Energy dependence of pion and kaon production in central Pb+Pb collisions

PHYSICAL REVIEW C 66, 054902 ~2002!

Energy dependence of pion and kaon production in central Pb¿Pb collisions

S. V. Afanasiev,9 T. Anticic,20 D. Barna,5 J. Bartke,7 R. A. Barton,3 M. Behler,15 L. Betev,10 H. Białkowska,17 A. Billmeier,10

C. Blume,8 C. O. Blyth,3 B. Boimska,17 M. Botje,1 J. Bracinik,4 R. Bramm,10 R. Brun,11 P. Buncic,10,11 V. Cerny,4

J. G. Cramer,19 P. Csato´,5 P. Dinkelaker,10 V. Eckhardt,16 P. Filip,16 Z. Fodor,5 P. Foka,8 P. Freund,16 V. Friese,15 J. Gal,5

M. Gazdzicki,10 G. Georgopoulos,2 E. Gładysz,7 S. Hegyi,5 C. Hohne,15 G. Igo,14 P. G. Jones,3 K. Kadija,11,20

A. Karev,16 V. I. Kolesnikov,9 T. Kollegger,10 M. Kowalski,7 I. Kraus,8 M. Kreps,4 M. van Leeuwen,1 P. Levai,5

A. I. Malakhov,9 S. Margetis,13 C. Markert,8 B. W. Mayes,12 G. L. Melkumov,9 A. Mischke,8 J. Molnar,5 J. M. Nelson,3

G. Palla,5 A. D. Panagiotou,2 K. Perl,18 A. Petridis,2 M. Pikna,4 L. Pinsky,12 F. Puhlhofer,15 J. G. Reid,19

R. Renfordt,10 W. Retyk,18 C. Roland,6 G. Roland,6 A. Rybicki,7 T. Sammer,16 A. Sandoval,8 H. Sann,8 N. Schmitz,16

P. Seyboth,16 F. Sikler,5 B. Sitar,4 E. Skrzypczak,18 G. T. A. Squier,3 R. Stock,10 H. Strobele,10 T. Susa,20 I. Szentpe´tery,5

J. Sziklai,5 T. A. Trainor,19 D. Varga,5 M. Vassiliou,2 G. I. Veres,5 G. Vesztergombi,5 D. Vranic,8 A. Wetzler,10

C. Whitten,14 I. K. Yoo,15 J. Zaranek,10 and J. Zima´nyi5

~The NA49 Collaboration!1NIKHEF, Amsterdam, Netherlands

2Department of Physics, University of Athens, Athens, Greece3Birmingham University, Birmingham, England

4Comenius University, Bratislava, Slovakia5KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary

6MIT, Cambridge, Massachusetts 02139-43077Institute of Nuclear Physics, Cracow, Poland

8Gesellschaft fu¨r Schwerionenforschung (GSI), Darmstadt, Germany9Joint Institute for Nuclear Research, Dubna, Russia

10Fachbereich Physik der Universita¨t, Frankfurt, Germany11CERN, Geneva, Switzerland

12University of Houston, Houston, Texas 77204-550613Kent State University, Kent, Ohio 49292

14University of California at Los Angeles, Los Angeles, California 9002415Fachbereich Physik der Universita¨t, Marburg, Germany

16Max-Planck-Institut fu¨r Physik, Munich, Germany17Institute for Nuclear Studies, Warsaw, Poland

18Institute for Experimental Physics, University of Warsaw, Warsaw, Poland19Nuclear Physics Laboratory, University of Washington, Seattle, Washington 98195

20Rudjer Boskovic Institute, Zagreb, Croatia~Received 6 May 2002; published 27 November 2002!

Measurements of charged pion and kaon production in central Pb1Pb collisions at 40, 80, and 158A GeVare presented. These are compared with data at lower and higher energies as well as with results fromp1pinteractions. The mean pion multiplicity per wounded nucleon increases approximately linearly withsNN

1/4 witha change of slope starting in the region 15–40A GeV. The change from pion suppression with respect top1p interactions, as observed at low collision energies, to pion enhancement at high energies occurs at about40A GeV. A nonmonotonic energy dependence of the ratio ofK1 to p1 yields is observed, with a maximumclose to 40A GeV and an indication of a nearly constant value at higher energies. The measured dependencesmay be related to an increase of the entropy production and a decrease of the strangeness to entropy ratio incentral Pb1Pb collisions in the low SPS energy range, which is consistent with the hypothesis that a transientstate of deconfined matter is created above these energies. Other interpretations of the data are also discussed.

DOI: 10.1103/PhysRevC.66.054902 PACS number~s!: 25.75.2q

theus

fr

tae

lsingand

g ofvior

ofs.

