Nucleon-Gold Collisions at 200 A${\cdot}$GeV Using Tagged d+Au Interactions in PHOBOS

The PHOBOS detector Back et al. (2003a) at the Relativistic Heavy Ion Collider (RHIC) Hahn et al. (2003) is one of several experiments Adamczyk et al. (2003); Adcox et al. (2003a); Ackermann et al. (2003) that have measured the invariant yield of charged hadrons in collisions of deuterons with gold nuclei at a nucleon-nucleon center of mass energy of $\sqrt{s_{\scriptscriptstyle{{\rm NN}}}}=200\leavevmode\nobreak\ {\mbox{${\rm GeV}$}}$. In the referenced papers, charged hadron production is studied as a function of both transverse momentum ($p_{\mathrm{T}}$) and collision centrality (a measure correlated with the impact parameter of the deuteron). The particle yields for $p_{\mathrm{T}}$ above about 1.5–2.0 GeV$\kern-1.49994pt/\kern-1.19995ptc$ are similar to, or possibly slightly enhanced above, those observed in $p$+$\bar{p}$ collisions at the same energy Back et al. (2003b), somewhat reminiscent of the so-called Cronin effect seen in proton-nucleus collisions Cronin et al. (1975). Previous analyses of the $d$+Au charged hadron spectra by PHOBOS Back et al. (2003b) and the other RHIC experiments Adler et al. (2003a); Adams et al. (2003a); Arsene et al. (2003); Adams et al. (2006); Adler et al. (2006) have demonstrated that this enhancement stands in stark contrast to the observed suppression of high $p_{\mathrm{T}}$ hadrons in the (central) Au+Au collision system at $\sqrt{s_{\scriptscriptstyle{{\rm NN}}}}=200\leavevmode\nobreak\ {\mbox{${\rm GeV}$}}$ Adcox et al. (2002, 2003b); Adler et al. (2002); Back et al. (2004a). Since no suppression is found in $d$+Au collisions, the effect seen in central Au+Au interactions has been interpreted as evidence of final state effects, in particular parton energy loss. It should be noted that evidence of possible collective effects in systems such has $d$+Au and $p$+Pb have been found recently, but only for events with very high final state particle multiplicity (see, as one example, Ref. Chatrchyan et al. (2013)).

The choice of the reference system used in comparing to Au+Au data, and of the centrality measure, are both of critical importance to the understanding of the observed suppression. The data and Monte Carlo (MC) simulations presented in this paper are used to study the choice of centrality measure, as well as the choice of reference system. Centrality measures based on the multiplicity of particles in the high-pseudorapidity region as well as on the number of spectators in the gold nucleus are examined. To study the chosen reference system, a calorimetry-based technique is used to identify, on an event-by-event basis, the subsets of $d$+Au collisions in which only the proton or only the neutron participated in the collision. Specifically, a calorimeter on the side of the interaction region where the Au beam exits is used as part of the determination of collision centrality while a second calorimeter on the other side is used in the selection of $n$+Au and $p$+Au interactions. Similar tagging of the nucleon+Au component of the $d$+Au data has also been investigated by the PHENIX collaboration Adler et al. (2008); Adare et al. (2014). These nucleon-nucleus collisions are used to construct an ideal reference system for comparison with Au+Au collisions. Further, the charged hadron yields of $n$+Au and $p$+Au are compared in order to study the ability of nucleon-nucleus collisions to transport charge to the mid-rapidity region.

The PHOBOS experiment makes use of multiple detector components to measure particles produced by collisions at RHIC. Silicon pad detectors near the interaction point are used for particle tracking and collision vertex determination, see Sect. IV. Additional silicon pad detectors provide full azimuth and large pseudorapidity coverage, as described in Sect. III. Collision triggering is provided by plastic scintillator arrays at high pseudorapidity, see Sect. III, and by calorimeters measuring the number of neutral spectator nucleons, described below. More detail on these subsystems may be found in Ref. Back et al. (2003a).

To study nucleon-nucleus collisions, two calorimeters were added to the PHOBOS experiment prior to the 2003 $d$+Au physics run at RHIC. These detectors extend the measurement of forward-going nuclear fragments. Complementing the pre-existing zero-degree calorimeters (“ZDCs”) that collect energy from spectator neutrons Adler et al. (2003b), the proton calorimeter (“PCAL”) detectors measure energy from free spectator protons. Each PCAL detector is assembled from lead-scintillator bricks originally constructed for the E864 experiment Armstrong et al. (1998) at the AGS. The bricks are 117 ${\rm cm}$ in length with a $10\times 10$ ${\rm cm}$ cross section facing the interaction point. Each brick has an array of $47\times 47$ scintillating fibers running along its entire length. All of the fibers from a single detector element are read out by a Phillips XP 2262B phototube at the back.

