Collectivity in pPb Collisions with Femtoscopy

TL;DR

This work proposes proton–pion femtoscopy as a direct probe of initial‑state vorticity in small collision systems, focusing on toroidal, ring‑like flow (the "smoke ring") predicted in central $pA$ events. Using an iEBE‑MUSIC hybrid with a longitudinal shear parameter $f$ that generates vorticity, the study shows that the longitudinal emission offset $\langle z_p-z_π\rangle$ undergoes a sign change between $f=0$ and $f=1$, while the transverse offset $\langle x_p-x_π\rangle$ remains largely unchanged. The corresponding non‑identical particle correlation asymmetry, $\frac{C_v(\boldsymbol{q})}{C_v(-\boldsymbol{q})}-1$, provides a quantitative link to $\langle\boldsymbol{r}\rangle$, enabling extraction of emission shifts (e.g., $\langle x_p-x_π\rangle\approx0.6$ fm, $\langle z_p-z_π\rangle$ ranging from about $-0.25$ fm to $1.25$ fm) and a robust, observable signature of initial vorticity. The method complements hyperon polarization measurements and can be extended to other collision systems, enhancing constraints on 3D flow and informing spin dynamics in relativistic fluids.

Abstract

Collisions of protons with lead nuclei (pPb), such as those measured by the LHCb experiment, provide a unique environment to study the surprising emergence of collective, fluid-like phenomena in small systems. A key signature of this hydrodynamic behavior is the predicted formation of a toroidal vorticity structure. In this work, I use two-particle femtoscopic correlations of non-identical hadrons, specifically proton-pion ($pπ^+$) pairs, as a novel probe for this phenomenon. Previous works indicate that the collective flow of the system is consistent with the formation of a vortex ring created by the passage of the proton through the lead nucleus, which modifies the collective flow profile. I establish that the resulting emission asymmetry between protons and pions, driven by their mass difference and differential response to the vortical flow, is directly linked to the initial vorticity and can be measured using femtoscopy. This method therefore presents a new, sensitive observable for characterizing the rotational dynamics of the matter created in small collision systems.

Figures (3)

• Figure 1: Average relative displacement of proton and pion emission points from simulations with varying initial vorticity (controlled by $f$) for different pair velocities along the $x$-direction. (a) The transverse displacement $\langle x_p-x_\pi \rangle$ is not sensitive to the longitudinal shear. (b) The longitudinal displacement $\langle z_p-z_\pi \rangle$ is strongly affected by the initial shear, with a sign change between the $f=0$ (Bjorken-like) and $f=1$ (maximal vorticity) scenarios. This dependence weakens at large pair velocities.
• Figure 2: The asymmetry of the correlation function at $v_x=0.20c$, $v_y,v_x=0$, $\frac{C_{\vec{v}}(-q_i)}{ C_{\vec{v}}(q_i)}-1$, caused by the asymmetry of the source. This ratio is directly measurable and can be used to extract the source shifts $\langle x_p-x_\pi \rangle$ and $\langle z_p-z_\pi \rangle$ using Eq. (\ref{['eq:asymmetry_ratio']}). The sign change in the longitudinal direction (b) between the $f=0$ and $f=1$ cases is a clear signature of vorticity.
• Figure 3: Ratio of the correlation functions with maximal vorticity ($f=1$) to the case without vorticity ($f=0$) at $q_y=0$. The largest deviations (shown by contours) occur at finite relative momentum ($|q_z| \approx 50~\mathrm{MeV/c}$), making the signal less sensitive to experimental resolution at very low $q$.