I. INTRODUCTION

The primary purpose of the heavy ion program atCERN SPS is the search for a transient deconfined statstrongly interacting matter during the early stage of nuclenucleus collisions@1#. When a sufficiently high initial energydensity is reached, the formation of such a state of quasiquarks and gluons, the quark gluon plasma~QGP!, is ex-pected. A key problem is the identification of experimensignatures of QGP creation@2#. Numerous proposals wer

0556-2813/2002/66~5!/054902~9!/$20.00 66 0549

eof-

ee

l

discussed in the past@3#, but the significance of these signahas come under renewed scrutiny. A possible, promisstrategy is a study of the energy dependence of pionstrangeness yields. It was suggested@4–6# that the transitionmay lead to anomalies in this dependence: a steepeninthe increase of the pion yield and a nonmonotonic behaof the strangeness to pion ratio. The spacetime evolutionthe created fireball@7# and the event-by-event fluctuation@8# may also be sensitive to crossing the transition region

First experimental results from Pb1Pb ~Au1Au! colli-

©2002 The American Physical Society02-1

lt

AFANASIEV et al. PHYSICAL REVIEW C 66, 054902 ~2002!

FIG. 1. The experimentasetup of the NA49 experimen@13#.

sturg

e

nakafsce

m

er

innf

open

pabyn

ignt

n

id

ta

m

or-

Thead-ec-

e

ra at

sesheu-

the

cef

sions at top SPS~158AGeV! and AGS~11AGeV! energieshave suggested@4# that anomalies in pion and strangeneproduction may be located between these energies. The sof this hypothesis is the motivation for a dedicated enescan at the CERN SPS@9#. Within this ongoing projectNA49 has recorded central Pb1Pb collisions at 40 and 80AGeV during the heavy ion runs in 1999 and 2000, resptively. The data at the top SPS energy~158AGeV! weretaken in previous SPS runs. In this paper we report firesults on the energy dependence of charged pion andproduction. A preliminary analysis was presented in Re@10,11#. Pseudorapidity spectra of charged particles produin Pb1Pb collisions at 40 and 158AGeV were recently pub-lished by the NA50 experiment@12#.

The energy scan program at the CERN SPS will be copleted in 2002 by taking data at 20 and 30AGeV.

II. EXPERIMENTAL SETUP

The NA49 experimental setup@13# is shown in Fig. 1. Itconsists of four large volume time projection chamb~TPCs!. Two of these, the vertex TPCs~VTPC-1 and VTPC-2!, are placed in the magnetic field of two superconductdipole magnets. This allows separation of positively anegatively charged tracks and a precise measurement oparticle momentap with a resolution ofs(p)/p2>(0.327)31024 (GeV/c)21. The other two TPCs~MTPC-L andMTPC-R!, positioned downstream of the magnets weretimized for high precision measurement of the ionizationergy lossdE/dx ~relative resolution of about 4%!, whichprovides a means of determining the particle mass. Theticle identification capability of the MTPCs is augmentedtwo time of flight ~TOF! detector arrays with a resolutiosTOF>60 ps.

The acceptance of the NA49 detector is illustrated in F2, where we show the distribution of reconstructed unidefied particles versus the total momentump and transversemomentumpT for the 80AGeV data. The light~dark! shadedregion shows the coverage of the MTPCs~TOF! detectors.The resolution of thedE/dx measurement allows hadroidentification in the MTPCs forp.4 GeV. At each incidentenergy the TOF acceptance for kaons was kept at midrapby lowering the nominal magnetic field@B~VTX-1,2!'~1.5,1.1! T at 158AGeV# in proportion to the beam energy. Dawere taken for both field polarities.

05490

sdyy

c-

lon.d

-

s

gdthe

--

r-

.i-

ity

The target, a thin lead foil (224 mg/cm2>1% of the inter-action length!, was positioned about 80 cm upstream froVTPC-1.

Central collisions were selected by a trigger using infmation from a downstream calorimeter~VCAL !, which mea-sured the energy of the projectile spectator nucleons.geometrical acceptance of the VCAL calorimeter wasjusted for each energy in order to cover the projectile sptator region by a proper setting of a collimator~COLL!@13,14#.

III. ANALYSIS

Raw K1 and K2 yields were extracted from fits of thdistributions ofdE/dx and TOF~where available! in narrowbins of momentum and transverse momentum. The spectmidrapidity are obtained using the combineddE/dx andTOF information (TOF1dE/dx analysis!. The resulting dis-tributions were corrected for geometrical acceptance, losdue to in-flight decays, and reconstruction efficiency. Tfirst two corrections are calculated using the detector sim

FIG. 2. Distribution of accepted unidentified particles versustotal momentump and the transverse momentumpT at 80A GeVbeam energy. The light~dark! shaded area indicates the acceptanof the MTPCs~TOF detectors!. Also shown are two isolines oconstant rapidityy for kaons ~full curves! and pions ~dashedcurves!.

2-2

-th

di

sayffe

wae

th-c

io

ioal

nsedyuretti

tivn-tdngatre

tT

haxb

naottasyre

n

Fri-tic

d bycut

thetral

e-

se-rossns

nd

ENERGY DEPENDENCE OF PION AND KAON . . . PHYSICAL REVIEW C66, 054902 ~2002!

lation packageGEANT @15#. The procedure used for the efficiency calculation is discussed below, in the context ofpion analysis.

For pions at midrapidity the acceptance of thedE/dx andTOF1dE/dx methods is limited to the highpT region ~seeFig. 2!. To obtain thep2 spectra, yields of all negativelycharged particles were determined as a function of rapi~calculated assuming thep mass! and pT . The contamina-tion of K2, p, ande2 from the interaction vertex as well anonvertex hadrons originating from strange particle decand secondary interactions was subtracted using two dient methods.