The PCAL detector on the Au-exit side of the collision (see plan view in Fig. 1) consists of an array 8 bricks wide by 10 bricks high. The d-exit side PCAL (not shown in the figure) is a small $2\times 2$ array. As mentioned above, the former is used for centrality determination while the latter is used, along with the ZDC, for tagging $n$+Au and $p$+Au interactions. Both calorimeters are centered at the beam height and the smaller calorimeter is mounted with its elements at the same location transverse to the beam as the two closest elements shown in Fig. 1.

Because of their higher charge to mass ratio (compared to the deuteron and Au nuclei, as well as nuclear fragments), spectator protons emerging from either side of the interaction are bent out of the beam pipe and into a PCAL detector by the RHIC DX-magnets. The primary purpose of these DX-magnets is to direct the deuteron and gold ion beams into and out of the interaction region.

The larger Au-PCAL covers a pseudorapidity region $-3.6<\eta<-5.2$ and therefore could be struck by produced particles in addition to the spectator protons it was designed to detect. In order to prevent this, two shields consisting of 44 ${\rm cm}$ thick concrete blocks were installed between the calorimeter and the interaction region.

The energy coming from Au-side spectator protons (EPcal) is calculated using bricks in the the Au-PCAL which are located in the two rows at beam height, as well as the outer four columns away from the beam. The two rows at beam height are found to contain a majority of the hadronic shower energy in simulations of single nucleons having momenta comparable to nuclear thermal and fragmentation emission. The columns away from the beam supplement the shower containment. The remaining bricks, in columns near the beam but above and below beam height, are not included in EPcal. This reduces contamination from particles emitted in the neutron-induced hadronic showers which escape the ZDC.

The Au-PCAL modules have been calibrated relative to each other using energy deposited by cosmic rays. Fast scintillator detectors are installed above and below the Au-PCAL detector to serve as cosmic ray triggers during dedicated calibration data taking. Modules in the d-PCAL have been calibrated relative to each other by minimizing the width of the single-proton peak in the d-PCAL energy distribution.

The transverse momentum spectra of charged hadrons have been extracted from tracks reconstructed using hits in the 16 layers of silicon detectors that make up the two-arm magnetic spectrometer. Hit position information is obtained both inside and outside the 2 T magnetic field. Details of the vertex determination and particle tracking, as used in previous PHOBOS $d$+Au hadron spectra analyses, have been described in Refs. Back et al. (2003b, 2004a). However, the current studies make use of an expanded set of data and an updated reconstruction procedure. As the $d$+Au collision trigger (described in Sect. III.1) does not include a high $p_{\mathrm{T}}$ particle trigger, as employed in Back et al. (2003b), a less biased data sample has been used in the present analysis. To improve the efficiency of the particle reconstruction, the final minimization step of the tracking has been performed multiple times for each track. This helps prevent the reconstruction from falling into a local minimum, which reduces the number of both poor-quality track fits as well as ghost tracks.

In an effort to more accurately apply acceptance and efficiency corrections, several changes have been made to the procedure used to extract the hadron momentum spectra described in Ref. Back et al. (2003b). First, the geometrical acceptance and tracking efficiency correction have been applied separately for each of the two spectrometer arms. To account for acceptance effects as accurately as possible, the correction factors as a function of $p_{\mathrm{T}}$ have been applied as interpolated spline functions of the track-embedding results (described in Ref. Back et al. (2004a)), rather than as smooth analytic functions. Further, the minimum $p_{\mathrm{T}}$ of acceptable tracks has been lowered to correspond to the $p_{\mathrm{T}}$ value at which the acceptance and efficiency corrections are roughly 30% of their maximal value. This leads to a minimum $p_{\mathrm{T}}$ value of 0.3 to 0.4 GeV$\kern-1.49994pt/\kern-1.19995ptc$, depending on the longitudinal collision vertex position, for hadrons bending towards higher-$\eta$ (out of the PHOBOS spectrometer acceptance) and a minimum $p_{\mathrm{T}}$ of about 0.1 GeV$\kern-1.49994pt/\kern-1.19995ptc$ for hadrons bending towards negative $\eta$. Corrections for dead and hot channels in the spectrometer have also been applied independently for each spectrometer arm, to account for discrepancies on the level of 1% in the hot and dead channel fraction of the two arms. The number of ghost and secondary tracks passing the reconstruction cuts are corrected for as a function of $p_{\mathrm{T}}$. Due to improvements in the reconstruction software since the publication of Ref. Back et al. (2003b), these corrections are on the order of 1%. Finally, corrections have been applied for the momentum resolution of the tracking and the variable bin sizes of the spectra. These corrections are determined using a dedicated simulation of single particles through each spectrometer arm to determine the distribution of reconstructed transverse momentum in each (true) $p_{\mathrm{T}}$ bin.

