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Reminiscences of Wit Busza and 41 Years of p+A Physics

One of the more memorable (and easiest) proposal to deal with when I served on Bob Wilson's Program Advisory Committee at NAL (Now Fermilab) from 1972-75 was Proposal-178,"A study of the average multiplicity and multiplicity distributions in hadron-nucleus collisions at high energies", with only 4 authors, Wit Busza, Jerry Friedman, Henry Kendall and Larry Rosenson, as presented at the PAC meeting by Wit. What I remember was that he discussed only ONE 5 inch photomultiplier with a Cherenkov radiator in the beam to make this measurement of production of charged particles with angles up to 30 degrees in various nuclei, 40 hours requested. This turned out to be a"seminal"experiment leading to the Wounded Nucleon and other participant models. Subsequent p(d)+A experiments from the AGS to RHIC, as well as alpha-alpha measurements at the CERN-ISR, will be discussed together with the various `participants' that they revealed.


E-178
The first experiment specifically designed to measure the dependence of the charged particle multiplicity in high energy p+A collisions as a function of the nuclear size was performed by Wit Busza and collaborators ( Fig. 1) at Fermilab using beams of ∼ 50 − 200 GeV/c hadrons colliding with various fixed nuclear targets. The experiment was unique in the small (but distinguished) number of authors; and in its size, which would literally fit on a table top (Fig. 2).  They found the extraordinary result [1] that the average charged particle multiplicity N ch hA in hadron+nucleus (h+A) interactions was not simply proportional to the number of collisions (absorption-mean-free-paths), N coll = ν, but increased much more slowly, proportional to the number of participants N part . Thus, relative to h+p collisions (Fig. 3a) [2]: Since the different projectiles, h = π + , K + , p in Fig. 3a have different mean free paths, the fit to the same straight line in terms of ν is convincing. Figure 3: a)(left) R A = N ch hA / N ch hp as a function of the average thickness of each nucleus given in terms of the mean free path, ν = N coll [2] for 50 and 100 GeV/c h+A collisions; b) (right) Charged particle multiplicity density, dN ch /dη, as a function of A (represented by ν) for 200 GeV/c p+A collisions [3].
The other striking observation (Fig. 3b) [3] was that a relativistic incident proton could pass through e.g. ν = 4 absorption-mean-free-paths of a target nucleus and emerge from the other side; and furthermore there was no intra-nuclear cascade of produced particles (a stark difference from what would happen to the same proton in a macroscopic 4 mean-free-path hadron calorimeter). In the forward fragmentation region of 200 GeV/c p+A collisions, within 1 unit of rapidity from the beam, y beam = 6.0, there was essentially no change in dN ch /dη as a function of A, while at mid-rapidity (y cm N N ∼ 3.0), dN ch /dη increased with A together with a small backward shift of the peak of the distribution resulting in a huge relative increase of multiplicity in the target fragmentation region, η < 1 in the laboratory system. These striking features of the ∼ 200 GeV/c fixed target hadron-nucleus data ( √ s N N ∼ 19.4 GeV) showed the importance of taking into account the time and distance scales of the soft multi-particle production process including quantum mechanical effects [4,5,6,7,8,9].

The Wounded Nucleon Model
The observations in Fig. 3 had clearly shown that the target nucleus was rather transparent so that a relativistic incident nucleon could make many successive collisions while passing through the nucleus, and emerge intact. Immediately after a relativistic nucleon interacts inside a nucleus, the only thing that can happen consistent with relativity and quantum mechanics is for it to become an excited nucleon with roughly the same energy and reduced longitudinal momentum and rapidity. It remains in that state inside the nucleus because the uncertainty principle and time dilation prevent it from fragmenting into particles until it is well outside the nucleus. This feature immediately eliminates the possibility of a cascade in the nucleus from the rescattering of the secondary products. If one makes the further assumptions that an excited nucleon interacts with the same cross section as an unexcited nucleon and that the successive collisions of the excited nucleon do not affect the excited state or its eventual fragmentation products [10], this leads to the conclusion (c. 1977) that the elementary process for particle production in nuclear collisions is the excited nucleon, and to the prediction that the multiplicity in nuclear interactions should be proportional to the total number of projectile and target participants, rather than to the total number of collisions, or R A = N part−pA /N part−pp = (1 + ν)/2, as observed. This is called the Wounded Nucleon Model (WNM) [11] and, in the common usage, Wounded Nucleons (WN) are called participants.
In the fixed target experiments of the 1980's, the number of spectators (i.e. non-participants) N s in a B + A collion (Fig. 4a) could be measured directly with a Zero Degree Calorimeter in the beam. This enabled an unambiguous measurement of the (projectile) participants, N part−proj = B − N s ; and for a symmetric A+A collision, the total number of participants, N part = 2N part−proj = 2(A−N s ). In this way, the WA80 experiment [12] could directly verify the WNM, in beams of 16 O and 32 S of 60 and 200 A·GeV/c on vari-ous nuclear targets, by the measured linearity of the mid-rapidity transverse energy density, dE T /dη| max with N part (Fig. 4b).