In the first method each track measured in the TPCsextrapolated back to the target plane. The distance betwthe track and the interaction vertex was calculated inplane~track impact parameter!. The impact parameter distributions were used to establish cuts for the selection of trafrom the interaction vertex and to estimate the contributof the remaining nonvertex tracks. A correction forK2 con-tamination was calculated using parametrizedK2 spectra.

In the second method all tracks fitted to the interactvertex were accepted. The necessary corrections were clated based on a Venus@16# simulation of central Pb1Pbcollisions. The Venus events were processed byGEANT @15#and the NA49 software which simulates the TPC respoand produces files in raw data format. These events wreconstructed and the reconstructed tracks were matchethe Venus input. The obtained correction was scaled bfactor which matches the simulated Venus and the meashadron yields. The corrections determined using both mods are compatible. The Venus based correction, amounto 20–25 %, is used for the data presented in this paper.

The p1 spectra were not analyzed, because the posiparticles have a large and uncertain contribution of proto

The resultingK6 andp2 spectra were corrected for geometrical acceptance, and losses due to inefficiencies oftracking algorithms and quality cuts. These losses weretermined using the ‘‘embedding’’ method. Events containia few tracks were generated and processed by the simulsoftware. The resulting raw data were embedded intoevents. The combined raw data were reconstructed andinput tracks were matched with the reconstructed ones.calculated losses are about 5%.

In order to reduce the systematic errors, the analysisbeen restricted to regions of phase space where the bground and efficiency corrections are small and appromately uniform. The systematic errors were estimated tobelow 10%. This estimate is based on the comparisonresults obtained using different detectors~TOF, TPCs!, andvarying cuts and correction strategies~see above!. Addition-ally, data taken at the two magnetic field polarities were alyzed and the results were found to agree within 5%. Nthat the same experimental procedure was used to obresults at all three energies. Thus to a large extent thetematic uncertainties are common for the NA49 measuments.

The average number of wounded nucleons@17# ^NW& ~thenotation^¯& will be used to denote the mean multiplicity ifull phase space throughout the paper! as given in Table I

05490

e

ty

sr-

senis

ksn

ncu-

eretoaedh-ng

es.

hee-

ionalhehe

asck-i-e

of

-eins--

was not directly measured but was calculated using thetiof model @18#. In an unbiased sample of generated inelasinteractions a subsample of central events was selecteapplying a cut in the number of projectile spectators. Thiswas adjusted such that the selected fraction was equal tofraction of all inelastic interactions accepted by the centrigger in the experiment. The value of^NW& was then cal-

FIG. 3. Transverse mass spectra ofp2, K1, and K2 mesonsproduced at midrapidity (uyu,0.1 for kaons in the TOF1dE/dxanalysis, and 0,y,0.2 for pions! in central Pb1Pb collisions at40 ~triangles!, 80 ~squares!, and 158~circles! A GeV. The values for80A GeV and 158A GeV are scaled by factors of 10 and 100, rspectively. The lines are exponential fits to the spectra@see text, Eq.~1!# in the interval 0.2 GeV,mT2m, 0.7 GeV. Statistical errorsare smaller than the symbol size. The systematic errors are65% inthe region used for the fit and reach610% at the edges of theacceptance.

TABLE I. Numbers of analyzed events, cross sections oflected central interactions as percentage of total inelastic csection (s INEL57.15 b), and mean numbers of wounded nucleofor the selected central Pb1Pb collisions at 40, 80, and 158A GeV.The first error given in the last column is statistical, the secosystematic.

Energy~A GeV!

Number ofevents

sCENT/s INEL

~%! ^NW&

40 43105 7.2 349616580 33105 7.2 3496165

158 43105 5.0 3626165

2-3

.

ic

e

da

s

n

ge

e

a

ym

m-

. 4

-nsullrized

s

l

8th

atepid-

are

8


culated for the Fritiof Pb1Pb collisions selected in this wayFinally it was verified that theNW& value for central Pb1Pbcollisions at 158AGeV agrees~within several percent! withthe total number of net baryons determined from the partpant domain~in the rapidity interval22.6,y,2.6) forthese collisions@19#.

Note that in this papery denotes the rapidity of a particlin the collision center-of-mass system~c.m.s.!.

Table I summarizes the parameters characterizing thesamples used in this analysis.

IV. RESULTS

Spectra of transverse massmT5ApT21m2 (m is the rest

mass of the particle! for K1, K2 (TOF1dE/dx analysis!andp2 mesons produced near midrapidity (uyu,0.1 for ka-ons and 0,y,0.2 for pions! in central Pb1Pb collisions at40, 80, and 158AGeV are shown in Fig. 3. The full lineindicate a fit of the function

dn

mTdmTdy5C expS 2

mT

T D ~1!

to the data in the range 0.2 GeV,mT2m,0.7 GeV. Thevalues obtained for the inverse slope parameterT are pre-sented in Table II. TheT parameter is smaller for pions thafor kaons. A weak increase ofT with increasing energy issuggested by the pion data, whereas no significant chanseen for kaons.

