Elliptic flow of Lambda hyperons in Pb+Pb collisions at 158A GeV

0.25 MB·English

by  G. Stefanek

Elliptic flow of Λ hyperons in Pb+Pb collisions at 158A GeV
C. Alt,9 T. Anticic,21 B. Baatar,8 D. Barna,4 J. Bartke,6 L. Betev,10 H. Bia lkowska,19 C. Blume,9 B. Boimska,19
M. Botje,1 J. Bracinik,3 R. Bramm,9 P. Bunˇci´c,10 V. Cerny,3 P. Christakoglou,2 P. Chung,23 O. Chvala,15
J.G. Cramer,17 P. Csato´,4 P. Dinkelaker,9 V. Eckardt,14 D. Flierl,9 Z. Fodor,4 P. Foka,7 V. Friese,7 J. G´al,4
M. Ga´zdzicki,9,12 G. Georgopoulos,2 E. G ladysz,6 K. Grebieszkow,22 S. Hegyi,4 C. Ho¨hne,13 K. Kadija,21
A. Karev,14 M. Kliemant,9 S. Kniege,9 V.I. Kolesnikov,8 E. Kornas,6 R. Korus,12 M. Kowalski,6 I. Kraus,7
M. Kreps,3 R. Lacey,23 A. Laszlo,4 M. van Leeuwen,1 P. L´evai,4 L. Litov,18 B. Lungwitz,9 M. Makariev,18
A.I. Malakhov,8 M. Mateev,18 G.L. Melkumov,8 A. Mischke,7 M. Mitrovski,9 J. Molna´r,4 St. Mr´owczyn´ski,12
7
0 V. Nicolic,21 G. Pa´lla,4 A.D. Panagiotou,2 D. Panayotov,18 A. Petridis,2 M. Pikna,3 D. Prindle,17 F. Pu¨hlhofer,13
0 R. Renfordt,9 C. Roland,5 G. Roland,5 M. Rybczyn´ski,12 A. Rybicki,6 A. Sandoval,7 N. Schmitz,14 T. Schuster,9
2 P. Seyboth,14 F. Sikl´er,4 B. Sitar,3 E. Skrzypczak,20 G. Stefanek,12,∗ R. Stock,9 C. Strabel,9 H. Stro¨bele,9

n T. Susa,21 I. Szentp´etery,4 J. Sziklai,4 P. Szymanski,10,19 V. Trubnikov,19 D. Varga,4,10 M. Vassiliou,2 G.I. Veres,4,5
a G. Vesztergombi,4 D. Vrani´c,7 A. Wetzler,9 Z. W lodarczyk,12 A. Wojtaszek,12 I.K. Yoo,16 and J. Zim´anyi4,†
J
(The NA49 collaboration)
7
1 1NIKHEF, Amsterdam, Netherlands.
2Department of Physics, University of Athens, Athens, Greece.

2 3Comenius University, Bratislava, Slovakia.
v 4KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary.
6 5MIT, Cambridge, USA.
2 6The H.Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland.
0 7Gesellschaft fu¨r Schwerionenforschung (GSI), Darmstadt, Germany.
6 8Joint Institute for Nuclear Research, Dubna, Russia.
0 9Fachbereich Physik der Universit¨at, Frankfurt, Germany.
6
10CERN, Geneva, Switzerland.
0
11University of Houston, Houston, TX, USA.
/
x 12Institute of Physics S´wie¸tokrzyska Academy, Kielce, Poland.
e 13Fachbereich Physik der Universit¨at, Marburg, Germany.
- 14Max-Planck-Institut fu¨r Physik, Munich, Germany.
l
c 15Institute of Particle and Nuclear Physics, Charles University, Prague, Czech Republic.
u 16Department of Physics, Pusan National University, Pusan, Republic of Korea.
n 17Nuclear Physics Laboratory, University of Washington, Seattle, WA, USA.
v: 18Atomic Physics Department, Sofia University St. Kliment Ohridski, Sofia, Bulgaria.
i 19Institute for Nuclear Studies, Warsaw, Poland.
