Effect of the fluctuating proton size on the study of the chiral magnetic effect in proton-nucleus collisions

High energy proton-nucleus (pA) collisions provide an important constraint on the study of the chiral magnetic effect in QCD matter. Naively, in pA collisions one expects no correlation between the orientation of the event plane as reconstructed from the azimuthal distribution of produced hadrons and the orientation of the magnetic field. If this is the case, any charge-dependent hadron correlations can only result from the background. Nevertheless, in this paper we point out that in high multiplicity pA collisions a correlation between the magnetic field and the event plane can appear. This is because triggering on the high hadron multiplicity amounts to selecting Fock components of the incident proton with a large number of partons that are expected to have a transverse size much larger than the average proton size. We introduce the effect of the fluctuating proton size in the Monte Carlo Glauber model and evaluate the resulting correlation between the magnetic field and the second-order event plane in both pA and nucleus-nucleus (AA) collisions. The fluctuating proton size is found to result in a significant correlation between the magnetic field and the event plane in pA collisions, even though the magnitude of the correlation is still much smaller than in AA collisions. This result opens a possibility of studying the chiral magnetic effect in small systems.

Figure 1

A sketch of the proton configurations probed in the minimum bias (left) and high multiplicity (right) events.

Figure 2

(Left) Charged-particle multiplicity distribution in $pp$ collision at $\sqrt{\mathrm{s}}=13$ TeV from PYTHIA 8 event generator is shown. (Right) The fluctuating proton radius is shown.

Figure 3

Event displays of one high-multiplicity pPb (left) and a peripheral PbPb event (right) using MC Glauber simulation at $\sqrt{s_{{}_{\mathrm{NN}}}}=5.02$ TeV are shown. The red circle is the proton projectile, the green circles are the participant nucleons, and the blue circles are the spectator nucleons. The red and black arrows refer to the angle of the reaction plane (${\mathrm{\Psi }}_{\mathrm{RP}}$) and the participant plane (${\mathrm{\Psi }}_{\mathrm{PP}}$) in the transverse direction [21].

Figure 4

The impact parameter (left) and the number of participant (right) distributions in PbPb and pPb collisions with fixed and fluctuating proton size as computed within the MC Glauber model with one million simulated events. The statistical uncertainty is shown by the error bar.

Figure 5

The event-averaged impact parameter (left) and angular correlation (right) as a function of the number of participants in PbPb collisions and pPb collisions with fixed and fluctuating proton sizes, using the MC Glauber model with one million simulated events. The statistical uncertainty is shown by the error bar.

Figure 6

The correlator $\mathrm{\Delta }\gamma$ as a function of the number of participants in PbPb collisions and pPb collisions with fixed and fluctuating proton sizes as computed in the MC Glauber model with one million simulated events. For visibility, the PbPb collision data points are scaled by 0.1 to be compared with pPb data. The statistical uncertainty is shown by the error bar.