The efficiency of the event selection described in Sect. III.1 depends on centrality, particularly for peripheral events. Spectra uncorrected for this effect would correspond to an ensemble of events with a biased (higher) number of participants, rather than to a minimum bias selection using the same centrality binning. Instead, the efficiency determined as a function of centrality (see Fig. 2) is used to correct the spectra.

The spectra of charged hadrons for $d$+Au, $n$+Au and $p$+Au collisions are presented in Fig. 11 in four bins of $d$+Au centrality, as determined by the ERing variable. For $n$+Au and $p$+Au, the same ERing cuts were used as for $d$+Au. Therefore, these do not correspond to bins of the listed fractional cross-section for nucleon-gold interactions. Note that the difference in the $p_{\mathrm{T}}$ range between $d$+Au and the nucleon-nucleus spectra is simply due to fewer $p$+Au and $n$+Au collisions being collected compared to $d$+Au.

Systematic uncertainties on the measured charged hadron spectra have been quantified using the data. The largest correction, the acceptance and efficiency of the tracking, is the source of the largest systematic error (about 8% at $p_{\mathrm{T}}=2\leavevmode\nobreak\ \mbox{\rm GeV$\kern-1.49994pt/\kern-1.19995ptc$}$). This error has been estimated by comparing the yield in different subsets of the data for which the particle spectrum is expected to be the same. For example, the charged hadron yield of data taken with the spectrometer magnet in the positive polarity is compared to that of data taken with the magnet in the negative polarity. Similarly, yields measured separately in each spectrometer arm have been compared in order to derive uncertainties arising from the dead and hot channel correction. With these corrections applied separately to each arm, the systematic uncertainty on this effect is reduced to $\lesssim 3\%$ from $\sim 10\%$ in the previous analysis Back et al. (2003b).

For corrections in which such studies are not possible, the uncertainties are taken to be of the same order as the corrections themselves. At $p_{\mathrm{T}}=2\leavevmode\nobreak\ \mbox{\rm GeV$\kern-1.49994pt/\kern-1.19995ptc$}$, this gives a ghost track uncertainty of 1%, an uncertainty on the effect of secondary tracks of 3% and an uncertainty on the momentum resolution and momentum binning correction (which are applied together) of about 3.5%.

Uncertainty on the yield of nucleon-nucleus collisions due to tagging has been estimated. This is done by varying the d-PCAL and d-ZDC cuts used to tag events, which is expected to impact the number of interactions in the data set, but not the yield of those interactions. The total systematic uncertainties for the charged hadron spectra are shown in Fig. 12.

The charged particle multiplicity near mid-rapidity, at $\left<\smash[b]{\eta}\right>=0.8$, is shown in Fig. 13 for $d$+Au, $p$+Au and $n$+Au as a function of $N_{\rm part}$. The number of participants is determined using ERing centrality bins, since the ERing measurement of particles far from mid-rapidity has been shown to introduce at most a minimal bias on the measurement Back et al. (2005b). A consistent dependence of the multiplicity on $N_{\rm part}$ is observed across all three collision systems.

One of the fundamental conclusions drawn from examination of the nuclear modification factor is that the production of high-$p_{\mathrm{T}}$ charged hadrons in central Au+Au collisions at $\sqrt{s_{\scriptscriptstyle{{\rm NN}}}}=200\leavevmode\nobreak\ \mbox{${\rm GeV}$}$ is highly suppressed with respect to binary collision scaling Back et al. (2004a). However, it cannot be known from the nucleus-nucleus data alone whether the suppression is due to initial Kharzeev et al. (2003a) or final Baier et al. (1997) state effects. Nucleon-nucleus collisions at the same center of mass energy would provide a control experiment capable of distinguishing between the two possibilities, as such collisions should provide a nucleus in the same initial state but should not produce an extended medium in the final state. At RHIC these studies have been performed using $d$+Au rather than nucleon-nucleus collisions Back et al. (2003b); Adams et al. (2003a); Adler et al. (2003a, 2006); Arsene et al. (2004, 2003). The assumption was made that, due to the small size and weak binding of the deuteron nucleus, $d$+Au collisions would provide as good a control experiment for Au+Au interactions as nucleon-nucleus collisions.

