Charged pion production in fixed target Pb + Pb collisions at 158 GeV per nucleon

Changes in pion production as a function of the impact parameter of the collision or the incident energy, may reveal characteristics of a possible rst order phase transition from nuclear to quark matter, as predicted by lattice quantum chromodynamics. In this paper we investigate charged pion production in Pb+Pb collisions at 158 GeV per nucleon near zero degree production angle and at forward rapidity (4:3 y 6:3). The centrality dependence of pion production is shown in the impact parameter range 2 to 12 fm at the rapidities y=5.7 and 6.3. An enhancement in the = + ratio has been measured near beam rapidity, indicating Coulomb interaction of charged pions with the spectator protons. The charged pion yield per nucleon participating in the collision (Np) at y=5.7 increases faster than linearly with Np, up to Np 100 and then it saturates, while at y=6.3 it does not exhibit any sudden change as a function of Np. Charged pion production in xed target Pb+Pb collisions at 158 GeV per nucleon 2


Introduction
Pions are the most abundantly produced particles in heavy ion collisions at 158 GeV per nucleon.They carry a large part of the entropy, the other part being carried mostly by baryons.Typically, the number of pions in a central Pb+Pb collision is six times the number of baryons [1].It is expected that a possible rst order phase transition of nuclear matter to quark and gluon matter (the so called Quark Gluon Plasma state {QGP), predicted by quantum chromodynamics on the lattice [2], would result in an enhanced entropy which m a y show up in a sudden increase of the number of pions as a function of incident energy or impact parameter.
We report in this paper results on invariant dierential cross sections and yields of charged pions measured near zero degree production angle in the forward rapidity region (4:3 y 6:3) in minimum bias Pb+Pb collisions at 158 GeV per nucleon [3].
Yields are measured as a function of the impact parameter of the collision at y=5.7 and 6.3.Preliminary results of this study were published in [4,5,6].

Experimental setup
The NA52 apparatus uses the H6 beamline of the SPS North Area at CERN as a mass spectrometer.H6 is a 540 m long double-bend focussing beamline which transports charged particles within a momentum acceptance (p=p) of 2.8% and an angular acceptance () of 2.2 sr.The rigidity (p=Z) of the spectrometer can be selected between 5 and 200 GeV.Due to the small detector acceptance mostly single particles are detected in the beam line per recorded event.
A s c hematic diagram of the spectrometer is given in gure 1.The incident lead ux was measured with a 0.4 mm thick segmented quartz Cerenkov counter (TOF0).The target was located in the target ladder noted as target1 in gure 1.During the 1995 run two lead/quartz ber electromagnetic calorimeters (QFC) [7,8] of 25 radiation lengths (X 0 ) with pseudorapidity acceptance of 2.7< < 4.1, positioned 0.6 m downstream of the target were used to measure the impact parameter of the collision.A set of scintillation counters, 8-fold segmented time-of-ight hodoscopes (TOF1-5) and three beam counters (B0-2) allowed to determine the charge and the velocity o f the particles transported in the beam line.Three threshold ( C0, C1, C2) and one dierential (CEDAR) Cerenkov counters provided additional particle identication capabilities.Seven multiwire proportional chambers (W1T-W5T, W2S, W3S) were used for tracking measurements.
A segmented uranium/scintillator hadronic calorimeter was installed at the end of the beam line to provide pion identication.The calorimeter [9] has a total depth of 7.1 interaction lengths and is longitudinally segmented in ve modules (gure 2), each made from uranium absorber plates alternating with scintillator plates.The trigger and data acquisition systems were implemented in two independent parts, allowing for recording events either over the full length of the spectrometer for the study of particles with a life time of at least 1.8 s, or only up to the counter B1 for particles with a life time of at least 0.9 s.A more detailed description of the experimental setup can be found in Ref. [9].
Charged pion production in xed target Pb+Pb collisions at 158 GeV per nucleon 3