Other Extreme Independent Models
Interestingly, at mid-rapidity, the WNM works well only at roughly √ s N N ∼ 20 GeV where it was discovered. At lower √ s N N < ∼ 5.4 GeV, particle production is smaller than the WNM due to the large stopping [13] with reduced transparency as shown by measurements by E802 at the BNL-AGS in an EM Calorimeter (Fig. 5) [14]. The large stopping at √ s N N < ∼ 5.4 GeV is indicated by the fact that the maximum energy in O+Cu is the same as in O+Au, even though the maximum thickness of a Cu nucleus is only ≈ 2/3 that of Au. Also the upper edge of the O+Cu spectrum is identical to that in O+Au but a factor of 6 lower in amplitude. Both these observations can be understood by representing the O+Cu and the O+Au spectra by sums of from 1 to 16 convolutions of the measured p+A spectrum according to the relative probability of the number of projectile participants, the Wounded Projectile Nucleon Model (WPNM) [15,16,14]. The stopping is more strikingly illustrated by the mid-rapidity E T distributions for 14.6 GeV/c protons on Be and Au targets (Fig. 6) [17], which vary in shape as a function of the laboratory rapidity interval δη, but in each δη interval, the p+Be and p+Au spectra are identical in shape. There is no evidence of multiple collisions in the target! This confirms a previous observation that the pion distribution from a second collision is shifted in rapidity by δη > 0.8 which is out of the aperture of the E T measurent. For the same reason, the Au+Au spectra [17] are also well represented by the WPNM, a sum of convolutions of the measured p+Au (or p+Be) spectra.
It is interesting to note that the representation of the upper edge of the mid-rapidity O+Pb spectrum by 16 convolutions of the measured p+Au spectrum at √ s N N ∼ 19.4 GeV was first shown by NA35 at CERN (Fig. 7) [18], which inspired the WPNM [15], but does not contradict the WNM because a 'centrality selected' p+Au spectrum was used [19], not the minimum bias p+Au spectrum. For √ s N N ≥ 31 GeV, particle production is larger than the WNM [20,21]; and a new model, the Additive Quark Model (AQM) [22,23], which is equivalent to a wounded projectile quark (color-string) model, has been used successfully (Fig. 8).
All three of the above models as well as another to be described below are of the type referred to as "Extreme Independent Models" in which the effect of the nuclear geometry of the interaction can be calculated independently of the dynamics of particle production, which can be derived from experimental T measured in an EM calorimeter at mid-rapidity |∆y| < 0.9 , ∆φ = 1.8π, in p+p, d+d, α + α collisions at √ s N N =31 GeV at the CERN ISR [20]. Lines on the right are fits to the p-p data plus WNM and AQM calculations [23] as indicated.
measurements, usually the p+p (or p+A) measurement in the same detector which typically follows a Γ distribution. A characteristic of these models can be seen in Fig. 8b in which the WNM line is parallel to the p+p spectrum because the 8-wounded-nucleon (4 collision) nuclear geometry is exhausted so that the shape of the 4-th convolution of the p+p spectrum (a Γ distribution with the same exponential slope) dominates. 2

Measurements at RHIC and LHC-Ions
Wit's PHOBOS experiment produced the first published measurement at RHIC [24]. The speciality of PHOBOS was its large rapidity coverage (Fig. 9a); but a legacy of PHOBOS is that this first publication established the standard of quoting the mid-rapidity multiplicity distribution in A+A collisions as dN AA ch /dη/(0.5 N part ) which would equal the value in p-p collisions at the same √ s if the data followed the WNM. The deviation from the VOLUME 85, NUMBER 15 distribution agrees well between simulation and data, confirming our understanding of detector geometry and tracklet efficiency. Based on the comparison of data and MC tracklet distributions, the comparison of results from the SPEC and VTX tracklet analysis and the comparison of tracklet and single hit multiplicities, we estimate the overall systematic uncertainty to be less than 8%. The largest single source of systematic uncertainty is the correction for combinatorial noise in the SPEC subdetector. As a further cross-check we repeated the analysis procedure using the VENUS [6] event generator and by using a͑z vtx ͒ obtained from running the event generators at various different energies. For all MC runs, a agreed to within 62.5%, demonstrating the robustness of the tracklet counting procedure.

