Centrality determination with a forward detector in the RHIC Beam Energy Scan

Recently, Chatterjee et al. [Phys. Rev. C 101, 034902 (2020)] used a hadronic transport model to estimate the resolution with which various experimental quantities select the impact parameter of relativistic heavy ion collisions at collision energies relevant to the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC). Measures based on particle multiplicity at forward rapidity were found to be significantly worse than those based on midrapidity multiplicity. Using the same model, we show that a slightly more sophisticated measure greatly improves the resolution based on forward rapidity particles; this improvement persists even when the model is filtered through a realistic simulation of a recent upgrade detector to the STAR experiment. These results highlight the importance of optimizing centrality measures based on particles detected at forward rapidity, especially for experimental studies that search for a critical point in the QCD phase diagram. Such measurements usually focus on proton multiplicity fluctuations at midrapidity, hence selecting events based on multiplicity at midrapidity raises the possibility of nontrivial autocorrelations.

Figure 1

The QCD phase diagram, showing various states of QCD matter as functions of baryon chemical potential (${\mu }_B$) and temperature ($T$). The CP location (and existence) is at this time not confirmed [20].

Figure 2

Charged particle pseudorapidity distributions for BES energies of $\sqrt{s_{NN}}=19.6$ (magenta triangle), 14.5 (blue triangle), 11.5 (red square), 7.7 (black circle) GeV. There is no centrality selection for these distributions. The EPD acceptance is shown as a green box.

Figure 3

The sum of all charged particle yields in the EPD acceptance ($X_{\mathrm{FWD}}$) vs impact parameter $b$ for the four collision energies considered in this paper.

Figure 4

The sum of charged particle yields for a given EPD ring using simulated UrQMD events at $\sqrt{s_{NN}}=7.7$ GeV. Ring 1 is the ring closest to the beam pipe and Ring 16 is the closest to midrapdity. The precise acceptance boundaries for each ring are listed in Table 1.

Figure 5

A low-flux tile which is dominated by either one or two particles passing per collision event. The colored peaks show the 1 (grey) and 2 (red) particle Landau distributions, whereas the spectrum (black circles) is a sum of the convoluted distributions (green line).

Figure 6

A high-flux tile which experiences a range of particle multiplicities, resulting in a spectrum (black circles) that is a sum of convoluted Landau distributions (green line). The colored peaks show the 1 (grey), 2 (red), 3 (blue), 4 (purple), and 5 (dark grey) particle Landau distributions.

Figure 7

$X_{\zeta }$ value versus impact parameter for $\sqrt{S_{NN}}=19.6$ GeV UrQMD simulations. The extended tail of the distribution is due to Landau fluctuations.

Figure 8

$X_{{\zeta }^{\prime }}$ value versus impact parameter for $\sqrt{s_{NN}}=19.6$ GeV UrQMD simulations. The truncation of $\zeta$ [from Eq. (3)] reduces the noise from Landau fluctuations seen in the correlation between $X_{\zeta }$ and $b$ in Fig. 7.

Figure 9

The weights for both forward $\eta$ particles and ${\zeta }^{\prime }$ when using the linear weight scheme from Sec. 2c, by EPD ring. The sign change in ring weights is motivated by spectator proton intrusion into the EPD's acceptance window, as can be seen in Fig. 2.

Figure 10

Correlation between the impact parameter, $b$, and three observables: $X_{W,{\zeta }^{\prime }}$ (top), $X_{RM3}$ (middle), $X_{{\zeta }^{\prime }}$ (bottom), for four different collision energies.

Figure 11

The impact parameter distributions for centrality selections 0–5%, 20–30%, and 90–100%. The black histograms are the $b$ impact parameter distributions if the centrality selection is determined from the impact parameter directly. The green circles are determined using $X_{RM1}$ (closed) and $X_{RM3}$ (open), the triangles are determined using $X_{{\zeta }^{\prime }}$ (open blue) and $X_{W,{\zeta }^{\prime }}$ (closed red), and the squares are determined using $X_{\mathrm{FWD}}$ (open blue) and $X_{W,\mathrm{FWD}}$ (closed red).

Figure 12

Centrality resolution (in %) for collision energies $\sqrt{s_{NN}}=19.6$, 14.5, 11.5, and 7.7 GeV. The observables based on midrapidity multiplicity are $X_{RM1}$ (green closed circles) and $X_{RM3}$ (dark green open circles). The observables based on unweighted distributions from the forward region are $X_{\mathrm{FWD}}$ (blue open square) for particle yield and $X_{{\zeta }^{\prime }}$ (blue open triangle) for truncated energy loss in the EPD. The observables based on linear weights are $X_{W,\mathrm{FWD}}$ (closed dark red square) and $X_{W,{\zeta }^{\prime }}$ (closed red triangle).