Higher moments of net-proton multiplicity distributions in a heavy-ion event pile-up scenario

High-luminosity modern accelerators, like the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) and Large Hadron Collider (LHC) at European Organization for Nuclear Research (CERN), inherently have event pile-up scenarios which significantly contribute to physics events as a background. While state-of-the-art tracking algorithms and detector concepts take care of these event pile-up scenarios, several offline analytical techniques are used to remove such events from the physics analysis. It is still difficult to identify the remaining pile-up events in an event sample for physics analysis. Since the fraction of these events is significantly small, it may not be as serious of an issue for other analyses as it would be for an event-by-event analysis. Particularly when the characteristics of the multiplicity distribution are observable, one needs to be very careful. In the present work, we demonstrate how a small fraction of residual pile-up events can change the moments and their ratios of an event-by-event net-proton multiplicity distribution, which are sensitive to the dynamical fluctuations due to the QCD critical point. For this study, we assume that the individual event-by-event proton and antiproton multiplicity distributions follow Poisson, negative binomial, or binomial distributions. We observe a significant effect in cumulants and their ratios of net-proton multiplicity distributions due to pile-up events, particularly at lower energies. It might be crucial to estimate the fraction of pile-up events in the data sample while interpreting the experimental observable for the critical point.

Figure 1

The minimum bias proton (a) and antiproton (b) multiplicity distributions are shown for two different center-of-mass energies $\sqrt{s_{{}_{NN}}}=7.7$ and 200 GeV.

Figure 2

The proton, antiproton, and net-proton multiplicity distributions are shown with (open symbol) and without (solid line) pile-up events for $\sqrt{s_{NN}}=7.7$ and 200 GeV. The proton and antiproton multiplicities from minimum bias events as pile-up events are added to the individual $p$ and $\overline{p}$ distributions, assuming each of the distributions are negative binomial distributions (NBD).

Figure 3

Collision energy dependence of individual cumulants of net-proton distributions for different fractions of pile-up events for central $\left(0-5\%\right)$ $\mathrm{Au}+\mathrm{Au}$ collisions. The individual $p$ and $\overline{p}$ multiplicity distributions are assumed to be Poisson. The pile-up events from central collisions are mixed with the original distribution from the same centrality.

Figure 4

Collision energy dependence of cumulant ratios $(C_2/C_1,C_3/C_2,C_4/C_2$, and $C_3/C_1)$ of net-proton distributions for different fractions of pile-up events for central $\left(0-5\%\right)$ $\mathrm{Au}+\mathrm{Au}$ collisions. The individual $p$ and $\overline{p}$ multiplicity distributions are assumed to be Poisson. The pile-up events from central collisions are mixed with the original distribution from the same centrality.

Figure 5

Similar as Fig. 4. The pile-up events from minimum bias collisions are mixed with the original distribution from the same central collisions.

Figure 6

Variation of cumulants of net-proton distributions as a function of $\sqrt{s_{{}_{NN}}}$ for different fractions of pile-up events for central $\left(0-5\%\right)$ $\mathrm{Au}+\mathrm{Au}$ collisions. The individual $p$ and $\overline{p}$ multiplicity distributions are assumed to be NBD. The pile-up events from central collisions are mixed with the original distribution from the same centrality.

Figure 7

Variation of cumulant ratios $(C_2/C_1,C_3/C_2,C_4/C_2$, and $C_3/C_1)$ of net-proton distributions as a function of $\sqrt{s_{{}_{NN}}}$ for different fraction of pile-up events for central $\left(0-5\%\right)$ $\mathrm{Au}+\mathrm{Au}$ collisions. The individual $p$ and $\overline{p}$ multiplicity distributions are assumed to be NBD. The pile-up events from central collisions are mixed with the original distribution from the same centrality.

Figure 8

Similar to that mentioned in Fig. 7. The pile-up events from minimum bias collisions are mixed with the original distribution from the same centrality.

Figure 9

Variation of cumulants of net-proton distributions as a function of $\sqrt{s_{{}_{NN}}}$ for different fraction of pile-up events for central $\left(0-5\%\right)$ $\mathrm{Au}+\mathrm{Au}$ collisions. The individual $p$ and $\overline{p}$ multiplicity distributions are assumed to be binomial. The pile-up events from central collisions are mixed with the original distribution from the same centrality.

Figure 10

Variation of cumulant ratios $(C_2/C_1,C_3/C_2,C_4/C_2$, and $C_3/C_1)$ of net-proton distributions as a function of $\sqrt{s_{{}_{NN}}}$ for different fraction of pile-up events for central $\left(0-5\%\right)$ $\mathrm{Au}+\mathrm{Au}$ collisions. The individual $p$ and $\overline{p}$ multiplicity distributions are assumed to be binomial. The pile-up events from central collisions are mixed with the original distribution from the same centrality.

Figure 11

Similar to that mentioned in Fig. 10. The pile-up events from minimum bias collisions are mixed with the original distribution from the same centrality.