P H Y S I C A L R E V I E W L E T T E R S
As a result of the procedure we obtain a primary charged-particle density of dN͞dhj jhj,1 408 6 12͑stat͒ 6 30͑syst͒ for p s NN 56 GeV and 555 6 Normalizing per participant pair, we deduce dN͞dhj jhj,1 ͞0.5͗N part ͘ 2.47 6 0.1͑stat͒ 6 0.25͑syst͒ and 3.24 6 0.1͑stat͒ 6 0.25͑syst͒, respectively. Taking the strong correlation between the systematic errors at the two energies into account, we observe an increase in the charged-particle density per participant by a factor of 1.31 6 0.04͑stat͒ 6 0.05͑syst͒ from 56 to 130 GeV.
In Fig. 4 we show the normalized yield per participant obtained for Au 1 Au collisions, proton-antiproton (pp) collisions [7], and central Pb 1 Pb collisions at the CERN SPS [8]. The dN͞dh value for the Pb 1 Pb data was obtained by numerically integrating the momentum distributions shown in [8].
Several important features of the data emerge: First, the central Au 1 Au collisions show a significantly larger charged-particle density per participant than, for example, nonsingle diffractive (NSD) pp collisions at comparable energies. This rules out simple superposition models such as the wounded nucleon model [9] and is compatible with predictions of models like HIJING that include particle production via hard-scattering processes.
Second, the observed increase by 31% from 56 to 130 GeV in central Au 1 Au collisions is significantly steeper than the increase shown by a pp parametrization (see Fig. 4) for the same energy interval [7]. Finally, comparing our data to those obtained at the CERN SPS for Pb 1 Pb collisions at p s NN 17.8 GeV, we find a 70% higher particle density per participant near h 0 at p s NN 130 GeV. General arguments (cf. Bjorken's estimate [10]) suggest that this increase should correspond to a similar increase in the maximal energy density achieved in the collision. We acknowledge the generous support of the entire RHIC project personnel and the C-A and Chemistry Departments at BNL. We thank Fermilab and CERN for help in silicon detector assembly. We thank the MIT School of Science and LNS for financial support. This work was partially supported by U.S.  PHOBOS has also made some interesting observations regarding two wellestablished scaling laws in p+p physics, namely, the "effective energy", or "leading particle effect" [25], (Fig. 10) [26] and "limiting fragmentation" [27] ( Fig. 11) [28]. The "leading particle" effect is shown in Fig. 10b: the total charged multiplicity in p+p collisions plotted at half the c.m. energy, i.e. at √ s/2, is the same as that in e + e − collisions at √ s. The reason is that the available or effective energy for making secondaries in p+p collisions is only 1/2 the c.m. energy because the two leading protons carry away half the energy [25]. PHOBOS has discovered [26] that the leading particle effect vanishes in A+A collisions, i.e. N AA ch /dη/(0.5 N part ) in A+A is the same as that in e + e − at the same value of √ s (Fig. 10), because the leading protons in the first collision lose the rest of their energy via particle production on subsequent collisions.
Figure 11 [28] shows that the width of the dN ch /dη distribution for Au+Au collisions narrows for more central collisions, with relatively fewer particles at beam and target rapidity; and that dN AA ch /dη /(0.5 N part ) measured with respect to the beam rapidity, η = η−y beam , is universal in Au+Au collisions as it is in p+p collisions.
collisions which span a factor of 10 in collision energy ( s NN p ). The results are folded about midrapidity (positive and negative bins are averaged). The distributions are observed to be independent of collision energy over a substantial 0 range. This is consistent with and extends a similar observation made by BRAHMS [10] over a more restricted 0 range. Both the 19.6 and 130 GeV data reach 85%-90% of their maximum value before deviating significantly (more than 5%) from the common limiting curve. These data demonstrate that limiting fragmentation applies well in the Au Au system and that the ''fragmentation region'' is rather broad, covering more than half of the available range of 0 over which particles are produced. In particular, the fragmentation region grows significantly between 19.6 and 130 GeV, extending more than two units away from the beam rapidity. A particle production appears to approach a fixed limiting curve which extends far from the original beam rapidity, indicating that this universal curve is an important feature of the overall interaction and not simply a nuclear breakup effect. This result is in sharp contrast to the boost-invariance scenario [18] which predicts a fixed fragmentation region and a broad central rapidity plateau that grows in extent with increasing energy. Figure 2(b) shows the scaled pseudorapidity distributions for a set of noncentral collisions, which also exhibit limiting fragmentation over a broad range of 0 . Figure 3 shows the centrality dependence of the dN ch =d 0 = hN part =2i distribution at the two extreme energies: 19.6 and 200 GeV. These data demonstrate that particle production in the fragmentation region changes significantly with centrality. Figure 4 shows the ratio of noncentral to central data with (90% C.L.) systematic errors included. The error in the ratio involves a partial cancellation of the systematic errors in the individual measurements. For 0 > ÿ1:5, the scaled pseudorapidity density actually grows in the peripheral data with respect to the more central data. This effect has already been observed for   FIG. 1. The charged particle pseudorapidity distribution, dN ch =d, measured for Au Au at s NN p 200, 130, and 19.6 GeV for the specified centrality bins. Note: the 45%-55% bin is not reported for the 19.6 GeV data due to uncertainties caused by the very low multiplicity in these events. The typical systematic errors (90% C.L.) are shown as bands for selected centrality bins. The statistical errors are negligible.

