Differential elliptic flow at forward rapidity in 200 GeV AuAu collisions

0.11 MB·English

by  S. J. Sanders

xx xx Vol.xx,No.xx
200x xx HIGH ENERGY PHYSICS AND NUCLEAR PHYSICS xxx.,200x
Differential elliptic flow at forward rapidity in 200 GeV AuAu
collisions *
S.J. Sanders1) (for the BRAHMS Collaboration)
1(TheUniversityofKansas,Lawrence, Kansas66045USA)
Abstract
Identified particle elliptic flow results are presented for the Au+Au reaction at √sNN = 200 GeV as a
7 function of transverse momentum and pseudorapidity. Data at pseudorapidities η 0, 1, and 3.4 were
0 ≈
0 obtained using the two BRAHMS spectrometers. Differential v2(η,pt) values for a given particle type are
2 foundtobeessentially constantoverthecoveredpseudorapidityrange,incontrasttotheintegralv values
2

n which have previously been observed to decrease at forward rapidities. A softening of the particle spectra
a
at forward angles is found to account for at least part of the integral v falloff. The data are found to be
J 2
1 consistent with existing constituent quark scaling systematics.
3

Key words elliptic flow, rapidity dependence
1
v
8
7
0 1 Introduction dorapidities) 90o(η=0), 40o(η=1), and 4o(η=3.4).
1
0 The analysis of the elliptic flow behavior together
7
The azimuthal anisotropy of particle production with the particle spectra makes it possible to deter-
0
/ in relativistic heavy-ion reactions is believed to re- minetheextenttowhichthefalloffoftheintegralv
x 2
e flect pressure gradients of the thermalized medium valuescanbe attributedtoasofteningofthe particle
-
l formed earlyin the collisions. In a Fourier expansion spectra going to forward rapidity.
c
u of the azimuthal behavior, the 2nd-harmonic term,
n
withcoefficientv ,definesthe“ellipticflow”ofthere- 2 Experimental Details
: 2
v
action. Measurementsnearmid-rapidityatRHICen-
i
X
ergieshaveshownthatellipticflowforparticlesbelow Elliptic flow measurements characterize the az-
r
a 2 GeV is close to that expected from hydrodynamic imuthal dependence of the particle production with
modelsthatassumetheformationofastronglyinter- respect to the reaction plane. For any given colli-
acting quark-gluon plasma[1,2,3]. However, integral sion, an empirical reaction plane can be established
v values, which are based solely on the asymmetry by measuring the particle yield observed in detec-
2
of the overall charged-particle production, are found tors mounted symmetrically about the beam axis.
to fall off going away from mid-rapidity, dropping by BRAHMS used several different detector systems for
about 35% by pseudorapidity η=3[4]. this purpose: Two rings of modestly segmented Si
BRAHMS has now measured v and the associ- stripdetectors(7segmentsperstrip)wereconfigured
2
ated particle spectra as a function of transverse mo- with42activesegmentssurroundingthebeamaxisin
mentumforpions,kaons,andprotonsatangles(pseu- eachring. AnotherringusingthesametypeofSistrip
Received31January2007
*ThisworkwassupportedinpartbytheOfficeofNuclearPhysicsoftheU.S.DepartmentofEnergyundercontractDE-FG03-
96ER40981.
1)E-mail:[email protected]
1 — 4
2 (HEP & NP)
detectorwasconfiguredwithsixsegmentsaroundthe determination. The general procedure for determin-
axis,andsevensegmentsalongtheaxis. Ascintillator ingthereactionplaneandthecorrespondingreaction-
tileringwithsixpanelswasalsoarrangedaroundthe planecorrectionfactorisdescribedbyPoskanzerand
beam axis. Depending on the location of the beam Voloshin[8]. The reaction plane corresponding to the
vertex, for collisions within 20cm of the nominal second moment of the angular distribution is found
±
vertexlocationtheSiandtiledetectorscoveredpseu- with
1 w sin(2φ )
dorapidity values from -3 to +1.5. At a somewhat Ψ = i i , (1)
2 2 w cos(2φ )
i i
largerrapidity( 3),Cherenkovradiatorsmounted i
≈− X
tophototubesinoneoftheexperiment’sBeam-Beam where the sum is over all detector elements with ge-