The nucleon-nucleon reference comes from the UA1 measurement Albajar et al. (1990) of the $p$+$\bar{p}$ inelastic cross section. Note that data for $p$+$\bar{p}$ is used since data for the preferable $p$+$p$ system is not available at this energy. As described in Ref. Back et al. (2003b), corrections are applied to the UA1 results to account for (a) the conversion from rapidity to pseudorapidity and (b) the difference between the UA1 acceptance ($\left|\smash[bt]{\eta}\right|<2.5$) and the PHOBOS acceptance ($0.2<\eta<1.4$). An inelastic $p$+$\bar{p}$ cross section of 41 ${\rm mb}$ is used to estimate the yield of $p$+$\bar{p}$ collisions given the differential cross section measurements from UA1.

The nuclear modification factor as a function of $p_{\mathrm{T}}$ in the nucleon+Au system, $R_{\mathit{pnAu}}$, is compared to that of $d$+Au, $R_{\mathit{dAu}}$, for each centrality bin in Fig. 14. Common systematic errors among the two systems on the determination of $N_{\rm coll}$ affect the overall scale of the ratios, as shown by the height of the grey band. Further systematic errors in the determination of $N_{\rm coll}$ for the tagged nucleon+Au system are shown as boxes around the $R_{\mathit{pnAu}}$ points.

Qualitatively similar results have been found for a narrower window of pseudorapidity by PHENIX Adler et al. (2008). The $R_{\mathit{N}\mathrm{Au}}$ presented in that work is a simple average of $p$+Au and $n$+Au, as opposed to the weighted combination shown in Eq. 4. While the shapes of the modification factors are similar in this work and Ref. Adler et al. (2008), the latter appear to be slightly shifted to larger values, most likely due to the use of different reference spectra.

No significant difference between $R_{\mathit{pnAu}}$ and $R_{\mathit{dAu}}$ is observed. This measurement supports the conclusions drawn from the nuclear modification factor measurements of $d$+Au collisions Back et al. (2003b); namely, that high-$p_{\mathrm{T}}$ hadron production in central Au+Au collisions is significantly suppressed with respect to the expectation of binary collision scaling of $p$+$\bar{p}$ Back et al. (2004a), while the production in $d$+Au collisions is not. It should be noted that no claim of binary collision scaling in $d$+Au or nucleon+Au interactions has been made.

It has been observed that the nuclear modification factor in $d$+Au exhibits a dependence on pseudorapidity Back et al. (2004c); Arsene et al. (2003, 2004, 2006). Thus, the apparent tendency of $R_{\mathit{pnAu}}$ and $R_{\mathit{dAu}}$ to take the value of unity at high $p_{\mathrm{T}}$ is likely a consequence of the PHOBOS pseudorapidity acceptance. Further, as will be discussed in Sect. VI, the hadron production of $d$+Au collisions is known to be enhanced with respect to binary collision scaling in a certain range of transverse momentum. Any statement that $d$+Au lacks a suppression of high-$p_{\mathrm{T}}$ hadrons is therefore contingent upon the magnitude of this enhancement; see Ref. Accardi (2005) for a discussion.

Nevertheless, the stark discrepancy observed between nucleon+Au and Au+Au collisions at $\sqrt{s_{\scriptscriptstyle{{\rm NN}}}}=200\leavevmode\nobreak\ \mbox{${\rm GeV}$}$ demonstrate that final state effects play a much stronger role in the high-$p_{\mathrm{T}}$ hadron production of central Au+Au collisions than do initial state effects. While the pseudorapidity dependence of $R_{\mathit{dAu}}$ may provide evidence of some initial modification of the gold nucleus Kharzeev et al. (2003b); Jalilian-Marian and Kovchegov (2006), it is clear that interactions with some dense, large volume medium produced only in the nucleus-nucleus system forms the dominant source of high-$p_{\mathrm{T}}$ hadron suppression in Au+Au collisions. The data presented here demonstrate that this conclusion is not biased by the use of deuteron-nucleus rather than nucleon-nucleus interactions as the control experiment for Au+Au.