Experimental method
The (m=Z) 2 spectrum in gure 3 illustrates the particle identication capability of the time-of-ight measurements.As is seen from the gure, electrons, muons and pions can not be separated with this method.The calorimeter information provides a w a y to identify these light particles.Figure 4 demonstrates the method of particle separation with the hadronic calorimeter at a spectrometer rigidity of 20 GeV. Figure 5 shows the result of the combined particle identication using the time of ight and the calorimeter information at 20 GeV rigidity.At l o w er rigidities (p=Z 10 GeV) particle identication was performed by means of the threshold Cerenkov counters C0 and C1.
Data were taken at spectrometer rigidities p=Z of 5, 10, 20 and 40 GeV (corresponding to pion rapidity of y=4.3, 5.0, 5.7 and 6.3) with a 4 mm thick lead target.The pion cross sections were measured between 5 to 40 GeV rigidity (p=Z) since the lowest tunable rigidity for the H6 beamline is 5 GeV and the separation of pions from other hadrons was not possible for rigidities p=Z > 40 GeV because of the limited resolution of the time-of-ight measurements and of the threshold Cerenkov counters.Empty target runs were taken in order to take i n to account the contribution of interactions outside the target.At rapidities 5.7 and 6.3 the invariant pion yields have been investigated as a function of the mean total number of nucleons participating in the collision.In the runs at rapidity y=4.3 and 5.0 the lead/quartz ber calorimeters were not available, therefore no information on the centrality of the collision exists for these data samples.
The particle yields are investigated in ve centrality regions.The mean total number of participant nucleons in the collision in each centrality region has been deduced by comparing the energy spectrum of the lead/quartz ber calorimeter with the energy spectrum obtained within the event generator VENUS 4.12 [10].The experimental energy resolution was implemented in the generator.The cross section in each centrality region was obtained by i n tegrating the calorimeter energy spectrum over an energy interval: The resulting cross section, the mean number of participating nucleons and the mean impact parameter of each centrality region are shown in table 1.For a more detailed description of the centrality dependence analysis see [11].
The particle cross sections and yields have been calculated taking into account the absorption of the incident ions in the target and their pile up in the electronic readout of the quartz counter, the spectrometer acceptance, the particle decay, interactions with material in the beamline, absorption in the target and the reconstruction eciency.For more details on these corrections see reference [12].The number of empty target background events was subtracted for each centrality bin.Reinteractions in the target were not corrected.
The systematic error of the cross sections due to uncertainties in the spectrometer Charged pion production in xed target Pb+Pb collisions at 158 GeV per nucleon 4 acceptance are estimated to be 15%.The systematic error due to uncertainties in the empty target correction is 10% ( [3], [11]).In the systematic error of the pion invariant yields an additional contribution of 7 % due to the centrality analysis [11] has to be added.The resulting total systematic error for the pion cross sections is 18% and for the pion yields 19%, where the dierent contributions to the systematic error have been quadratically added.The error on the mean number of participating nucleons is 13% [11].In the following only the statistical errors are shown unless stated dierently.

Results
The transverse momentum (p T ) acceptance of the particles ranges from zero to a maximum p T value, which is dierent for each rigidity and can be calculated as: p T (max) 0:0013 p, with p being the momentum of the particle (see reference [13] for a discussion of the spectrometer acceptance).The invariant dierential pion cross sections in minimum bias Pb+Pb collisions at 158 GeV per nucleon are shown in table 2 and in gures 6 and 7 as a function of rapidity.The results on K + , p, d, 3 He , t, K , p, d and 3 H eproduction in gure 6 and 7 were published in Ref. [12]. Figure 8 shows the resulting antiparticle to particle ratios as a function of rapidity.The = + ratio is found to peak around y=5.7.
The invariant pion yields are shown in table 3 for rapidities 5.7 and 6.3 and for dierent centrality regions.Figures 9 and 10 show the invariant yield of + and at y=5.7 and 6.3 divided by the mean number of participants N p as a function of N p .The p+Be data [14] shown in the same pictures have been measured near zero p T and at the same ratio of rapidity o v er beam rapidity ( y=y beam ) as the Pb+Pb data.
They were measured at an incident beam energy of 450 GeV per nucleon and have been rescaled to the incident energy of 158 GeV per nucleon.The systematic error on the particle yields in p+Be interactions is between 5 and 10% depending on the beam momentum [14].The systematic error in the NA56 experiment is improved as compared to the NA52 measurements though they use the same apparatus, because they were performed with dierent beam line conditions improving the acceptance uncertainties in the NA56 experiment.The energy rescaling factors were calculated from the measured energy dependence of the total multiplicities in p+p collisions [15].The mean number of participants in p+Be collisions was estimated with VENUS 4.12 to be N p =2.34 0.06.The total cross section for the reaction p+Be was taken from [16] t o b e =0.268 barn (for energy between 80 and 240 GeV). Figure 11 show the = + ratios at rapidities 5.7 and 6.3 as a function of the mean number of participant nucleons.

