Centrality categorization for $R_{p\left(d\right)+A}$ in high-energy collisions

High-energy proton- and deuteron-nucleus collisions provide an excellent tool for studying a wide array of physics effects, including modifications of parton distribution functions in nuclei, gluon saturation, and color neutralization and hadronization in a nuclear environment, among others. All of these effects are expected to have a significant dependence on the size of the nuclear target and the impact parameter of the collision, also known as the collision centrality. In this article, we detail a method for determining centrality classes in $p\left(d\right)+A$ collisions via cuts on the multiplicity at backward rapidity (i.e., the nucleus-going direction) and for determining systematic uncertainties in this procedure. For $d+\text{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV we find that the connection to geometry is confirmed by measuring the fraction of events in which a neutron from the deuteron does not interact with the nucleus. As an application, we consider the nuclear modification factors $R_{p\left(d\right)+A}$, for which there is a bias in the measured centrality-dependent yields owing to auto correlations between the process of interest and the backward-rapidity multiplicity. We determine the bias-correction factors within this framework. This method is further tested using the hijing Monte Carlo generator. We find that for $d+\text{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV, these bias corrections are small and vary by less than 5% (10%) up to $p_T=10$ (20) GeV/$c$. In contrast, for $p+\text{Pb}$ collisions at $\sqrt{s_{{}_{NN}}}=5.02$ TeV we find that these bias factors are an order of magnitude larger and strongly $p_T$ dependent, likely attributable to the larger effect of multiparton interactions.

Figure 1

Probability density distribution for the proton-neutron distance in the deuteron given by the square of the Hulthén wave function [13].

Figure 2

MC-Glauber event display for a single $d+\text{Au}$ collision. All nucleons are shown as open circles and nucleons with at least one inelastic collision are highlighted as solid circles.

Figure 3

(a) Real-data $d+\text{Au}$ BBC Au-going direction charge distribution is shown as open points and $\mathrm{Glauber}+\mathrm{NBD}$ calculation as a histogram. Shown as different color regions are the centrality selections of 0%–5%, 5%–10%, 10%–20%, 20%–30%, 30%–40%, 40%–50%, 50%–60%, 60%–70%, and 70%–88%. (b) The ratio of real data to $\mathrm{Glauber}+\mathrm{NBD}$ calculation. The line is a fit to the experimental trigger efficiency turn-on curve.

Figure 4

Extracted distribution of the number of binary collisions in each of the nine centrality quantiles (from right to left): 0%–5%, 5–10%, 10%–20%, 20%–30%, 30%–40%, 40%–50%, 50%–60%, 60%–70%, and 70%–88%.

Figure 5

ZDC energy distribution in the deuteron-going direction for MB $d+\text{Au}$ collisions. The data are well described by an exponential background component, a single spectator neutron peak, and a much smaller contribution from two neutrons owing to double interactions.

Figure 6

Data points are the measured fraction of events where there is a spectator neutron from the deuteron projectile. In comparison, the yellow band is the MC-Glauber result with systematic uncertainties.

Figure 7

Data distributions for the BBC charge (in the Au-going direction) from low-luminosity data recorded in 2003 [18], medium-luminosity data from early in 2008, and high-luminosity data from late in 2008. The upper set of curves are for MB $d+\text{Au}$ interactions and the lower set of curves feature the additional requirement of a neutron spectator from the deuteron. The differences in the distributions are the result of contributions from double interactions. The results of a calculation of these contributions with input rates relevant to match the medium- and high-luminosity 2008 data are also shown.

Figure 8

The variation relative to the mean $N_{\mathrm{coll}}$ value for variations in the input assumptions for the MC-Glauber extraction. The final mean and rms systematic uncertainties are shown in Table 1.

Figure 9

Multiplicative bias-factor corrections and their systematic uncertainties as a function of collision centrality.

Figure 10

(a) Shown as a dashed blue line is the mean BBC charge on one side for inclusive $p+p$ interactions, corresponding to ${\sigma }_{\text{inelastic}}=42$ mb. The systematic uncertainty is shown as a band. Shown as a dashed black line is the mean BBC charge on one side when a midrapidity charged hadron with $p_T>1.5$ GeV/$c$ is in coincidence. The red points are the mean BBC charge when there is a ${\pi }^0$ measured with a $p_T$ as indicated by the $x$ axis. (b) The same quantities as before, but for the fraction of interactions that fire the BBC coincidence trigger. The bias-factor corrections were originally calculated in 2003 with inputs that the BBC trigger fires on $52\%\pm 4$% of inclusive inelastic $p+p$ interactions corresponding to 42 mb and $75\%\pm 3\%$ of inelastic $p+p$ interactions with a charged hadron of $p_T>1.5$ GeV/$c$. For the 2008 analysis, the BBC thresholds were adjusted and the most accurate determination indicates that the BBC trigger fires on $55\%\pm 5\%$ of inclusive inelastic $p+p$ interactions corresponding to 42 mb and $79\%\pm 2\%$ of inelastic $p+p$ interactions with a charged hadron of $p_T>1.5$ GeV/$c$, as shown above. The ${\pi }^0$ points shown above are from data taken with these thresholds adjusted. These differences result in negligible changes to the bias-factor correction values used.

Figure 11

The ratio of the mean multiplicity at $-3.9<\eta <-3.0$ in triggered events with a particle with a given $p_T$ produced at midrapidity to all inelastic $p+p$ collisions from hijing at $\sqrt{s_{{}_{NN}}}=200$ GeV. The dashed line at 1.55 represents the mean reference value measured in the data.

Figure 12

Bias-factor corrections as a function of $p_T$ for hijing $d+\text{Au}$ events at $\sqrt{s_{{}_{NN}}}=200$ GeV.

Figure 13

The ratio of the mean multiplicity at $-4.9<\eta <-3.1$ in triggered events with a particle with a given $p_T$ produced at midrapidity to all inelastic $p+p$ collisions from hijing at $\sqrt{s_{{}_{NN}}}=5.02$ TeV. The dashed line corresponds to the inclusive mean multiplicity ratio.

Figure 14

Bias-factor corrections as a function of $p_T$ for hijing $p+\text{Pb}$ events at $\sqrt{s_{{}_{NN}}}=5.02$ TeV. Correction factors for each centrality are plotted with different vertical scales to better illustrate the magnitude of the effect.

Figure 15

Multiplicity distribution at $-4.9<\eta <-3.0$ for hijing $p+p$ events for (a) $\sqrt{s}=200$ GeV at RHIC and (b) $\sqrt{s}=5.02$ TeV at the LHC. Dashed lines indicate the mean values of each distribution.

Figure 16

A comparison of the MPI effect in hijing for $d+\text{Au}$ and $p+\text{Pb}$ collisions at 200 GeV and 5.02 TeV, respectively. Plotted is the number of hard scatterings ($N_{\mathrm{hard}}$) divided by the number of nucleon-nucleon collisions ($N_{\mathrm{coll}}$) as a function of $N_{\mathrm{coll}}$.