The rapidity distributionsdn/dy plotted in Fig. 4 wereobtained by summing the measuredmT spectra and using thfitted exponential function@Eq. ~1!# to extrapolate to fullmT . For most bins the necessary correction is sm(>5%). Thevalues ofdn/dy at midrapidity (uyu,0.6) aregiven in Table II. An increase of rapidity density with energis seen for all particles. The rapidity spectra were para

TABLE II. Inverse slope parametersT of the transverse masspectra fitted in the interval 0.2 GeV,mT2m, 0.7 GeV at midra-pidity (uyu,0.1 for kaons in the TOF1dE/dx analysis, and 0,y,0.2 for pions!, rapidity densitiesdn/dy averaged over the intervauyu,0.6 as well as total mean multiplicities ofp2, p1, K2 andK1 mesons produced in central Pb1Pb collisions at 40, 80, and 15A GeV. The first error is statistical, the second systematic. Note^p1& is not directly measured.

40A GeV 80A GeV 158A GeV

T(p2)(MeV) 16962610 17963610 18063610T(K1)(MeV) 2326366 2306566 2326466T(K2)(MeV) 2266366 2176366 2266966dn/dy(p2) 106.160.466 140.460.567 175.460.769dn/dy(p1) 96.660.466 132.060.567 170.160.769dn/dy(K1) 20.160.361.0 24.660.261.2 29.660.361.5dn/dy(K2) 7.5860.1260.4 11.760.1060.6 16.860.260.8^p2& 32263616 47465623 639617631^p1& 29363615 44665622 619617631^K1& 59.161.963 76.96264 103.06565^K2& 19.260.561.0 32.460.661.6 51.961.963

05490

i-

ta

is

ll

-

etrized by the sum of two Gauss distributions placed symetrically with respect to midrapidity:

dn

dy5NFexpS 2

~y2y0!2

2s2 D 1expS 2~y1y0!2

2s2 D G . ~2!

The results of the fits are indicated by the full lines in Figand the obtained values of the parametersN, y0, ands aregiven in Table III. Since bothy0 ands increase with increasing energy, the width of the observed rapidity distributioclearly increases with energy. The mean multiplicities in fphase space were calculated by integrating the paramet

at

FIG. 4. Rapidity distributions ofp2, K1, andK2 mesons pro-duced in central Pb1Pb collisions at 40, 80, and 158A GeV. Forkaons, squares, and circles indicate the results of TOF1dE/dx anddE/dx only analyses, respectively. The closed symbols indicmeasured points, open points are reflected with respect to midraity. The lines indicate 2-G fits to the spectra@see Eq.~2!#. Theplotted errors, which are mostly smaller than the symbol size,statistical only, the systematic errors are65%.

TABLE III. Fitted parameters of the 2-G parametrization@seetext, Eq. ~2!# of rapidity distributions measured forp2, K2, andK1 mesons produced in central Pb1Pb collisions at 40, 80, and 15A GeV. Only statistical errors are given.

40A GeV 80A GeV 158A GeV

N(p2) 74.060.5 97.060.7 107.661.8N(K1) 16.260.4 19.360.3 23.460.6N(K2) 6.0360.13 9.1660.12 12.860.3s(p2) 0.87260.005 0.97460.007 1.1860.02s(K1) 0.72560.016 0.79260.018 0.8860.04s(K2) 0.63560.011 0.70560.010 0.8160.02y0(p2) 0.66660.006 0.75660.006 0.7260.02y0(K1) 0.69460.008 0.74260.008 0.83960.012y0(K2) 0.56960.010 0.66860.005 0.72760.010

2-4

Is

re

us

-idd

it

n

r.

th

te

atai-nore

en-

re

V.

For

the

s

ed

he

ul

tss

e

d inize.


rapidity spectra. The resulting numbers are given in TableThe mean multiplicity ofp1 mesons given in Table II wacalculated by scalingp2& by thep1/p2 ratio ~0.91, 0.94,and 0.97 at 40, 80, and 158AGeV, respectively! measured inthe region where bothdE/dx and TOF measurements aavailable. Similar ratios~within 2%! are predicted by theVenus model@16#. We have also checked, with the Venmodel, that thep1/p2 ratio of total multiplicities is, within1.5%, equal to the ratio in the TOF1dE/dx acceptance. Results ondn/dy and inverse slope parameters near midrapity at 158AGeV are compatible with previously publishemeasurements@20#.

V. ENERGY DEPENDENCE

The energy dependence of the mean pion multiplic^p&51.5( p1&1^p2&) is shown in Fig. 5. In this figure theratio ^p&/^NW& is plotted as a function of the collisioenergy, expressed by Fermi’s measure@21#: F[(AsNN

22mN)3/4/AsNN1/4, where AsNN is the c.m.s. energy pe

nucleon-nucleon pair andmN the rest mass of the nucleonMeasurements by NA49 are compared to results from oexperiments on central nucleus-nucleus collisions@4,22,23#and to a compilation of data fromp1p( p) interactions~seereferences in Ref.@4#!.

