Femtoscopic signatures of unique nuclear structures in relativistic collisions

TL;DR

The paper addresses imaging nuclear structure in high-energy collisions using femtoscopy to connect initial-state deformation to final-state pion correlations. It models the pion-source as a 3D elliptically contoured Lévy-stable distribution $D( ho) = \,\mathcal{L}(\alpha,R^2,\rho) = \int \frac{d^3\vec{q}}{(2\pi)^3} e^{i\vec{q}\cdot\vec{\rho}} e^{- frac{1}{2}|\vec{q}^T R^2 \vec{q}|^{\alpha/2}}$, introducing a Lévy exponent $\alpha$ and a scale matrix $R^2$. Azimuthal dependence is probed via the 1D Lévy projection $\mathcal{L}^{1D}(\rho_\nu,\alpha,R_\nu)$ and by angular modulations $R^2_\mu(\varphi_{\rm pair}-\Psi_2) = R^2_{\mu,0} + 2 R^2_{\mu,2} \cos(2(\varphi_{\rm pair}-\Psi_2))$ (with sine terms for some directions), from which the freeze-out eccentricity is defined as $\varepsilon_F = 2 \frac{R^2_{\text{side},2}}{R^2_{\text{side},0}}$. The results indicate that Pb+Ne with an alpha-cluster (NLEFT) initial state yields a larger $\varepsilon_F$ and a stronger elliptic distortion than Woods-Saxon or Pb+O, demonstrating that azimuthally sensitive femtoscopy can robustly signal deformed nuclear structures and motivating future studies with non-identical particles, higher-order event planes, and hydrodynamic/hybrid modeling.

Abstract

One of the most vital topics of today's high-energy nuclear physics is the investigation of the nuclear structure of the collided nuclei. Recent studies at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) have shown that several observables, such as the collective flow and transverse-momentum correlations of the produced particles, can be sensitive to various nuclear structure and deformation parameters. Femtoscopy, another essential tool for investigating the space-time geometry of the matter created in nuclear collisions, has not yet been widely applied to such studies. Using a multiphase transport model (AMPT), in this Letter, it is demonstrated that the femtoscopic source parameters of pion pairs can also serve as a robust signal of unique nuclear structure. Through an analysis of $^{208}$Pb+$^{20}$Ne and $^{208}$Pb+$^{16}$O collisions at $\sqrt{s_{NN}}$ = 68.5 GeV, two collision systems especially relevant to the SMOG2 program of the LHCb experiment, it is shown that a deformed initial shape can significantly affect femtoscopic source parameters. This study highlights the importance of expanding the nuclear structure investigations to femtoscopic observables and serves as a baseline for numerous possible future studies in this new direction.

Figures (5)

• Figure 1: An example simultaneous fit to six projections of the three-dimensional source distribution of the same charge pion pairs, reconstructed in AMPT simulations of $\sqrt{s_{NN}}=68.5$ GeV Pb+Ne collisions with the NLEFT initial state nucleon configuration. Panels (a)-(f) show the one-dimensional projections of $D(\vec{\rho})$ with blue markers, corresponding to the directions detailed in Equation \ref{['e:dirs']}. The fit with one-dimensional Lévy-stable distributions, as described by Equation \ref{['e:1dlevy']}, is shown with red lines.
• Figure 2: Extracted pion pair source parameters in ${\sqrt{s_{NN}}=68.5\textnormal{ GeV}}$${^{208}\rm{Pb}+^{20}\rm{Ne}}$ collisions generated by AMPT, as a function of pair azimuthal angle relative to the second order event plane, in the average transverse momentum range of ${0.35 < k_T\;(\rm{GeV}/c) < 0.40}$. The source parameter values and their statistical uncertainties are shown with filled red markers and error bars for the NLEFT configuration, and empty blue markers and error bars for the Woods-Saxon configuration. Panel (a) shows the Lévy-exponent parameter $\alpha$, while panels (b)-(g) show the elements of the $R^2$ Lévy-scale parameter matrix. For each dataset, a fit is shown as well corresponding to Equations \ref{['e:Rmu1']} and \ref{['e:Rmu2']}.
• Figure 3: Extracted pion pair source parameters in ${\sqrt{s_{NN}}=68.5\textnormal{ GeV}}$${^{208}\rm{Pb}+^{16}\rm{O}}$ collisions generated by AMPT, as a function of pair azimuthal angle relative to the second order event plane, in the average transverse momentum range of ${0.35 < k_T\;(\rm{GeV}/c) < 0.40}$. The source parameter values and their statistical uncertainties are shown with filled red markers and error bars for the NLEFT configuration, and empty blue markers and error bars for the Woods-Saxon configuration. Panel (a) shows the Lévy-exponent parameter $\alpha$, while panels (b)-(g) show the elements of the $R^2$ Lévy-scale parameter matrix. For each dataset, a fit is shown as well corresponding to Equations \ref{['e:Rmu1']} and \ref{['e:Rmu2']}.
• Figure 4: Average transverse mass dependence of the freeze-out eccentricity calculated for four different configurations. The NLEFT and Woods-Saxon initial state configurations are plotted with red and blue markers, respectively. The Pb+Ne result is plotted with filled markers, while the Pb+O result is plotted with empty markers.
• Figure 5: Average transverse mass dependence of the freeze-out eccentricity ratios between Pb+Ne and Pb+O collisions. The NLEFT and Woods-Saxon initial state configurations are plotted with red and blue markers, respectively.