X 20Institute for Experimental Physics, University of Warsaw, Warsaw, Poland.
r 21Rudjer Boskovic Institute, Zagreb, Croatia.
a 22Warsaw University of Technology, Warsaw, Poland.
23Department of Chemistry, SUNY Stony Brook, USA.
TheellipticflowofΛhyperonshasbeenmeasuredbytheNA49collaborationattheCERN-SPSin
semi-centralPb+Pbcollisions at158A GeV. Thestandardmethodofcorrelatingparticleswiththe
eventplanewas used. Measurementsof v2 nearmid-rapidityarereported as afunction of rapidity,
centrality and transverse momentum. Elliptic flow of Λ particles increases both with the impact
parameter and with the transverse momentum. It is compared with v2 for pions and protons as
wellaswithmodelcalculations. Theobservationofsignificantellipticflowanditsmassdependence
suggeststrongcollectivebehaviorofthematterproducedincollisionsofheavynucleialreadyatthe
SPS. Scaling properties of elliptic flow of different particle species have been tested at 158A GeV.
The limited pT range of thedata does not allow for a decisive test of the coalescence model.
PACSnumbers: 25.75.Ld
I. INTRODUCTION
Elliptic flow in relativistic nuclear interactions has its
∗Correspondingauthor. E-mailaddress: [email protected] origin in the spatial anisotropy of the initial reaction
†Deceased
volume in non-central collisions and in particle rescat-
terings in the evolving system which convert the spatial
anisotropy into a momentum anisotropy [1]. The spatial
2
anisotropy decreases rapidly because of the fast expan- charged particles, which include the Λ decays into pro-
sion of the system [2] making the momentum anisotropy ton and π− (branching ratio 63.9%). The identification
measured at the end of this evolution strongly depen- method[14]reliesontheevaluationoftheinvariantmass
dent on the matter properties and the equation of state distributionandis enhancedby daughter particleidenti-
(EoS) at the early stage [3, 4]. Comparison of measured ficationapplying a cut in dE/dx aroundthe expectation
anisotropies with hydrodynamic model calculations pro- value derived from a Bethe-Bloch parametrization. The
vide an importanttest of the degree of thermalisationin extractedΛcandidateshaveabackgroundcontamination
the produced particle system at the early stage. Flow of of 5-9% in the p-π invariant mass window 1.108 1.124
heavy particles is affected more strongly by changes in GeV/c2, depending oncentrality. The yields of Λ−hyper-
the EoS than flow of pions [4, 5, 6]. onsareobtainedbycountingthenumberofentriesinthe
The anisotropic flow parameters measured to date at invariant mass peak above the estimated background as
SPSandlowerenergiesaremainlythoseofpionsandpro- a function ofthe azimuthalangleφ of Λ candidates with
tons[7,8]. RHICexperimentshavemeasuredellipticflow respect to the event plane angle Φ2EP. The background
for many particle species [9], including hyperons [9, 10]. is estimated from a fit of invariant mass spectra to the
In these experiments, the rapid rise of elliptic flow with sum of a Lorentz distribution and a polynomial. It is
transverse momentum (pT) up to 1.5 GeV/c and its subtracted in 16 bins of φ Φ2EP. The acceptance of
−
particle-mass dependence are well reproduced by hydro- Λ hyperons covers the range 0.4 . pT . 4 GeV/c and
dynamicmodels[9]. Athighervaluesofp quarknumber 1.5 . y . 1.0 but the detection efficiency strongly de-
T
−
scalingofellipticflowhasbeenobservedatRHIC[10,11] pends on azimuthal angle, pT and y. Thus we have to
which indicates that the quark coalescence mechanism introducedifferentialcorrectionstoavoidbiaseswhenav-
dominates hadron production in the intermediate pT re- eragingv2 overrapidityandtransversemomentum. Mul-
gion [12]. In order to test the validity of this scenario tiplicativefactorswereintroducedforeveryΛparticleto
at SPS energies we have extended elliptic flow measure- correct the Λ yields for detector and reconstruction effi-
ments in 158A GeV Pb+Pb (√sNN = 17.2 GeV) colli- ciency. They were determined as ratios of published Λ
sions to Λ hyperons. In this paper, results on Λ elliptic yields [15], parametrized by the Blast Wave model, to
flow as a function of the center of mass rapidity (y) and the measured raw Λ yields.