Discussion
The enhancement i n t h e = + ratio near beam rapidity (gure 8) may b e i n terpreted as being due to Coulomb interaction between the charged pions and the spectator protons.This eect would result in more than + falling into the small forward angular acceptance of the spectrometer.The enhancement is larger than would be expected from the excess of neutrons over protons in the lead nuclei, which yields a = + ratio of about 1.1.Another possible source of an enhanced to + ratio is Charged pion production in xed target Pb+Pb collisions at 158 GeV per nucleon 5 the associated production of K.According to a simulation based on VENUS this contribution as well as the initial isospin asymmetry yields a = + ratio of 1.2, which cannot explain the observed eect.
An enhancement of the = + ratio was also observed in Pb+Pb collisions by the NA44 experiment [17], however at midrapidity and for central collisions.This has also been interpreted as being due to Coulomb i n teractions.
The + invariant yield divided by the number of participants N p increases, whereas the yield over N p decreases with N p for both investigated rapidities (gures 9, 10).In these gures also p+Be data are displayed where measurements were available.Based on the expectation that both the positive and negative pion yields in peripheral Pb+Pb events should be equal or larger than in p+Be collisions at the same energy, the behaviour seen in gure 9 is indicative of Coulomb i n teraction enhancing the and decreasing the + yields in the most peripheral Pb+Pb data.Furthermore in p+Be reactions near beam rapidity and zero p T the presence of only one incident proton in the beam implies a higher + than yield, due to isospin and charge conservation.Indeed the = + ratio in p+Be at y=y beam = 0 : 98 drops to 0.55 (see gure 12).Both eects are suppressed when going away from beam rapidity.This is in line with gure 10, which shows that at rapidity 1.1 the + yields in peripheral Pb+Pb are higher than in p+Be collisions.The = + ratio at y=5.7 and 6.3 decreases with increasing centrality of the collision (gure 11).The decrease is stronger for y=5.7.The = + ratio is larger than one reaching a maximum value of 7 in the most peripheral events at y=5.7.This rapidity and centrality dependence of the = + ratio further supports the hypothesis of Coulomb i n teractions of charged pions with the projectile spectators.The Coulomb i n teraction near beam rapidity and zero p T is expected to be strongest for the most peripheral events, for which the number of spectator protons is largest.It is expected to be smallest when looking at central events in this phase space region since with increasing number of nucleons participating in the collision the positive c harge is shifted towards midrapidity and higher p T values.Furthermore the = + ratio is expected to be smaller at y=6.4 than at y=5.7 because of the fact that the latter is nearer to the beam rapidity where the Coulomb eect is more pronounced.
Figure 12 shows the = + ratio as a function of the rapidity normalized to the beam rapidity ( y=y beam ), for the most central, the most peripheral and the minimum bias Pb+Pb events as well as for central Au+Au collisions at 10.8 GeV per nucleon [18] and p+Be collisions at 450 GeV per nucleon [14].A similar increase of the = + ratio near beam rapidity due to the Coulomb i n teraction is expected in Pb+Pb and Au+Au collisions at the same centrality, independent of the incident energy per nucleon, since the number of spectators is about the same.On the contrary, the = + ratio measured in p+Be interactions at 450 GeV per nucleon near zero p T do not exhibit any enhancement near y beam , instead it remains below one.
In order to search for dependence of the pion production properties on the number of participants that could reveal a possible phase transition we h a v e studied the geometrical mean of the invariant + and yields ( environment of positive charge behaves as e X (repulsive) for + , with X being a positive function of the ne structure constant and the momentum k.Similarly for the correction is e +X (attractive).The geometrical mean of the yields eliminates this correction to a large extend, whereas for the arithmetic mean it is not corrected.On the other hand for the geometrical mean the isospin asymmetries are not corrected, while this is the case for the arithmetic mean.We assume therefore that the inuence of Coulomb i n teraction at this particular rapidity and p T is larger than the inuence of the asymmetry between proton and neutron numbers.This assumption is supported by the comparison of the data to the VENUS event generator and by our calculation of the = + ratio due to isospin asymmetry in the lead nucleus as discussed previously.This quantity is plotted in gure 13 together with p+Be data at 158 GeV per nucleon.The Coulomb corrected pion yield per participant n ucleon in Pb+Pb collisions at y=5.7 increases with centrality up to N p = 100 and then it saturates.The straight line extrapolation of the spectrum towards small N p points back to the p+Be value.In central Pb+Pb events the pion yield per N p is larger than in p+Be collisions.The N p dependence of the pion yield per participating nucleon seen in the Pb+Pb data at y=5.7 can be interpreted as non thermal pion production for N p < 100 and a higher degree of equilibration for N p > 100.
The pion invariant cross sections are compared to those of charged kaons [12] at the same rapidity and p T in table 4. The K= ratio measures any excess production of ss quarks compared to the production of uu or dd quarks.The interest for this observable arises from the theoretical expectation of an enhanced ss quark as compared to light ( u , d ) quark production in case of a QGP phase transition [19].The K + = + ratio in minimum bias Pb+Pb data at y=4.3 is 1.50.4 times the one in p+Be data, whereas the K = ratio at y=4.3 and the K + = + ratio at y=5.0 are the same.The observation of a modest enhancement of the kaon to pion ratio at forward rapidity in minimum bias Pb+Pb collisions, is not in contradiction with the possibility of a QGP formation since the measurement is in forward rapidity and near zero p T .In particular since the kaon to pion ratio is expected to be maximal at midrapidity due to the maximal available energy and at higher p T due to the presence of transverse ow [25].Indeed an enhancement of a factor of 2 in strange particle to pion ratios in Pb+Pb and other heavy ion collisions, as compared to p+A collisions at the same energy, w as observed around midrapidity [20, 2 1 ].
Assuming that local thermal equilibrium is reached for the pions at all centralities we can estimate the centrality dependence of the entropy per baryon.This assumption is not supported for events with less than 100 participants as it is inferred from gure 13 but some degree of local equilibration among pions in peripheral events is not excluded.Figure 14 shows the centrality dependence of the entropy per baryon calculated within a thermal model as [22]: The deuterons and protons have been measured at y=3.7, the protons at y=4.4 [11] and the pions ( p + ) at y=5.7.The entropy per baryon in the mostly forward rapidity hemisphere (3:7 y 5:7) is seen to increase with centrality.Since the entropy per baryon should not depend on the volume, this increase cannot be understood as due to the enlarged freeze-out volume of the system [11].It could be a consequence of the increased energy density in the more central events.The centrality Charged pion production in xed target Pb+Pb collisions at 158 GeV per nucleon 7 bins used in the gures 13 and 14 are subdivisions of the centrality regions presented in table 1 (see [11] for more informations).Note that due to the presence of collective transverse ow [25] the ratios of particles with dierent masses near zero transverse momentum and all parameters estimated from them like S/B dier from their values measured over the full p T range.Furthermore the centrality dependence of the =p ratio, measured within our small rapidity range, is sensitive t o c hanges of the baryon rapidity distribution with centrality.