counterarrays[7] werealsousedforthereaction-plane ometric weighting factors w and azimuthal angle φ .
i i
v20.25 ppiioonnss
0.2 h » 0 h » 1 h » 3
0.15
0.1
0.05
0
v20.25 kkaaoonnss
0.2
0.15
0.1
0.05 PRELIMINARY
0
v20.25 pprroottoonnss
0.2
0.15
0.1
0.05
0
0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3
p (GeV/c) p (GeV/c) p (GeV/c)
t t t
Figure 1: v (p ,η) for pions (both charges), kaons (both charges), and protons (filled symbols). Theoretical
2 t
values based on the hydrodynamic calculations of Hirano et al. [9] are shown by the open circles, squares,and
triangles. The open crosses correspondto η 4 calculations using the AMPT model [10]. The smaller (blue in
≈
color) points in the pion panels are from a mixed-event analysis, as discussed in the text.
The angular correlation with respect to the reac- reaction-plane correction factor R, with
tionplaneofparticlesdetectedintheBRAHMSmid-
v =vobs/R. (3)
rapidityandforwardspectrometersdeterminetheob- 2 2
served v values, with The reaction-plane correction for any given ring (or
2
vobs= cos(2[φ Ψ ]) . (2) ringcombination)isdeterminedusingtwoadditional
2 h − 2 i
rings that are far enough apart so as to avoid au-
Here the angular bracket denotes an average over all
tocorrelations. Considering rings A, B, and C, the
eventsofagivenclass,suchasallpionswithinagiven
reaction-plane correction factor for ring A is found
range of transverse momenta. Since the BRAHMS
as:
spectrometers are small acceptance devices, all par-
cos(2[ΨA ΨB]) cos(2[ΨA ΨC])
ticles detected in the mid-rapidity spectrometer have R = h 2 − 2 ih 2 − 2 i. (4)
φ 0o,whilethosedetectedbytheforwardspectrom- A s hcos(2[ΨB2 −ΨC2])i
≈
eter have φ 180o. The reaction-plane correction factor was typically in
≈
The true v value, which is based on the actual the range 0.18<R<0.25.
2
reactionplane, is found from the vobs value using the Figure 1 shows the resulting values (closed sym-
2
3
bols)ofv (p )forpions,kaons,andprotonsatthein- liptic flow has been determined. The average value
2 t
dicated pseudorapidities, selecting events in the 10% of transverse momentum for pions in the 10% - 50%
-50%centralityclass. Thebehaviorforthethreedif- centrality class at 90o is (475 60)MeV/c, falling to
±
ferent particle species shows very little change with (380 45)MeV/cat4o. Thesevaluesareobtainedby
±
pseudorapidity. The smaller (blue in color) filled cir- fitting apower-lawdependence to the respectivepar-
cles shown in the pion panels are the results of a ticle spectra. The softening of the particle spectrum
mixed event analysis, where the reaction-plane an- going to more forward rapidities can have a signif-
gle used for the analysis of a given identified pion is icant effect on the integral v values, as illustrated
2
takenasthatobtainedfromthepreviouseventwhere in Figure 2. The insert shows an assumed form of
a particle of any type is detected in the same spec- v (p ) that is taken as being constant as a function
2 t
trometer. Because of the limited angular acceptance of pseudorapidity. Folding this behavior with the ex-
of the spectrometers, the deduced v (p ) values from perimentallyobservednormalizedparticlespectrafor
2 t
the mixed-event analysis reflect the integral v be- pions at 90o and 4o results in the solid and dashed
2
havior. The scatter of the points with p mirrors the linesofthemainfigurepanel,respectively. Thesofter
t
statistical uncertainty in the measurements. The fall spectrumatthemoreforwardpseudorapidityleadsto
offoftheaveragebehavior,asindicatedbythedashed the weightedv distribution peakingatalowermean
2
lines, is consistentwiththe knownfall-offofthe inte- p value, resulting in a 22% smaller integral v value
t 2
gral v values going to forward rapidity. than a mid-rapidity. Two-thirds of the observed in-
2
We have also measured the p -dependent parti- tegral v change is then attributable to the softening
t 2
cle spectra for the channels where the differential el- of the particle spectrum.
