Compendium of data to test predictions of 200 GeV/A Au+Au collisions at RHIC

B. Jacak , Stony Brook

December 9, 2002

Global Observables

The first basic measurements achievable at RHIC are of global quantities such as the number and rapidity distribution of charged particles, and the amount of transverse energy produced. Already dN_ch/dh is a model killer, as is seen in Fig. 1, from the PHOBOS measurements at Ös = 130 GeV/A and 200 GeV/A.

Figure 2 shows a compendium of dN_ch/dh from all four RHIC experiments for both energies and Figure 3 shows the number of charged particles per participant nucleon pair for Ös = 19, 130 and 200 GeV/nucleon from PHOBOS.

Figure 3: PHOBOS dN_ch/dh for Ös= 19 (green), 130 (blue) and 200 GeV/nucleon (red)

Au+Au.

The ratios of 200/130 GeV/nucleon charged particle yields from the four experiments are as follows:

BRAHMS: 1.14 ± 0.05

PHENIX: 1.17 ± 0.03

PHOBOS: 1.14 ± 0.05

STAR: 1.19 ± (no sys. yet)

Figure 4 shows dN_ch/dh vs. h from PHOBOS for the 3 RHIC energies, while Figure 5 shows pion and kaon dN/dy measurements from BRAHMS at Ös=200 GeV/A.

	Figure 4 : PHOBOS	Figure 5: BRAHMS

Turning now to the transverse energy production, Figure 6 shows the comparison by PHENIX of dE_T/dh to dN_ch/dh, each per participant pair, and Figure 7 gives the ratio.

Figure 6: PHENIX Et and Nch in Ös = 130 and 200 GeV Au + Au

Figure 7: <Et>/<Nch> RHIC vs. SPS

Figure 7 shows that <ET>/<Nch> is approximately independent of energy at RHIC, and also compares the RHIC results to collisions at the SPS.

Particle Spectra

The particle spectra have been predicted using a number of different models of heavy ion collisions. Figure 8 shows the pion, kaon and proton spectra measured by PHENIX in Ös= 200 GeV/A Au+ Au collisions. Hadron yields and mean p_T are given as a function of centrality below.

		Figure 8: Hadron spectra from PHENIX. Different curves correspond to centralities: 0 – 5 %, 5 -10 %,10-15 % 15 – 20 %, 20 – 30 %, 30 – 40 %, 40–50%, 50 – 60 %, 60 – 70 %, 70 – 80 %, 80 – 93 %

Figure 9 shows a comparison of the hadron p_T spectra measured by all the four experiments at RHIC.

Fig. 9

The spectra have been fitted to extract the mean p_T, which is studied both as a function of centrality and a function of Ös. STAR and PHENIX both have determined the mean p_T by fitting the measured spectra with a power law shape and deriving the value from the fit. Figure 10 shows the STAR result for non-identified charged hadrons, and Figure 11 shows the result for pions, kaons, and protons from PHENIX. The mean p_T is nearly unchanged between Ös = 130 GeV/A and 200 GeV/A. The centrality dependence is stronger for protons and antiprotons than pions; the saturation of pion <p_T> with centrality dominates the results for non-identified particles.

Figure 10. Mean transverse momentum as a function of centrality for non-identified charged hadrons, measured by STAR.

The spectral shapes shown in figures 8 and 9, along with the mean transverse momenta imply that the proton/antiproton yield may become equivalent to that of pions at sufficiently high p_T. This is indeed the case near 2 GeV p_T for minimum bias collisions, as is visible from Figure 12 from the PHENIX collaboration. It should be noted that BRAHMS also sees the “crossing” of the baryon and pion spectra. The crossing is visible in the p/p ratios from PHENIX shown in Figure 13.

	Figure 12. Comparison of hadron pT spectra from PHENIX at Ös= 130 and 200 GeV/A. The yield of baryons becomes equivalent to the yield of mesons at around 2 GeV/c pT.