Conclusions
We present results on + and invariant production cross sections in minimum bias Pb+Pb interactions at 158 GeV per nucleon in the rapidity range 4.3 y 6.3 and near zero degree production angle.The centrality dependence of the charged pion yields were investigated at y=5.7 and 6.3.
The ratio of the over + yields show a signicant maximum near beam rapidity, 7 for the peripheral events, 1.8 for the central events.The eect may be due to Coulomb i n teractions between the pions and the spectator protons.It cannot be explained by other sources like the initial isospin asymmetry of the Pb nucleus or by associated K production, which yield a = + ratio of 1.2 only.
The Coulomb corrected charged pion yield ( p + ) measured at y=5.7 per participating nucleon increases with centrality u p t o N p = 100 and then it saturates.The straight line extrapolation of the spectrum towards small N p points back to the p+Be value.The charged pion yield per participant n ucleon is larger in central Pb+Pb than in p+Be collisions.Pion yields at y=6.3 increase slightly less than linearly with N p and show no sudden change as a function of N p .
The K + = + ratio at y=4.3 is slightly larger than in p+Be collisions at the same energy, whereas the K + = + ratio at y=5.0 as well as the K = ratio at y=4.3 are the same for both data.These observations do not contradict the measured increase by a factor of 2 o f t h e p T integrated strange particle to pion ratios in heavy ion reactions compared to p+A collisions at the same energy, since the latter occurs mostly around midrapidity.
The entropy per baryon extracted from the =pand d=p ratios at forward rapidity and near zero transverse momentum assuming thermal equilibrium is seen to increase with increasing collision centrality.and the corresponding cross section has been found [23] from a parametrization of experimental data taken from reference [24].The errors shown are the statistical errors, while the values in parenthesis are the standard deviations of the distributions in the considered centrality ranges.
p + ) divided by the number of participants N p as a function of N p .The leading Coulomb correction in an Charged pion production in xed target Pb+Pb collisions at 158 GeV per nucleon 6