P H Y S I C A L R E V I E W L E T T E R S
week ending 1 AUGUST 2003 VOLUME 91, NUMBER 5 particle production appears to approach a fixed limiting curve which extends far from the original beam rapidity, indicating that this universal curve is an important feature of the overall interaction and not simply a nuclear breakup effect. This result is in sharp contrast to the boost-invariance scenario [18] which predicts a fixed fragmentation region and a broad central rapidity plateau that grows in extent with increasing energy. Figure 2(b) shows the scaled pseudorapidity distributions for a set of noncentral collisions, which also exhibit limiting fragmentation over a broad range of 0 . Figure 3 shows the centrality dependence of the dN ch =d 0 = hN part =2i distribution at the two extreme energies: 19.6  FIG. 1. The charged particle pseudorapidity distribution, dN ch =d, measured for Au Au at s NN p 200, 130, and 19.6 GeV for the specified centrality bins. Note: the 45%-55% bin is not reported for the 19.6 GeV data due to uncertainties caused by the very low multiplicity in these events. The typical systematic errors (90% C.L.) are shown as bands for selected centrality bins. The statistical errors are negligible.

P H Y S I C A L R E V I E W L E T T E R S
week ending 1 AUGUST 2003 VOLUME 91, NUMBER 5  would indicate that the total charged-particle production is underestimated by Eq. (17).

Factorization
Similar to what was shown for the midrapidity multiplicity (Sec. IVA2) the total participant-scaled charged-particle TABLE II. Summary of the midrapidity dNch dη | |η|<1 / N part /2 charged-particle multiplicity for Au + Au and Cu + Cu for 0%-6% central collisions. The data are averaged over those obtained from the tracklet counting and single-Si-layer analysis. Errors represent averages of the 90%-confidence-limit systematic errors for the two methods. Statistical errors are negligible.
is seen to describe the Au + Au and Pb + Pb data quite accurately over the two orders of magnitude of collision energy, but it also appears that the Cu + Cu data fall slightly below this trend. Also, the 56 and 62.4 GeV Au + Au points fall slightly below this line, which may indicate a curvature to the collision-energy dependence consistent with the dashdotted curve given by [50] 2 N part which describes well the RHIC and LHC A + A data, but overestimates lower-energy measurements. The dashed curve is a fit to the inelasticpp and pp data; namely,