One observes that the mean pion multiplicity inp1p( p) interactions is approximately proportional toF; thedashed line in Fig. 5 indicates a fit of the formp&/^NW&5aF to the data, yieldinga51.02560.005 GeV21/2. ForcentralA1A collisions the dependence is more complicaand it can not be fitted by a single linear function (x2/DOF'18). Below 40AGeV the ratio^p&/^NW& in A1A colli-sions is lower than inp1p interactions~pion suppression!,while at higher energiesp&/^NW& is larger inA1A colli-

FIG. 5. Dependence of the total pion multiplicity per woundnucleon on Fermi’s energy measureF ~see text! for centralA1A

collisions ~closed symbols! and inelastic p1p( p) interactions~open symbols!. The results of NA49 are indicated by squares. Tfull line shows a linear fit through the origin to theA1A data at andabove 158A GeV. The inset shows the difference between the resfor A1A collisions and the straight line parametrization ofp

1p( p) data~dashed line!. The inner error bars on the NA49 poinindicate the statistical uncertainty and the outer error bars thetistical and systematic uncertainty added in quadrature.

05490

I.

-

y

er

d

sions than inp1p( p) interactions~pion enhancement!. Inthe region between AGS and the lowest SPS energy~15–40AGeV! the slope changes from a51.0160.04 GeV21/2 (x2/DOF'0.9) for the fit to the points up tothe top AGS energy toa51.3660.03 GeV21/2 (x2/DOF'0.2) for the fit to the top SPS energy and the RHIC dpoints @23#. The fit to the top SPS and RHIC points is indcated by the full line in Fig. 5. The transition from piosuppression to pion enhancement is demonstrated mclearly in the inset of Fig. 5, where the difference betwe^p&/^NW& for A1A collisions and the straight line parametrization of thep1p data is plotted as a function ofF up tothe highest SPS energy.

Midrapidity and full phase space kaon to pion ratios ashown as a function ofAsNN in Figs. 6 and 7@4,22,24#,respectively. A monotonic increase withAsNN of theK2/p2

ratio is measured. For theK1/p1 ratio, a very different be-havior is observed: a steep increase in the low~AGS @22#!energy region is followed by a maximum around 40 A GeThe measurement at RHIC indicates that theK1/p1 ratiostays nearly constant starting from the top SPS energy.comparison, the results on the^K1&/^p1& ratio in p1p in-teractions@4# are also shown in Fig. 7. Thep1p data haverather large experimental uncertainties@4#, but suggest amonotonic increase of the ratio. It should be noted that^K1&/^p1& ratio is expected to be similar~within about10%! for p1p, n1p, andn1n interactions@27#.

The energy dependence of theK2/K1 ratio at midrapidityis shown in Fig. 8. The ratio increases withAsNN from about0.15 at low AGS energy@22# to about 0.5 at SPS energieand reaches about 0.9 at RHIC@24#.

ts

ta-FIG. 6. Energy dependence of the midrapidityK1/p1 and

K2/p2 ratios in central Pb1Pb and Au1Au collisions. The resultsof NA49 are indicated by squares. Open triangles indicate thA1A results for which preliminary data were used@25#. The errorson the NA49 points are the statistical and systematic errors addequadrature. The statistical errors are smaller than the symbol s

2-5

ty

d

kf

edss

ion

ap-

ft a

ecialin

ieldsleusb-

dpen-the

gehe

leashean

-tics

ndi-as

rly-

yntssta-


The difference between the dependence of theK1 andK2

yields onAsNN can be attributed to their different sensitivito the baryon density. Kaons (K1 andK0) carry a dominantfraction of all produceds quarks~more than 95% in Pb1Pbcollisions at 158AGeV if open strangeness is considere!.Therefore theK1 yield (^K1&>^K0& in approximately isos-pin symmetric collisions of heavy nuclei! is nearly propor-tional to the total strangeness production and only weasensitive to the baryon density. As a significant fraction os

FIG. 7. Energy dependence of full phase space^K1&/^p1& and^K2&/^p2& ratios in central Pb1Pb ~Au1Au! collisions. The re-sults of NA49 are indicated by squares. The data forp1p interac-tions are shown by open circles for comparison. Open triangindicate theA1A results for which a substantial extrapolation wnecessary@26#. The inner error bars on the NA49 points indicate tstatistical uncertainty and the outer error bars the statisticalsystematic uncertainty added in quadrature.

FIG. 8. Energy dependence of the midrapidityK2/K1 ratio incentral Pb1Pb ~Au1Au! collisions. The results of NA49 are indicated by squares. The errors on the NA49 points are the statisand systematic errors added in quadrature. The statistical errorsmaller than the symbol size.

05490

ly

quarks ~e.g., '50% in central Pb1Pb collisions at158AGeV! is carried by hyperons, the number of producantikaons (K2 and K0) is sensitive to both the strangeneyield and the baryon density.

In Fig. 9 an alternative measure of the strangeness to pratio,ES5(^L&1^K1K&)/^p&, is plotted as a function ofFfor A1A collisions @22# and p1p interactions@4#. For A1A collisions theL multiplicity, when not published~e.g.,for the NA49 points!, was estimated as L&5(^K1&2^K2&)/0.8, based on strangeness conservation andproximate isospin symmetry of the colliding nuclei@27#. Thewealth of data onL and KS

0 (KS050.5 K01K0&'0.5 K1

1K2&) production inp1p interactions@4# allows a muchmore precise determination ofES ~open circles in Fig. 9!than of the^K1&/^p1& ratio ~open circles in Fig. 7!. Byconstruction,ES should be almost independent~an expectedvariation of several percent! of the charge composition ocolliding nuclei. One may conclude from Figs. 7 and 9 thanonmonotonic energy dependence~or a sharp turnover! ofthe total strangeness to pion ratio appears to be a spproperty of heavy ion collisions, which is not observedelementary interactions.