transversemomentumwillbepresentedandcomparedto Theelliptic flowanalysisisbasedonthestandardpro-
model calculations. cedure outlined in [8, 16] to reconstruct the event plane
for each event and the corrections for the event plane
resolution. The eventplaneis anexperimentalestimator
II. ANALYSIS of the true reaction plane and is calculated from the az-
imuthaldistributionofprimarychargedπ mesons. Iden-
tificationofpionsisbasedondE/dxmeasurementsinthe
The main components of the NA49 detector [13] are
TPCs. To avoid possible auto-correlations, tracks asso-
four large-volume Time Projection Chambers (TPCs)
ciated with Λ candidates are excluded from the event
for tracking and particle identification by energy loss
plane calculation. The method to determine the event
(dE/dx) measurement with a resolution of 3 6%. The
TPC system consists of two vertex chambers−inside the plane azimuthal angle Φ2EP uses the elliptic flow of pi-
ons, according to the formula:
spectrometermagnetsandtwomainchambersplacedbe-
hindthemagnetsatbothsidesofthebeam. Downstream N
i i
of the TPCs a veto calorimeter detects projectile spec- X = p [cos(2φ ) cos(2φ) ],
2 T −h i
tators and is used for triggering and centrality selection. Xi=1
The data sample consists of3 106 semi-centralPb+Pb N
events after online trigger sel×ection of the 23.5% most Y = pi [sin(2φi) sin(2φ) ], (1)
2 T −h i
centralcollisions. Theeventsweredividedintothreedif- Xi=1
ferentcentralitybins,whichcorrespondto thefirstthree 1 Y
bins used in a previous analysis (see Table 1 in [8]) and Φ2EP = tan−1 2 ,
2 (cid:18)X (cid:19)
2
are defined by centrality ranges 0-5% (bin 1), 5-12.5%
(bin 2), and 12.5-23.5% (bin 3). Many model predic- where X ,Y are the components of the eventplane flow
2 2
tions are published for impact parameter ranges similar vector Q and the sums run over accepted charged pion
2
tothoseofourcentralityclasses,whichare: 0-3.4fm(bin tracks in an event. The acceptance correction is based
1), 3.4-5.3fm (bin 2), and 5.3-7.4fm (bin 3) for our cen- ontherecenteringmethod[8]whichconsistsofsubtract-
trality classes. The measurement in the centrality range ing in Eq. 1 the mean values cos(2φ) and sin(2φ) .
h i h i
σ/σTOT = 5 23.5% (called mid-central) is obtained by These mean values are calculated in bins of pT and ra-
−
averaging the results of bins 2 plus 3 with weights cor- pidity for all pions inthose events which containat least
responding to the fractions of the total cross section in one Λ hyperon candidate. The values were stored in a
these bins. 3-dimensional matrix of 20 p intervals, 50 rapidity in-
T
TheΛhyperoncandidateswereselectedfromthesam- tervals, and eight centrality bins. A second level accep-
ple of V0-track configurations consisting of oppositely tance correctionis done by using mixed events. We used
3
bins 1, 2 and 3, respectively. The total errors in Figs. 2-
4 are given by the quadratic sum of contributions from
the statistical error of the signal, the uncertainty due to
the background subtraction, the mixed event correction
and event plane resolution. The observed hexadecupole
obs
anisotropy v is consistent with zero within statistical
4
errors for all centrality bins.
