Accessing proton number fluctuations in limited regions of phase space

TL;DR

The paper addresses the challenge of isolating local baryon-number fluctuations in heavy-ion collisions from global volume and flow fluctuations. It proposes a framework that analyzes proton fluctuations within restricted azimuthal windows $\Delta\phi$, using meson fluctuations as a volume-fluctuation baseline via a joint emission-volume model with $P(N,M)$ and a 2D Gaussian covariance $\Sigma$, yielding $C_2^{vol}=\frac{Cov(p,m)^2}{C_2^{meson}}$ to subtract the volume effect. The main findings show that local baryon fluctuations can elevate the proton second factorial cumulant $C_2$ beyond the volume baseline, while the back-to-back covariance is largely explained by volume fluctuations; the pair of observables $C_2$ and $Cov$ together provide a robust signal of localized fluctuations and can inform critical-point searches. The work outlines validation paths including net-baryon studies, baryon diffusion, and 3+1D hydrodynamics to assess sensitivity to correlation length and acceptance, offering a practical path to probe localized baryon-density fluctuations in heavy-ion collisions.

Abstract

In heavy ion collisions particle distributions fluctuate from event to event. It is interesting to study local fluctuations of a specific particle specie, e.g. baryons, in the transverse plane. Fluctuations of the harmonic flow provide an integrated measure of such fluctuations. An alternative approach is to study proton number fluctuations measured in a relatively narrow azimuthal angle window. Due to the transverse flow, particles registered in a narrow azimuthal angle window are emitted predominantly from a region of the fireball located at the same azimuthal angle. Similarly, it is informative to measure the covariance of the number of protons emitted in two opposite windows of azimuthal angles. The main difficulty lies in distinguishing effects of local baryon density fluctuations in the transverse plane from global particle density and collective flow fluctuations. These global volume and flow fluctuations can be estimated using some reference particles, e.g. charged mesons. Reliable estimates of such fluctuations can be constructed both for the second factorial cumulant of the proton number in an azimuthal angle window and for the covariance between two such windows. The simultaneous measurement of both quantities provides a sensitive probe of local baryon number fluctuations superimposed on top of a fluctuating fireball background density.

Figures (8)

• Figure 1: Factorization breaking coefficient (\ref{['eq:fact']}) between the harmonic flow of protons and mesons as a function of the strength of fluctuations in baryon deposition. The solid, dashed and dotted lines represent the results for the harmonic flow of order 2,3, and 4, respectively.
• Figure 2: View of the fireball in the transverse plane. The trans- verse flow (red arrows) induces a correlation between the position of the baryon excess in a region of the transverse plane and the number of protons emitted in the corresponding azimuthal angle interval. The multiplicities of protons emitted back to back are mostly correlated due to the presence of the global collective flow. On the other hand, additional local fluctuations of the baryon number do not induce any significant correlation between the multiplicities of protons emitted in opposite directions.
• Figure 3: Second factorial cumulant of the proton number as a function of the width of the azimuthal angle window. The case where the baryon distribution follows the entropy density is shown with the solid line, the results with additional fluctuations of width $\sigma_B=0.5$ in the baryon density are represented with the dotted line. The dashed and dash-dotted lines show the corresponding estimated contribution of volume fluctuations to the proton number cumulant (Eq. \ref{['eq:c2flow']}).
• Figure 4: Second factorial cumulant of the proton number, in an azimuthal angle window of width $\Delta\phi=\pi/4$, as a function of the strength of fluctuations in baryon deposition (solid line). The dashed line shows the estimated contribution of volume fluctuations to the proton factorial cumulant (Eq. \ref{['eq:c2flow']}).
• Figure 5: Ratio of the second factorial cumulant of the proton number, in an azimuthal angle window of width $\Delta\phi=\pi/4$, to the estimate of the contribution from volume fluctuations as a function of the strength of fluctuations of the number of stopped baryons . The solid line is for protons with $0<p_T<3GeV$ and the dashed line for protons with $0.8GeV<p_T<3GeV$.