VI. COMPARISON WITH MODELS

The energy dependence of pion and strangeness ywas discussed within various approaches to nucleus-nuccollisions. In this section we compare our results with pulished model predictions.

It was suggested@4,5# that a transition to a deconfinestate of matter may cause anomalies in the energy dedence of pion and strangeness production. This led toformulation of the statistical model of the early sta~SMES! @5,6#, which is based on the assumption that t

s

d

alare

FIG. 9. Energy dependence of theES5(^L&1^K1K&)/^p& ra-tio in central Pb1Pb ~Au1Au! collisions andp1p interactions.The results of NA49 are indicated by squares. Open triangles icate theA1A results for which a substantial extrapolation wnecessary@26#. The experimental results onA1A collisions arecompared with the predictions of the statistical model of the eastage~line! @6#. Different line styles indicate predictions in the energy domains in which confined matter~dashed line!, mixed phase~dash-dotted line!, and QGP~dotted line! are created at the earlstage of the collisions. The inner error bars on the NA49 poiindicate the statistical uncertainty and the outer error bars thetistical and systematic uncertainty added in quadrature.

2-6

thr

e

on

lofpeem

g

isof

tit

eth

iig

ese

ise

,dby

kin

drlyth

ehai-sthetethn-ex

itce

andess

ili-

vel-

nicded

cat-

atde-e

ch is

ti-0%

thel

apeof

let

tral.gies

xi-nn

lns:


system created at the early stage~be it confined matter or aQGP! is in equilibrium and a transition from a reaction wipurely confined matter to a reaction with a QGP at the eastage occurs when the transition temperatureTC is reached.For TC values of 170–200 MeV the transition region rangbetween 15–60AGeV @6#.

Due to the assumed generalized Fermi-Landau initial cditions @6,21,28# the ^p&/^NW& ratio ~a measure of entropyper baryon! increases approximately linearly withF outsidethe transition region. The slope parameter is proportionag1/4 @5#, whereg is an effective number of internal degreesfreedom at the early stage. In the transition region a steeing of the pion energy dependence is expected, becausactivation of a large number of partonic degrees of freedoThis is, in fact, observed in the data on central Pb1Pb ~Au1Au! collisions, where the steepening starts in the ran15–40AGeV ~see Fig. 5!. The linear dependence onF isobeyed by the data at lower and higher energies~includingRHIC!. An increase of the slope by a factor of about 1.3measured~see Sec. V!, which corresponds to an increasethe effective number of internal degrees of freedom byfactor of 1.34>3, within the SMES@5#.

In the SMES model theK1&/^p1& and ES ratios areroughly proportional to the total strangeness to entropy rawhich is assumed to be preserved from the early stagefreeze-out. At low collision energies the strangeness totropy ratio steeply increases with collision energy, due tolow temperature at the early stage (T,TC) and the highmass of the carriers of strangeness (mS>500 MeV, the kaonmass! in the confined state. When the transition to a QGPcrossed (T.TC), the mass of the strangeness carriers is snificantly reduced (mS>170 MeV, the strange quark mass!.Due to the low mass (mS,T) the strangeness yield becom~approximately! proportional to the entropy, and the strangness to entropy~or pion! ratio is independent of energy. Thleads to a ‘‘jump’’ in the energy dependence from the largvalue for confined matter atTC to the QGP value. Thuswithin the SMES, the measured nonmonotonic energypendence of the strangeness to entropy ratio is followedsaturation at the QGP value~see Figs. 7 and 9!, which is adirect consequence of the onset of deconfinement taplace at about 40AGeV.

Numerous models have been developed to explain haproduction in reactions of heavy nuclei without explicitinvoking a transient QGP phase. The simplest one isstatistical hadron gas model@29# where independent of thcollision energy the hadrochemical freeze-out creates aron gas in equilibrium@30#. The temperature, baryon chemcal potential and hadronization volume are free parameterthe model, which are fitted to the data at each energy. Informulation, the hadron gas model does not predict theergy dependence of hadron production. Recently, an exsion of the model was proposed, in which it is assumedthe values of the thermal parameters~temperature and baryochemical potential! evolve smoothly with the collision energy @31#. The energy dependence calculated within thistended hadron gas model for the^K1&/^p1& ratio is com-pared to the experimental results in Fig. 10. Due toconstruction, the prevailing trend in the data is reprodu

05490

ly

s

-

to

n-of.

e

a

o,illn-e

s-

-

r

e-a

g

on

e

d-

ofisn-n-at

-

sd

by the model, but the decrease of the ratio between 40158 AGeV is not well described. The measured strangento pion yield in central Pb1Pb collisions at 158AGeV isabout 25% lower than the expectation for the fully equbrated hadron gas@31,32#.