III. RESULTS
The finalstatistics inoursample consistsofabout106
Λcandidates. Thisallowsflowanalysisforseveralrapid-
ityandp bins. TwosampleazimuthaldistributionsofΛ
T
FIG.1: (coloronline).AzimuthaldistributionsofΛhyperons
withrespecttotheeventplaneforrealevents(solidsymbols)
andmixed-events(opensymbols) intwocentralitybins. The
curvesare Fourier expansion fits (see text Eq. (2)).
10 mixed events for each real event. Particles for mixed
events arerandomly selectedfromdifferent eventsin the
samecentralitybinwithatleastoneΛhyperon. Thefinal
angulardistributions areobtainedbydividing the realΛ
angular distribution by the mixed event distribution to
remove the acceptance correlations remaining after re-
centering. The corrected Λ azimuthal distributions are
then fitted with a truncated Fourier series:
dN
=
d(φ Φ )
2EP
− FIG.2: (coloronline).EllipticflowofΛhyperonsasafunction
obs
const×(1 + v2 cos[2(φ−Φ2EP)] (2) of rapidity (top) and pT (bottom). The open points in the
+ vobscos[4(φ Φ )]). top graph havebeen reflected about midrapidity.
4 − 2EP
The elliptic flowv is evaluatedbydividing the observed
2
obs hyperonswithrespecttotheestimatedreactionplanefor
anisotropy v by the event plane resolution R:
2
real and mixed events are shown in Fig. 1. The curves
vobs represent results of fits with the truncated Fourier se-
v2 = 2 . (3) ries Eq. (2). The distributions exhibit a strong corre-
R
lation for real events (full symbols and curves). As ex-
The resolution, pected,nocorrelationisobservedformixed-events(open
symbols, dashed curves). The p averaged elliptic flow
T
R=q2hcos[2(Φa2EP−Φb2EP)]i, icsutosb.tIatineexdhibfriotsmnoalsligidneifinctaifinetddeΛpehnydpeenrcoenosnwriatphioduittypaTs
is calculated from the correlation of two planes shown in Fig. 2(top). The absence of a rapidity depen-
a b
(Φ ,Φ )forrandomsub-eventswithequalmultiplic- dence of v (y) was also observed for protons (see Fig. 6
2EP 2EP 2
ity. TheresultsareR=0.27,0.34and0.40forcentrality in Ref. [8]) in mid-central events. We use the Λ sample
4
0.15
π STAR 5 - 30 %
2
v π NA49 5 - 23.5 %
0.1
0.05
0
protons STAR 5 - 30 %
protons NA49 5 - 23.5 %
-0.05
0 1 2 3
p (GeV/c)
T
FIG. 4: (color online). Elliptic flow for charged pions (cir-
cles) and protons (triangles) as a function of pT from mid-
centraleventsmeasuredbytheSTAR[9](opensymbols)and
NA49[8] (solid symbols) experiments.
FIG. 3: (color online). Elliptic flow of Λ hyperons as a func-
tionofpTfrommid-central(top)andcentral(bottom)events cantly (Fig. 3 bottom). A comparisonof v2 of pions and
measuredbytheSTAR(opensymbols)andNA49(solidsym- protons obtained by NA49 [8] and STAR [9] for mid-
bols)experiments. Curvesarehydrodynamicalmodelpredic- central collisions is shown in Fig. 4. The NA49 values
tions at RHICenergy for thetwo different centrality bins. were obtained as the cross section weighted averages of
the measurements published in [8] for the appropriate
centralityrange. AsobservedforΛhyperons,v ofpions
2
also rises faster with p at RHIC than at SPS. Protons
T
from the full rapidity range of the data in Fig. 2(top) seemto exhibita similartrend, but the limited pT range
for the study of v as a function of p . The p de- and the larger measurement errors do not allow a firm
2 T T
pendence of rapidity-averaged Λ elliptic flow is shown conclusion.