Figure 3 .
Figure 3.Typical example of a (m=Z) 2 spectrum of positive particles obtained from time-of-ight measurements at p=Z = 20 GeV.The shaded area indicates particles which g a v e no light in the Cerenkov counter.

Figure 4 .
Figure 4. Dierence of the energy deposited in the rst and second hadronic calorimeter module (E1 E2) over the total energy deposited in the calorimeter E, displayed as a function of the latter, for negative particles with p=Z = 20 GeV.

Figure 8 .Figure 9 .
Figure 8. Rapidity dependence of particle cross section ratios in minimum bias Pb+Pb collisions at 158 A GeV near zero p T .Closed symbols refer to the measured points; the open symbols are points reected over midrapidity (ycm = 2 : 9).The lines are drawn to guide the eye.

Figure 10 .Figure 11 . 4 Figure 12 .Figure 13 .Figure 14 .
Figure 10.Charged pion invariant yields in Pb+Pb collisions at 158 A GeV near zero p T divided by the mean number of participating nucleons in the reaction (Np) as a function of Np at rapidity 6.3.The p+Be data were measured at 450 GeV per nucleon in the same p T and y=y beam[14] and have been rescaled to 158 A GeV (see text).

Table 1 .
Cross section (cut), mean number of participant nucleons in the collision (< N p > ) and mean impact parameter (< b > ) for the ve centrality bins used in the tables 4 and 5 and in most gures.cut is the cross section of each centrality region, dened as cut =

Table 2 .
Invariant cross sections of + and produced in minimum bias Pb+Pb collisions at 158 GeV per nucleon and near zero transverse momentum as a function of rapidity.

Table 3 .
Invariant yields of + and produced in Pb+Pb collisions at 158GeV per nucleon and near zero transverse momentum as a function of rapidity and centrality.

Table 4 .
[14]ged kaon to pion ratios near zero p T and at rapidities 4.3 and 5.0 in minimum bias Pb+Pb collisions at 158 A GeV and in p+Be collisions at 450 GeV per nucleon[14].The latter were rescaled to 158 GeV per nucleon.The errors quoted include systematic and statistical errors.