Several dynamical hadron-string models have been deoped to study hadron production inA1A collisions. Thesemodels treat the elementary collisions with a string-hadroframework as a starting point. The models are then extenwith effects which are expected to be relevant inA1A col-lisions~such as string-string interactions and hadronic restering!. The predictions of the RQMD@33,34# and theUrQMD @35,36# models are shown in Fig. 10. It is seen thRQMD, like the hadron gas model, fails to describe thecrease of theK1&/^p1& ratio in the SPS energy range. ThUrQMD model predicts a ratio which, aboveAsNN>5 GeV,does not show any sizable energy dependence and whisignificantly lower~e.g., by about 40% at 40AGeV! than thedata. This is mainly due to the fact that UrQMD overesmates pion production at SPS energies by more than 3@36#.

The RQMD prediction of the energy dependence ofK1/p1 ratio at midrapidity is shown in Fig 11. The modealso fails to reproduce the experimental data both in shand magnitude. In addition, Fig. 11 presents the predictionthe HSD model@37# ~another version of the dynamicahadron-string approach! which shows a monotonic increasof the K1/p1 ratio with energy. This trend is very differenfrom the measured one.

VII. SUMMARY

Results on charged pion and kaon production in cenPb1Pb collisions at 40, 80, and 158AGeV are presentedThese are compared with data at lower and higher eneras well as with results fromp1p interactions. The meanpion multiplicity per wounded nucleon increases appromately linearly withsNN

1/4 with a change of slope starting ithe region 15–40AGeV. The change from pion suppressio

FIG. 10. Energy dependence of the full phase space^K1&/^p1&ratio in central Pb1Pb and Au1Au collisions. The experimentaresults taken from Fig. 7 are compared to model predictioRQMD @33# ~dashed line!, UrQMD @35# ~dotted line!, and the ex-tended hadron gas model@31# ~dash-dotted line!.

2-7

i-rshea

siq

cesnd a

er-ofient

ea-ction

n-of

t of-

heny,er-tate

one-

s-E

/

-

o-

art.

.

ed-

hens

of

sD


with respect top1p interactions, as observed at low collsion energies, to pion enhancement at high energies occuabout 40AGeV. A nonmonotonic energy dependence of tratio of K1 to p1 yields is observed, with a maximum closto 40AGeV and an indication of a nearly constant valuehigher energies. This characteristic energy dependence iobserved in elementary interactions and seems to be a un

@1# For review seeQuark Matter ’99, Proceedings of the 14thInternational Conference on Ultra-Relativistic NucleuNucleus Collisions, edited by L. Riccati, M. Masera, andVercellin @Nucl. Phys.A661, 1c ~1999!#.

@2# J. C. Collins and M. J. Perry, Phys. Rev. Lett.34, 1353~1975!;E. V. Shuryak, Phys. Rep.61, 71 ~1980!; 115, 151 ~1984!.

@3# J. Rafelski and B. Mu¨ller, Phys. Rev. Lett.48, 1066~1982!; T.Matsui and H. Satz, Phys. Lett. B178, 416 ~1986!.

@4# M. Gazdzicki and D. Ro¨hrich, Z. Phys. C: Part. Fields65, 215~1995!; 71, 55 ~1996!, and references therein.

@5# M. Gazdzicki, Z. Phys. C: Part. Fields66, 659 ~1995!.@6# M. Gazdzicki and M. I. Gorenstein, Acta Phys. Pol. B30, 2705

~1999!, and references therein.@7# C. M. Hung and E. Shuryak, Phys. Rev. Lett.75, 4003~1995!.@8# M. Stephanov, K. Rajagopal, and E. Shuryak, Phys. Rev. D60,

114028~1999!.@9# J. Bachler et al., NA49 Collaboration, Report Nos. SPSLC

P264 and CERN/SPSC 97, 1997.@10# C. Blumeet al., NA49 Collaboration, Nucl. Phys.A698, 104

~2002!.@11# T. Kolleggeret al., NA49 Collaboration, J. Phys. G28, 1689

~2002!.@12# M. C. Abreuet al., NA50 Collaboration, Phys. Lett. B530, 33

~2002!; 530, 43 ~2002!.@13# S. Afanasievet al., NA49 Collaboration, Nucl. Instrum. Meth

ods Phys. Res. A430, 210 ~1999!.@14# H. Appelshauseret al., NA49 Collaboration, Eur. Phys. J. A2,

383 ~1998!.@15# GEANT, Detector Description and Simulation Tool, CERN Pr

gram Library Long Writeup W5013.

FIG. 11. Energy dependence of the midrapidityK1/p1 ratio incentral Pb1Pb and Au1Au collisions. The experimental resulttaken from Fig. 6 are compared with model predictions: RQM@33# ~dashed line! and HSD@37# ~dash-dotted line!.

05490

ate

tnotue

feature of heavy ion collisions. The measured dependencan be related to an increase of the entropy production adecrease of the strangeness to entropy ratio in central Pb1Pbcollisions in the low SPS energy range. They can be undstood within the statistical model of the early stagenucleus-nucleus collisions, which assumes that a transstate of deconfined matter is created in Pb1Pb collisions forenergies larger than about 40AGeV. Currently availablemodels without this assumption do not reproduce the msured energy dependence of pion and strangeness produequally well.