in the bottom plot of Fig. 2 for two centrality ranges. A comparison of v (p ) for pions, protons and Λ hy-
2 T
The v parameter significantly increases with transverse perons as measured by the NA49 experiment in mid-
2
momentum, the rise being stronger for more peripheral central events is displayed in Fig. 5. The elliptic flow
events. Fig. 3 shows a comparison of v (p ) of Λ hyper- growslinearlywithp forallparticlespeciesbuttherise
2 T T
ons for mid-central and central (0-5%) events measured for pions starts from p close to zero while for protons
T
by the NA49 and STAR experiments [17]. The NA45 and Λ particles it starts from p 0.5 GeV/c. The el-
T
≈
collaboration recently also presented preliminary results liptic flow for pions is significantly larger than that for
in Pb+Au collisions at the top SPS energy [18] which heavier particles although at p 2 GeV/c the flow
T
≈
agree well with the NA49 results (not shown). For mid- becomes similar for all particle species. Data are re-
central collisions at SPS energy the elliptic flow grows produced by blast wave fits [5, 21] (dashed curves in
linearly with p up to 2 GeV/c, but the increase is Fig. 5) with the following parameters: freeze-out tem-
T
∼
steeper atRHIC than atSPS energy. It should be noted peratureT =92MeV,meantransverseexpansionrapid-
that RHIC mid-central data have been measured in the ity of the shell ρ = 0.82,its secondharmonic azimuthal
0
centrality range σ/σTOT = 5 30%while SPS events are modulation amplitude ρa = 0.021, and a spatial eccen-
−
somewhat more central. The effect of different central- tricity parameter s = 0.033. The values of freeze-out
2
ity ranges has been estimated by hydrodynamic calcula- temperature and expansion rapidity are consistent with
tions [19, 20] at RHIC energy for the slightly different those obtained from m spectra and Bose-Einstein cor-
T
centralitybinsofNA49andSTAR.Asshownbythecor- relations[22]. InFig.5themeasuredvaluesofv arealso
2
responding curves in Fig. 3 this explains only partially comparedto hydrodynamicalmodel calculations [23] as-
the difference between both measurements. For central suming a first-order phase transition to a QGP at the
collisions NA49 and STAR results do not differ signifi- critical temperature T = 165 MeV. The initial condi-
c
5
plain the quark number scaling observed at RHIC for
v in the intermediate p region. Fig. 6 shows the scal-
2 T
0.2
σ/σ = 5.0 - 23.5 %
TOT
2
v NA49 data
0.15 π+, π-
p
Λ
0.1
0.05
Hydro Model
0
Blast Wave fits
-0.05
0 1 2 3
p (GeV/c)
T
FIG.5: (coloronline).Ellipticflowforchargedpions(circles),
protons(triangles) andΛhyperons(squares)asafunctionof
pT from 158A GeV Pb+Pb mid-central events measured by
the NA49 experiment. Curves are blast wave fits and hydro-
dynamicmodel predictions for √sNN =17.2 GeV.
tions employed for the hydrodynamical calculations at
SPSare: initialenergydensityǫ =9.0GeV/fm3,baryon
0
densitynb=1.1fm−3,thermalizationtimeτ0=0.8fm/c.
The initial conditions were fixed as in [24] by requiring
a good fit to the p spectra of protons and negatively
T
chargedparticlesincentralPb+PbcollisionsattheSPS.
With the freeze-out temperature T = 120 MeV tuned
f
toreproduceparticlespectra,themodelcalculationssig-
nificantly overestimate the SPS results for semi-central
collisions (full curves in Fig. 5) in contrast to predic-
tions at RHIC energy which agree quite well with data
for p . 2 GeV/c [17] (see Fig.3). The discrepancy at
T
SPS may indicate a lack of complete thermalisation or a FIG.6: (coloronline).Ellipticflowforchargedpions(circles),
viscosity effect. However, the model reproduces qualita- protons (triangles) and Λ hyperons (squares) scaled by the
tively the characteristic hadron-mass ordering of elliptic numberofconstituentquarksv2/nasafunctionofpT/n(top)
flow. Thus the data support the hypothesis of early de- and KET/n (bottom) from 158A GeV Pb+Pb mid-central
velopmentofcollectivity. Onthe other hand,the magni- eventsmeasured bythe NA49experiment.