Although no clear evidence for enhancements above unity are seen in the nuclear modification factor shown in Fig. 14, the $p_{\mathrm{T}}$ dependence may be related to the so-called Cronin effect. This effect refers to the larger ratio of hadron production seen at high $p_{\mathrm{T}}$ compared to lower $p_{\mathrm{T}}$ in proton-nucleus collisions Cronin et al. (1975) relative to $p$+$p$ collisions scaled by the effective thickness of the nucleus. General aspects of the enhancement of inclusive charged hadron production (that is, unidentified hadrons) in $p$+Au collisions can be described by models in which partons undergo multiple scattering at the initial impact of the $p$+Au collision Accardi (2005). However, the observed difference in the strength of enhancement for mesons and baryons Shao (2006) is not easily explained by initial state partonic scattering models. While other theories, such as those based on the recombination model of hadronization Hwa and Yang (2004), may be better suited to describe the enhancement of individual hadron species, the shape of the $d$+Au $p_{\mathrm{T}}$ spectrum relative to that of $p$+$\bar{p}$ is not a thoroughly understood phenomenon. Of particular importance is the dependence of the spectral shape on the nuclear thickness probed by the projectile (i.e. the deuteron in a $d$+Au collision) Accardi and Gyulassy (2004).

The centrality dependence of the nuclear modification factor in $d$+Au and Au+Au collisions at RHIC has been studied extensively Back et al. (2005b); Adcox et al. (2005); Adams et al. (2005); Arsene et al. (2005). A particularly convenient method for exploring how the shape of the transverse momentum spectra changes relative to $p$+$\bar{p}$ has been suggested in Ref. Back et al. (2003b). This method involves studying the centrality dependence of the charged hadron yield in $d$+Au collisions relative to $p$+$p$ at several values of $p_{\mathrm{T}}$.

The procedure for determining the so-called relative yield is as follows. First, the transverse momentum spectrum in a particular $d$+Au centrality bin is compared to the spectrum of $p$+$\bar{p}$. To compare only the shape of the two spectra, they are then normalized such that the spectra match at $p_{\mathrm{T}}=0.35\leavevmode\nobreak\ \mbox{\rm GeV$\kern-1.49994pt/\kern-1.19995ptc$}$. While this specific value of $p_{\mathrm{T}}$ is arbitrary, it has been intentionally chosen to be in a region where soft processes drive particle production. Matching the $d$+Au spectra to the $p$+$\bar{p}$ spectra serves to remove any trivial enhancement of hadron production in $d$+Au that is simply due to the larger number of nucleon-nucleon collisions occurring in that system. However, matching in this way does not assume $N_{\rm coll}$ scaling, nor does it have any effect on the relative shape of the spectra.

Next, the ratio of the normalized $d$+Au spectra and the $p$+$\bar{p}$ spectra is determined. The value of this ratio at certain transverse momentum values are selected, as shown in Fig. 15. Finally, the centrality dependence of the normalized ratio, the relative yield, at the chosen $p_{\mathrm{T}}$ values is studied.

The relative yield of $d$+Au collisions to $p$+$\bar{p}$ is shown in Fig. 16 as a function of $d\!N_{\mathrm{ch}}/\mathit{d\!\eta}$, for four different values of transverse momentum. It is expected that systematic effects on the relative yield are highly correlated between the spectra measured with different centrality bins. Thus, shifts in the relative yield will tend to move all points together. See Table 1 for a description of the systematic uncertainties on the centrality variables measured with ERing. With centrality parametrized by the experimentally measured integrated yield, no bias or (Glauber) model dependence is introduced by the choice of centrality variable.

From Fig. 16, it is clear that the difference between the $d$+Au and $p$+$\bar{p}$ spectra depends on both centrality and $p_{\mathrm{T}}$. If the shape of the two spectra were identical, the relative yield would be constant at unity for all values of $p_{\mathrm{T}}$ and centrality. Instead, the $d$+Au spectra show an enhancement over $p$+$\bar{p}$ that increases with centrality. The strength of this enhancement is observed to increase at higher $p_{\mathrm{T}}$. It would be interesting to study the relative yield of much higher $p_{\mathrm{T}}$ hadrons, on the order of 10 to 100 GeV$\kern-1.49994pt/\kern-1.19995ptc$, in order to test whether the shape of the $p$+$\bar{p}$ spectra is recovered in hard scattering processes. However, such particles are produced very rarely and too few are present in the PHOBOS data set to allow such a study.