ACKNOWLEDGMENTS

This work was supported by the Director, Office of Eergy Research, Division of Nuclear Physics of the OfficeHigh Energy and Nuclear Physics of the U.S. DepartmenEnergy ~DE-ACO3-76SFOOO98 and DE-FG0291ER40609!, the U.S. National Science Foundation, tBundesministerium fur Bildung und Forschung, Germathe Alexander von Humboldt Foundation, the U.K. Engineing and Physical Sciences Research Council, the Polish SCommittee for Scientific Research~5 P03B 13820 and 2P03B 02418!, the Hungarian Scientific Research Foundati~T14920 and T23790!, the Hungarian National SciencFoundation, OTKA~F034707!, the EC Marie Curie Foundation, and the Polish-German Foundation.

.

@16# K. Werner, Phys. Rep.232, 87 ~1993!.@17# A. Bial”as, M. Bl”eszynski, and W. Czyz˙, Nucl. Phys.B111, 461

~1976!.@18# B. Andersson, G. Gustafson, and Hong Pi, Z. Phys. C: P

Fields57, 485 ~1993!.@19# H. Appelshauseret al., NA49 Collaboration, Phys. Rev. Lett

82, 2471~1999!.@20# I. Beardenet al., NA44 Collaboration, Phys. Lett. B471, 6

~1999!.@21# E. Fermi, Prog. Theor. Phys.5, 570 ~1950!.@22# L. Ahle et al., E802 Collaboration, Phys. Rev. C57, 466

~1998!; 58, 3523 ~1998!; 60, 044904~1999!; E866 and E917Collaboration, Phys. Lett. B476, 1 ~2000!; 490, 53 ~2000!; J.Barretteet al., E877 Collaboration, Phys. Rev. C62, 024901~2000!; D. Pelteet al., FOPI Collaboration, Z. Phys. A357,215 ~1997!.

@23# B. B. Backet al., PHOBOS Collaboration, Phys. Rev. Lett.85,3100~2000!; 87, 102303~2001!; 88, 022302~2002!, the meancharged particle multiplicity in central Au1Au collisions atAsNN5200 GeV was obtained by integrating the publishpseudorapidity distribution. AtAsNN556 GeV the measurement at midrapidity was extrapolated to 4p assuming scalingof the shape of the distribution with the beam rapidity. Tcharged hadron multiplicities were corrected for contributioof charged kaons and protons.

@24# K. Adcox et al., PHENIX Collaboration, Phys. Rev. Lett.88,242301 ~2002!; B. B. Back et al., PHOBOS Collaboration,ibid. 87, 102301~2001!.

@25# J. L. Klay, E895 Collaboration, Ph.D. thesis, UniversityCalifornia, Davis, 2001.

2-8

thdi

nisJ.

Xu

C

.

,

ys.


@26# The ratios at low AGS energies were calculated based onmeasured midrapidity ratios and assuming that the midrapito 4p ratio is the same as at 10.74A GeV @22#.

@27# M. Gazdzicki and O. Hansen, Nucl. Phys.A528, 754 ~1991!.@28# L. D. Landau, Izv. Akad. Nauk SSSR, Ser. Fiz.17, 51 ~1953!.@29# R. Hagedorn, CERN Report CERN-TH-7190-94; inProceed-

ings of NATO Advanced Study Workshop on Hot HadroMatter: Theory and Experiment, Divonne-les-Bain,Switzerland, 1994, edited by J. Letessier, H. Gutbrod, andRafelski @Hot Hadronic Matter346, 13 ~1994!#; J. Cleymansand H. Satz, Z. Phys. C: Part. Fields57, 135 ~1993!; J. Soll-frank, M. Gazdzicki, U. Heinz, and J. Rafelski,ibid. 61, 659~1994!; P. Braun-Munzinger, J. Stachel, J. Wessels, and N.Phys. Lett. B365, 1 ~1996!: G. D. Yen, M. I. Gorenstein, W.Greiner, and S. N. Yang, Phys. Rev. C56, 2210~1997!; G. D.Yen and M. I. Gorenstein,ibid. 59, 2788~1999!.

05490

ety

c

,

@30# R. Stock, Phys. Lett. B456, 277 ~1999!.@31# J. Cleymans and K. Redlich, Phys. Rev. C60, 054908~1999!;

P. Braun-Munzingeret al., Nucl. Phys.A697, 902 ~2002!.@32# F. Becattini, M. Gaz´dzicki, and J. Sollfrank, Eur. Phys. J. C5,

143 ~1998!.@33# H. Sorge, H. Sto¨cker, and W. Greiner, Nucl. Phys.A498, 567c

~1989!; H. Sorge, Phys. Rev. C52, 3291~1995!.@34# F. Wang, H. Liu, H. Sorge, N. Xu, and J. Yang, Phys. Rev.

61, 064904~2000!.@35# S. A. Basset al., UrQMD Collaboration, Prog. Part. Nucl

Phys.41, 255 ~1998!.@36# H. Weber et al., UrQMD Collaboration, nucl-th/0205030

Phys. Lett. B~to be published!.@37# W. Cassing, E. L. Bratkovskaya, and S. Juchem, Nucl. Ph

A674, 249 ~2000!.

2-9

Documents

Energy dependence of pion and kaon production in central Pb+Pb collisions