tude and trends of elliptic flow, measured by the second
Fourier coefficient v2 is found to be underpredicted by a ingbehaviorofthev2 measurementsofNA49attheSPS.
hadronic cascade model [25]. A more comprehensive de- Thevaluesofv showninFig.5weredividedbythenum-
2
scriptionofexperimentalresultswasfoundbycouplinga ber of constituent quarks n = 3 for baryons and n = 2
hadronic rescattering phase to the hydrodynamical evo- for mesons.
lution and hadronisation [4]. This model can reproduce When plotting v /n versus p /n approximate scaling
2 T
mT spectraandelliptic flow bothattopSPSenergyand wasobservedatRHIC[9,11]exceptforpions. TheNA49
RHICconsistently,althoughpredictionsofv2 forexactly measurements(Fig.6,top)areconsistentwiththisresult
the centrality range of the present analysis are not pub- in the p range covered by the data. The deviation of
T
lished in the literature. One should note, however, that the pions from the universal curve has been attributed
none of the hydrodynamical models have yet been able to the Goldstone nature of the pion (its mass is smaller
to describe Bose-Einstein correlations successfully. than the sum of masses of its constituent quarks) or to
Quark coalescence models [12] have been used to ex- the effect of resonance decays [26].
6
The variable KE =m m, where m is the trans- dence suggest strong collective behaviour of the matter
T T T
−
verse mass and m the rest mass of the particle, was producedincollisionsofheavynucleialreadyattheSPS.
proposed in [27] as an alternative to p since pressure Hydrodynamicmodels witha deconfinementphasetran-
T
gradients which give rise to azimuthal asymmetry may sition and a microscopic freezeout treatment appear to
naturally lead to collective transverse energy of pro- provide a consistent description of v and m spectra
2 T
duced particles. Good scaling for all particle species is at both top SPS and RHIC energies [4]. Quark number
seen when v /n is plotted versus KE /n in the range scaling of elliptic flow (v /n versus KE /n) was shown
2 T 2 T
KE /n.0.8GeVcoveredbytheSPSdata(Fig.6,bot- to hold also at the SPS. However, the limited p reach
T T
tom). ThisbehaviourwasfirstobservedatRHICandin- of the data does not allow a decisive test of the quark
terpretedasaresultofhydrodynamicevolution[27]. The coalescence hypothesis.
dataofNA49donotreachhighertransversemomentaat
whichadecisivetestofcoalescencemodelswouldbepos-
sible.
Acknowledgments
IV. SUMMARY ThisworkwassupportedbytheUSDepartmentofEn-
ergyGrantDE-FG03-97ER41020/A000,theBundesmin-
In summary, we report the first measurement of the isteriumfu¨rBildungundForschungGrant06F-137,Ger-
anisotropicflowparameterv forΛparticlesfromPb+Pb many,theVirtualInstituteVI-146ofHelmholtzGemein-
2
collisions at √sNN = 17.2 GeV. Elliptic flow of Λ hy- schaft, Germany, the Polish State Committee for Scien-
peronsexhibits no significantdependence onrapidityfor tificResearch(1P03B00630,1P03B09729,1P03B121
1.5 . y . 1.0. It rises linearly with p and is smaller 29, 1 P03B 127 30), the Hungarian Scientific Research
T
−
than v for pions. Both features are quantitatively re- Foundation (T032648, T032293, T043514), the Hungar-
2
produced by the Blast Wave parametrization but only ianNationalScienceFoundation,OTKA,(F034707),the
qualitatively by the hydrodynamic model. The increase Polish-German Foundation, the Korea Science & Engi-
ofv withp isweakeratSPSthanatRHICenergy. The neeringFoundation(R01-2005-000-10334-0)andtheBul-
2 T
observationofsignificantellipticflowanditsmassdepen- garian National Science Fund (Ph-09/05).
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