Centrality dependence and factorization
The midrapidity charged-particle multiplicities normalized to the number of participant pairs, N part /2, are shown for Au + Au collisions (solid symbols) in Fig. 13 as a function of centrality of the collision expressed by N part and listed in Table V, column 4 (see Appendix). The corresponding data for Cu + Cu collisions are given in Fig. 14 Table VII (see Appendix). The shaded ovals represent estimates of the 90%-confidence-level systematic errors in the measured dN ch /dη values and the calculated number of participant pairs, N part /2. One observes that the normalized charged-particle production at all energies increases with N part and exceeds the measurements for pp As demonstrated in a previous PHOBOS publication [9], the collision energy and centrality dependencies of chargedparticle production in Au + Au collision at midrapidity exhibit factorization such that In PHOBOS' final multiplicity paper [29], the systematics of charged particle production at RHIC were neatly summarized in two panels (Fig. 12). At RHIC, for √ s N N from 19.6 to 200 GeV (Fig. 12a), the WNM works in Au+Au collisions for the total multiplicity, N ch /(0.5 N part ) and over the range |η| < 5.4, while at mid-rapidity (Fig. 12b), the WNM fails-the multiplicity density per participant pair, dN AA ch /dη/(0.5 N part ), increases with increasing number of participants, in a characteristic shape that was first observed by PHENIX [30] (Fig. 13a).
With the recent startup of Heavy Ion Physics at the LHC, a huge increase in √ s N N of more than an order of magnitude from 200 GeV to 2.76 TeV became avalable. The results for dN AA ch /dη/(0.5 N part ) in Pb+Pb at midrapidity as first published by the ALICE experiment [31] (Fig. 13b) were astounding: the ratio of dN AA ch /dη/(0.5 N part ) from LHC to RHIC is simply a factor of 2.1 in every centrality bin. The LHC and RHIC measurements lie one on top of each other by simple scaling by a factor of 2.1. In Fig. 14a new results from Au+Au collisions at √ s N N =7.7 GeV at RHIC scaled by a factor of 7.7 also lie on this curve. The identical shape of the centrality dependence of charged particle production for all √ s N N indicates that the dominant effect is the nuclear geometry of the A+A collision. It has been shown [32,33] using PHOBOS Au+Au data from RHIC, and also discussed for other RHIC data [34], that the geometry represents the number of constituent-quark participants, N qp : i.e. in Au+Au collisions, the mid-rapidity dN AA ch /dη as a function centrality is linearly proportional to the number of constituent-quark participants (NQP). However, for symmetric systems, the NQP cannot be distinguished from the number of color-strings, the Additive Quark Model (AQM) [22,35]. In the AQM, only one color string can be attached to a wounded quark. Thus, for asymmetric systems such as d+Au, the AQM is a "wounded projectile quark" model since in this model, only 6 color strings can be attached between the wounded quarks in the d-projectile and Au-target, while the d+Au system can have many more quark participants. The PHENIX preliminary results (Fig. 14b) show that in fact it is the NQP not the AQM (color string model) that works.

Some Personal Observations
I have spent a lot of my research time on measurements and "Extreme Independent Models" based on and inspired by Wit's work. I have also greatly enjoyed collaborating on E802 at the AGS with the MIT group: Lee Grodzins, Steve Steadman, George Stephans and many great MIT graduate students who are now among the leaders of the field. I am also impressed with the excellent group that Wit has built up here at MIT and the outstanding contributions that they have made to RHI physics both at RHIC on PHOBOS and now at LHC on CMS. However, I also must confess that my personal favorite RHIC result from the MIT group does not relate to N part or N coll , but rather to "triangular flow" [36].
For the first 10 years of RHIC running and dating back to the Bevalac, all of the experts, with possibly one exception [37], thought that the odd harmonics of collective flow vanished at mid-rapidity due to the symmetry of the source for φ → π + φ, even though 'head and shoulders' or "Mach Cones" were observed at ∆φ = π ± π/3 which prevented me from understanding the two-particle correlations from di-jets [38]. In 2006 at the Correlations and Fluctuations conference in Florence, Italy, I was chair of a session at which Burak Alver presented some ideas of how to measure the fluctuations of v 2 , σ 2 v 2 = v 2 2 − v 2 2 , in PHOBOS [39]. Frankly I was skeptical about the method he proposed, and George Stephans was skeptical about my skepticism. However, in 2010 [36], Burak and his Professor, Gunther Roland, realized that due to fluctuations in the collision geometry on an event by event basis, the eccentricity of participants on any given event did not respect the average symmetry, resulting in "Triangular Flow", or v 3 , another legacy of MIT to RHI physics.