Yields and ratios

The centrality dependence of p/ p for central and peripheral collisions is shown in Figure 14 from PHENIX.

Figure 14. p/p ratios from PHENIX for positive (top) and negative (bottom) particles, as a function of p_T. The red (or upper points) show the 5% most central collisions, while blue gives the ratios in peripheral collisions. The solid lines are the p/p ratios observed in gluon jets in e+e- collisions.

The p_T integrated hadron yields from Ös= 200 GeV/A Au+Au collisions from PHENIX are shown in Figure 15, as a function of centrality.

Figure 15. PHENIX yields of p (top), K (middle) and p (bottom). Left side shows positive and right gives negatives. Bands show systematic errors, while black points give the Ös=130 GeV/A results for comparison.

All four experiments show that p-/p+ ~ 1.0 and K-/K+ is ~0.95. These values are p_T and centrality independent, as shown by the PHENIX results in Figure 16.

Figure 16. Ratios of negative to positive pions and kaons in central and peripheral collisions, measured as a function of p_T by PHENIX.

Figure 17. pbar/p ratio as a function of pT from PHENIX, for central and peripheral collisions.

Figure 17 shows the antiproton/proton ratio as a function of pT from PHENIX; the ratio is near, but not quite, unity. This result is observed by all four experiments. The centrality dependence of negative/positive hadron ratios and proton and antiproton yields have been measured by BRAHMS. These are shown in Figures 18 and 19, respectively. At midrapidity there are 29 protons per unit rapidity and 7 net-protons, implying that ¾ of the observed protons arise from baryon-antibaryon pair production.

	Figure 18: BRAHMS particle ratios vs. y. Figure 19. Rapidity distributions of protons, antiprotons and net protons, measured by BRAHMS.

Hadron Flavor Observables

The ratios reported above have been analyzed in terms of thermal models by all four experiments. Figure 20 shows the observed ratios of positive to negative kaons and protons from PHOBOS, plotted as a function of the baryo-chemical potential.

Figure 20. PHOBOS chemical analysis of kaon and proton ratios.

Figure 21 shows a similar kind of chemical analysis, using the model of Becattini, from BRAHMS. The figure compares the Ös= 200 GeV/A data to 130 GeV/A data (also from BRAHMS) and to kaon and proton ratios in lower energy collisions. BRAHMS finds that a good empirical fit going through all the data points is given by (K-/K+) = (pbar/p)^1/4.

Figure 21. BRAHMS compilation of kaon and proton ratios, comparing also to lower energy results.

Figure 22 shows the compilation, also made by BRAHMS, of the K/p ratios as a function of Ös. The figure shows that K+/p + is higher at y=3 than at midrapidity, as would be expected from the above empirical fit. The midrapidity K+/p+ ratio is smaller at RHIC than at lower energy where the baryon rapidity density is larger due to more stopping.

Figure 22.

Figure 23 shows K⁰* production measured by STAR, compared to results at lower Ös by plotting its ratio to K. Three centrality bins and also an (uncorrected!) result for pp is shown. Figure 24 shows the ratio of f/ K⁰* as a function Ös.

Figure 23. STAR K⁰*/K for central, peripheral Figure 24. STAR f/ K⁰*, compared to

and pp collisions, compared to lower energy lower energy results.

results.

STAR has also measured W yields in Au+Au, and seen whether these can be explained with a chemical equilibrium picture. They find that W/h- = 0.000887 ± 0.000111, and anti-W /h- = 0.000935 ± 0.000105, at 200 GeV/A Ös, with systematic uncertainties of 15%. Figure 25 shows all the measured ratios at Ös= 130 GeV/A from STAR (along with their chemical equilibrium fit), while Figure 26 shows the summary of ratios in 200GeV/A collisions from all four experiments.

Figure 26.

