
Figure4: PHENIXpreliminarymultiplicityfluctua- Figure5: PHENIXpreliminarymultiplicityfluctua-
tionsfor inclusivechargedhadronsin termsof s 2/m tionsforinclusivechargedhadronsin termsof s 2/m
as a function of N and the transverse mo- as a function of N and the transverse mo-
participants participants
mentumrange0.2<p <p GeV/cfor200GeV mentum range 0.2< p < p GeV/c for 62 GeV
T T,max T T,max
Cu+Cu collisions. The data have been corrected to Cu+Cu collisions. The data have been corrected to
remove impact parameter fluctuations and have been remove impact parameter fluctuations and have been
extrapolatedto2p azimuthalacceptance. extrapolatedto2p azimuthalacceptance.
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FluctuationsandlowtransversemomentumcorrelationresultsfromPHENIX JefferyMitchell
2 1
m22/ 1 PHENIX Preliminary ms2/ PHENIX Preliminary
s
10-1
10-1
200 GeV Au+Au
62 GeV Au+Au
200 GeV Cu+Cu
200 GeV Au+Au
62 GeV Cu+Cu
62 GeV Au+Au
22 GeV Cu+Cu
200 GeV Cu+Cu 10-2
10-2 62 GeV Cu+Cu
22 GeV Cu+Cu
102
102 N Nparticipants
participants
Figure 7: Multiplicity fluctuations for inclusive
Figure 6: Multiplicity fluctuations for inclusive
charged hadrons in the transverse momentum range
charged hadrons in the transverse momentum range
0.2< p <0.75GeV/cintermsofs 2/m 2 asafunc-
0.2<p <2.0GeV/cintermsofs 2/m 2asafunction T
T
tion of N for 200 GeV Au+Au, 62 GeV
ofN for200GeVAu+Au,62GeVAu+Au, participants
participants
Au+Au, 200 GeV Cu+Cu, 62 GeV, and 22 GeV
200 GeV Cu+Cu, 62 GeV, and 22 GeV Cu+Cu col-
Cu+Cu collisions. Thedata havebeenscaled byfac-
lisions. The data have been scaled by factors of 1.0,
tors of 1.0, 0.73, 1.43, 0.73, and 1.0, respectively, in
0.73, 1.43, 0.73, and 1.0, respectively, in order to
ordertoemphasizetheuniversalscalingofallspecies.
emphasize the universal scaling of all species. The
Thedashedcurveisapowerlawfitasdescribedinthe
dashedcurveisapowerlawfitasdescribedinthetext.
text.
Figure 8: Near-side correlation amplitudes for like- Figure 9: Near-side correlation amplitudes for like-
sign pairs as a function of the transverse rapidity of sign pairs as a function of the transverse rapidity of
each particle in the pair for minimum bias 200 GeV each particle in the pair for 0-5% central 200 GeV
d+Aucollisions. Au+Aucollisions.
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FluctuationsandlowtransversemomentumcorrelationresultsfromPHENIX JefferyMitchell
PHENIX Preliminary: |D h |<0.7, Like-Sign, Near-Side
e 1.4
d 200 GeV Au+Au, 0-5% Central
u
Correlation Amplit 1.21 6220 0G GeVeV A du++AAuu,, M0-i5n%. B Ciaesntral Near-side Correlation Amplitude (flow subtracted)10-1 P00MM--H55iinn%%E.. N BBCCiiIeeaaXnnss tt22Prraa00rll00 e26 GGl02i0 eemGVV Gei ndpVe++Va AAp rA,uuy |u+D,, +A| DLhAu |ih<u,k |0,|<De .|0D1 -h.s 1h|<i|g<0.0n1. 1pairs
0.8 0 50 100 150 200 250 300 350 400
11 11..55 22 22..55 N
participants
yy
TT
Figure11: Near-sidecorrelationamplitudesforlike-
sign pairs with p between 200 and 500 MeV/c and
T
D h < 0.1 for p+p, d+Au, and Au+Au collisions.
Figure10: Near-sidecorrelationamplitudesforlike-
| |
Flow hasbeensubtractedfromtheAu+Audata. The
signpairswithp binschosensuchthatp =p for
T T,1 T,2
errorsaredominatedbysystematicerrorsduetothefit
Au+Auandd+Aucollisions.Thesecorrelationampli-
procedure.
tudes include contributions from flow in the Au+Au
collisions. The error bars include statistical and sys-
tematicerrors.
w subtracted) [degrees] 12235500 PHENIX Preliminary, Like-sign pairs Amplitude (flow subtracted)10-11 PHENIX Preliminary. Like-sign pairs.
s (floNear-side peak 1050 0MM0--55iinn%%.. BBCCiieeaannss tt22rraa00ll00 26 GG020 eeGVV Ge dpVe++V AAp A,uu |u+D, +A| DhAu |h<u, |0,|<D .|0D1 h. 1h|<|<0.01.1 Near-side Correlation 1100--32 00MM--55iinn%%.. BBCCiieeaannss tt22rraa00ll00 26 GG020 eeGVV Ge dpVe++V AAp Auuu++AAuu
0 50 100 150 200 250 300 350 400 1
Nparticipants pT [GeV/c]
Figure12: Near-sidecorrelationwidthsforlike-sign Figure13: Near-sidecorrelationamplitudesforlike-
pairswithpT between200and500MeV/cand D h < sign pairs both with pT within the given pT bin and
0.1 for p+p, d+Au, and Au+Au collisions. Flo|w h|as with D h < 0.1 for p+p, d+Au, and 0-5% central
| |
beensubtractedfromtheAu+Audata. Theerrorsare Au+Aucollisions. Flowhasbeensubtractedfromthe
dominated by systematic errors due to the fit proce- Au+Audata. Theerrorsaredominatedbysystematic
dure. errorsduetothefitprocedure.
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