Nevertheless, the data show a smooth extrapolation of the relative yield of $d$+Au collisions to that of $p$+$\bar{p}$ as the $d$+Au collisions become more peripheral. Thus, distortions of the $d$+Au spectra caused by nuclear effects diminish in a smooth way as the amount of nuclear material probed by the deuteron is reduced. The integrated charged particle yield near $\left<\eta\right>\approx 0.8$ has been chosen as the centrality measure, since it provides a model-independent variable with which to study the centrality dependence of hadron production in nucleon-nucleus and nucleus-nucleus systems.

The availability of both $p$+Au and $n$+Au collision data presents a unique opportunity to study baryon transport in nucleon-nucleus collisions. Since a $p$+Au collision contains one more charged hadron than an $n$+Au collision, a search for this extra charge near the mid-rapidity region is possible. Previous measurements Alber et al. (1998) of $p$+Au collisions at $\sqrt{s_{\scriptscriptstyle{{\rm NN}}}}=19.4\leavevmode\nobreak\ \mbox{${\rm GeV}$}$ found that the number of net protons (p - p̄) per unit of rapidity is less than one in the mid-rapidity region. In addition, studies have shown a decrease in the mid-rapidity net proton yield with increasing center of mass energy; see Ref. Back et al. (2007) for a discussion. Further, it has been inferred that hadrons traversing nuclear material do not lose more than about two units of rapidity Busza and Goldhaber (1984). Thus, it is expected that any charge asymmetry between hadrons measured at mid-rapidity in $p$+Au and $n$+Au collisions would be small.

Nevertheless, a comparison of charged hadron production in $p$+Au and $n$+Au allows the transport of charge explicitly from the projectile proton to be studied. Assuming that baryons from the gold nucleus undergo transport to mid-rapidity via the same process in both $p$+Au and $n$+Au collisions, any charge transport to mid-rapidity of protons in the gold nucleus would not lead to an asymmetry.

The charge asymmetry defined by Eq. 5 is presented in Fig. 17 for positive hadrons and in Fig. 18 for negative hadrons. The grey band in each figure represents the systematic uncertainty in the asymmetry ratio, propagated from the nucleon tagging component of the systematic uncertainty on the momentum spectra (see Sect. IV). Only uncertainties specific to reconstructing the nucleon-nucleus $p_{\mathrm{T}}$ spectra contribute to this systematic error, as all other effects divide out in the ratio. No evidence for asymmetry between $p$+Au and $n$+Au collisions is observed at $\left<\smash[b]{\eta}\right>=0.8$, which is slightly forward on the deuteron-going side.

The addition of two forward proton calorimeters to the PHOBOS detector allows the extraction of $p$+Au and $n$+Au collisions from the $d$+Au data set. Centrality parameters have been determined for each of the collision systems using observables based on the multiplicity at high rapidity and on the number of spectators. The number of particles produced near mid-rapidity is found to scale with $N_{\rm part}$ across all collision systems. The charged hadron spectra have been measured for $p$+Au, $n$+Au, and $d$+Au collisions and used to construct an ideal nucleon-nucleus reference for Au+Au collisions. The nuclear modification factor of this ideal reference is found to agree with that of $d$+Au. The shape of the nuclear modification factor has been studied in detail and is found to depend on both centrality and transverse momentum. A larger ratio of the $d$+Au over $p$+$\bar{p}$ spectra is found at larger values of $p_{\mathrm{T}}$ and this enhancement is found to extrapolate smoothly as a function of multiplicity at mid-rapidity from $p$+$\bar{p}$ to central $d$+Au collisions. Finally, a comparison of the yield of positively and negatively charged hadrons in $p$+Au and $n$+Au has been conducted in a direct search for evidence of charge transport to mid-rapidity. No significant asymmetry between the charged hadron yields in $p$+Au and $n$+Au is observed at $\left<\smash[b]{\eta}\right>=0.8$.

This work was partially supported by U.S. DOE grants DE-AC02-98CH10886, DE-FG02-93ER40802, DE-FG02-94ER40818, DE-FG02-94ER40865, DE-FG02-99ER41099, and DE-AC02-06CH11357, by U.S. NSF grants 9603486, 0072204, and 0245011, by Polish MNiSW grant N N202 282234 (2008-2010), by NSC of Taiwan Contract NSC 89-2112-M-008-024, and by Hungarian OTKA grant (F 049823).