Transverse flow

The now-traditional analyses of transverse flow, by looking at the mass dependence of spectral slopes as well as HBT analysis were performed at RHIC. The HBT results are given in the next section. Figure 27 shows the mass dependence of the slopes, in a “Nu Xu plot”; however, it is important to use caution when comparing to values from this plot. The spectra are not all measured in the same p_T range, and the extracted means depend on the range, along with the shape used in making the fits. Though the slopes are shown for 130 GeV/A data, the 200 GeV/A results are very similar.

Figure 27. <pT> vs. particle mass from STAR. The green line shows the <pT> prediction with Tth and <b> obtained from blastwave fit, while the dotted line shows the <pT> predicted for Tch = 170 MeV and <b>=0. p+p collisions should have no rescattering or flow, and lack equilibration.

Figure 28 shows the first transverse mass spectrum of W from STAR. The different curves correspond to blast wave spectra with different values of the freezeout temperature and transverse velocity. Clearly, the parameters are not well constrained, but this plot represents only a subset of the data.

Figure 28. W transverse mass spectra measured by STAR in Ös=200 GeV/A Au+Au.

HBT

Two particle correlations are measured extensively by three of the four collaborations. I will focus here only on those features which were predicted prior to RHIC start-up. This topic presents one of the interesting mysteries at RHIC right now. Figure 29 shows the transverse momentum dependence of the 3-D HBT radius parameters for positive and negative pion pairs in Ös = 200 GeV/A and 130 GeV/A Au+Au collisions from PHENIX.

	Figure 29. HBT radius parameters, as a function of the positive and negative pion transverse momenta, from PHENIX.

PHENIX also measured the K+ and K- HBT radii for the 30% most central collisions. The kaon radius parameters fall on or within 1 standard deviation above the pion trends. The results are given in the table:

	K+K+	K-K-
Rside	4.18 ± 0.54 fm	3.65 ± 0.43
Rout	3.72 ± 0.69	3.23 ± 0.47
Rlong	4.27 ± 0.65	4.48 ± 0.68
l	0.815 ± 0.181	0.785 ± 0.181

The K_T dependence of Rout/Rside is shown in figure 30 from PHENIX at Ös = 200 GeV/A collisions, compared to 130 GeV/A results from STAR and PHENIX. PHOBOS reports this ratio at 200 GeV/A to be 1.16 ± 0.09(stat) ± 0.25(syst) at K _T = 0.25 GeV/c

.

The centrality dependence has been studied by STAR, and the results for three centrality bins are shown in Figure 31. STAR has also made a first measurement of K⁰s correlations, and finds that R_inv = 5.75 ± 1.00 fm with a l of 0.76 ± 0.29.

Elliptic flow

There were many predictions of how much elliptic flow should be observed at RHIC. STAR, PHOBOS and PHENIX have measured the v2 characterizing the elliptic flow as a function of centrality, these are shown in Figure 32. PHOBOS has also measured the rapidity dependence of the elliptic flow in both Ös=130 and 200 GeV/A Au+Au collisions. This is shown in Figure 33.

The v2 predictions also gave specific values for different particles. Both STAR and PHENIX have measured v2 for identified particles. For Ös = 200 GeV/A collisions, STAR reported v2 for kaons and lambdas, while PHENIX showed pions + kaons and protons. Both compare mesons and baryons; Figure 34 shows the p + K and proton v2 values from PHENIX to compare to the early predictions. STAR results on strange hadron v2 can be found in the QM02 proceedings and eprint server.

The Ös = 200 GeV/A data allow the analysis of v2 to higher pT. Figure 35 shows the STAR result for minimum bias Au+Au collisions and Fig.36 for mid-central collisions.

		Figure 35.
	Figure 36. STAR v2 in mid-central collisions, extending to highest pT.

Jets

A great deal of discussion has ensued from the v2 near-saturation at high p_T. This result, combined with the observed suppression of high p_T particles already in 130 GeV/A data suggests that there should be an azimuthal asymmetry arising from the absorption of jets in dense matter. There now exist data at Ös= 200 GeV/A both for neutral pions and non-identified charged particles to investigate the magnitude of suppression and possible energy loss. In this section, I will start with identified pions.