)pt0.15
dNdy 0.05 (v2 0.1
N / dy 0.04 0.05
2d) pdptt0.03 00 0.5 p1t (G1e.5V/c)2
(v2 0.02
0.01
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
p (GeV/c)
t
Figure 2: Illustration of how the softening of the particle spectra going to forward angles affects the integral
v values. The insert shows the general behavior of the differential v (p ) values for pions, which for this
2 2 t
illustration is assumed to be independent of pseudorapidity. Folding this distribution with the corresponding
experimentally observed pion spectra at 4o and 90o results in the dashed and solid curves, with integral v
2
values of 0.046 and 0.036, respectively.
Thesmallchangeinthedifferentialv signalgoing cles in Figure 1 which show the results of the hy-
2
from mid- to forward rapidity suggests a longitudi- brid hydrodynamic calculations of Hirano et al. ([9],
nallyextendedregionforthemediumproducedinthe and private communication) that include dissipative
collision. Rapidity dependent changes in the radial effects of the late hadronic expansion stage. Good
flow or other rescattering behavior of the hadronic agreement is found with the experimental values.
stage might then account for most of the fall off of The open crosses in Figure 1 show the results of the
the integral v signal going to forward rapidities. AMPT modelfor pseudorapidityη=4. At this angle
2
Hydrodynamic calculations are able to reproduce the string melting mechanism that allows for a good
the observed behavior. This is seen by the open cir- reproduction of mid-rapidity results has been turned
4 (HEP & NP)
v2 0.02.52 a) ˛ ) /(nv2q 000..034..4555 b)
0.15
0.3
0.1 0.25
9400oo ppiioonn 0.2
0.05 4o pion 0.15
90o proton 0.1
0 440o op prorototonn 0.05 PRELIMINARY
0 0.5 1 1.5 2 2.5 3 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4
p (GeV/c) KE/n (GeV)
t t q
Figure 3: a) v (p ) vs. p for pions and protons at η=0,1, and 3. b) Constituent quark scaled values, as
2 t t
discussed in the text. The lines indicates the band containing most of the previous experimental results near
mid-rapidity.
off ([10], and private communication). Although the sults. This mayreflectasystematicerrorinthe mea-
comparison is subject to poor matching of pseudo- surementofthe reaction-planecorrectionfactororin
rapidity, there is a suggestion that the longitudinal the assumedGlauber eccentricity which is calculated
extent of the produced medium may be greater than forthetrigger-weightedcenterofthecentralityrange.
that assumed in current AMPT calculations. Anerrorineitherofthesequantitieswilltendtohave
The mid-rapidity elliptic flow behavior for many a similar scaling effect on all of our results.
different systems have been found to follow similar
constituent scaling behavior when the v value per 3 Conclusions
2
valence quark, scaled by the inverse of the Glauber-
model eccentricity, is plotted as a function of the BRAHMShasmeasuredv (p ,η)forpions,kaons,
2 t
meantransversekineticenergypervalencequark[11]. and protons at √sNN = 200 GeV for the Au+Au re-
It Figure 3a we show the v vs. p behavior of pi- action. Theresultsindicatealongitudinallyextended
2 t
onsandprotonsforthe threemeasuredanglesonthe region is produced where the eccentricity of the cre-
same plot. In Figure 3b these same data are now ated medium and the corresponding pressure gradi-
shownin terms oftheir constituent-quark scalingbe- entsremainremarkablyconstant. Hydrodynamiccal-
havior. The two solid curves mark the approximate culations with final stage dissipation are found to be
limitsestablishedbythepreviousmeasurements. The inexcellentagreementwith the measureddifferential
currentdatashowaverysimilartrend,althoughwith v values. The data are consistent with constituent
2
a tendency to fall somewhat below the previous re- quark scaling over the coveredpseudorapidity range.
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