Figure 37 shows the pion spectrum measured by PHENIX in Ös =200 GeV p+p collisions.

Figure 37.

Charged hadron spectra were measured by all four experiments. Figure 39 shows the results from BRAHMS and figure 40 from PHOBOS.

		Figure 40. PHOBOS

Figures 41 and 42 show the charged spectra from STAR and PHENIX, respectively.

Figure 41. STAR Figure 42. PHENIX

Figure 43 shows a compendium of R_AA from all the experiments, and Figure 44 shows the centrality dependence of high pT particle yields, to look for scaling with N_part or N_coll.

Figure

43.

Figure 44. Centrality dependence of charged particle yields at p_T > 4 GeV/c from PHENIX. The top plot shows the yield per binary collision, plotted vs. the number of participants, while the bottom plot shows the yield per participant pair.

Of course, the study of jets has traditionally been carried out by analysis of more than just the leading particles. STAR and PHENIX have both seen evidence of jets in 2-particle azimuthal angle difference distributions. After subtracting the soft background, and accounting for the azimuthal asymmetry represented by v2, both see a non-zero jet strength, which increases with the p_T of the trigger particle and also with the p_T of the accompanying, or partner, particle. PHENIX has quantified the correlations on the near side (same side in azimuth as the high p_T trigger particle). Fitting the charged particle correlations with a cos(2f) shape plus a Gaussian, shows a clear jet signal as illustrated in Figure 45. The width of the near-side Gaussian decreases with p_T, as expected from the transverse momentum distribution of jet fragments in the jet frame observed in p+p collisions.

Figure 45. Gaussian width of near-angle charged particle correlations from PHENIX, as a function of centrality. Dotted lines show the particle p_T dependence for jet correlations in p-p collisions.

One of the most important predictions from jets energy loss in dense matter (or, perhaps, formation of color glass condensate) is the disappearance of back-to-back jets. This has been observed by STAR and is shown in Figure 46.

Figure 46. Particle pair results from STAR in 200 GeV/A Au+Au. The jet strength, compared to that in p+p collisions, is plotted as a function of the number of participants for two trigger particle thresholds. The upper set of points on each side is for same-side jets and lower for away-side

Other Penetrating Probes

Many predictions have been made about the magnitude and centrality dependence of J/Y suppression at RHIC. The data to confront those predictions suffers from limited statistics at the moment, but first glimpses are already possible. Figure 47 shows the J/Y yield in p+p and Au+Au measured via electron-positron pairs in PHENIX.

Figure 47. J/Y cross section * branching ratio per binary NN collision from PHENIX.

In addition to J/Y, PHENIX also measures the open charm cross section via the single electron yield at intermediate values of p_T. The measured hadron spectra and yields are used to construct a “cocktail” of hadronic lepton sources. This was subtracted from the data in Ös = 130 GeV/A Au+Au collisions, and compared to a measurement of photonic sources measured via conversion to electron-positron pairs in the 200 GeV/A data. Figure 48 shows the Ös dependence of the charm cross section per binary NN collision, compared to predictions from Pythia with a K factor tuned to reproduce lower Ös data. The PHENIX points from 130 GeV/A are included in the plot.

Figure 48.

Charm cross section per binary NN collision vs. Ös, including the PHENIX results. The upper curve is p_T integrated, the lower ones are in the given ranges.

In the 200 GeV/A, PHENIX collected sufficient electron statistics to study the charm cross section as a function of centrality. Figure 49 shows the charm cross section compared to the Pythia prediction, scaled up by the mean number of binary NN collisions for 4 centrality bins. No suppression or enhancement of charm is observed.

	Figure 49. Charm yield from 200 GeV/A Au+Au collisions, in four centrality bins from PHENIX. Solid lines show predictions from Pythia, scaled up by the mean number of binary NN collisions in each centrality bin.