Nuclear-geometry-tagging events in high-energy Ne--Ne collisions

Technical Summary: Nuclear-geometry-tagging events in high-energy Ne–Ne collisions

Problem Statement
Ultrarelativistic nucleon-nucleon collisions offer a unique probe for many-body correlations within atomic nuclei, as the initial geometry of the produced system reflects the intrinsic nuclear structure. While nuclear deformation is known to influence anisotropic flow observables (such as $v_2$), standard theoretical modeling often treats nuclei as one-body densities using modified Woods–Saxon distributions. Recent state-of-the-art calculations, specifically Nuclear Lattice Effective Field Theory (NLEFT) and the Projected Generator Coordinate Method (PGCM), predict that $^{20}\text{Ne}$ nuclei possess a highly deformed, $\alpha + ^{16}\text{O}$ "bowling-pin" shape. Although such nuclei have been collided at the LHC, a method is required to maximize sensitivity to these specific structural features. Specifically, the authors investigate whether distinct geometric configurations—body–body (side-on) and tip–tip (end-on) collisions—can be isolated from the general event ensemble to study the underlying nuclear structure.

Methodology
The study employs a Monte–Carlo Glauber model to simulate Ne–Ne collisions at $\sqrt{s_{NN}} = 5.36$ TeV.

• Nuclear Configurations: Initial nucleon positions are sampled from two distinct theoretical frameworks: NLEFT and PGCM. These are compared against a spherical Fermi distribution (Woods–Saxon) as a reference.
• Event Selection: The analysis focuses on central collisions ($N_{\text{spec}} \leq 2$). Events are classified into "tip–tip" and "body–body" categories based on the polar angles ($\theta$) of the nuclear symmetry axes relative to the beam and the azimuthal alignment ($\Delta\phi$).
• Geometry-Sensitive Observables: Two initial-state observables are utilized:
  1. Second-order eccentricity ($\varepsilon_2$): Measures the spatial anisotropy of the participant distribution.
  2. Transverse compactness ($d_\perp$): Derived from the transverse overlap area and participant number, representing the inverse transverse size. The analysis uses the normalized fluctuation $\delta d_\perp / \langle d_\perp \rangle$.
• Separation Technique: A Fisher linear discriminant is constructed to separate target classes (body–body or tip–tip) from the background (all other events, including the opposite orientation). The discriminant utilizes the correlation between $\varepsilon_2$ and $\delta d_\perp / \langle d_\perp \rangle$.
• Validation: Thresholds are optimized on a validation sample to retain 30% of the target class. Performance (efficiency and purity) is evaluated on an independent test sample. A toy model is also employed to assess the robustness of these selections against fluctuations in the mapping from initial geometry to final-state observables (elliptic flow and mean transverse momentum).

Key Contributions and Results

• Distinct Distributions: The study confirms that body–body and tip–tip configurations produce distinct, albeit overlapping, distributions in the $\varepsilon_2$–$d_\perp$ plane. Body–body events cluster at high $\varepsilon_2$ and low compactness, while tip–tip events favor low $\varepsilon_2$ and high compactness.
• Sensitivity Beyond Central Collisions: The sensitivity to nuclear deformation is not limited to the most central collisions. The difference between spherical and deformed configurations remains visible down to $N_{\text{part}} \sim 13$, suggesting that deformation effects persist over a wider centrality range than previously assumed.
• Model Differences: While NLEFT and PGCM show similar results at high multiplicities, considerable differences emerge in the range $13 < N_{\text{part}} < 25$, particularly regarding the transverse compactness ($d_\perp$). This suggests that $d_\perp$ could serve as a probe to distinguish between different many-body nuclear structure predictions.
• Classification Performance: Using the Fisher linear discriminant with a 30% efficiency constraint:
  • Body–body selection: Achieves a purity of 0.201 (NLEFT) and 0.156 (PGCM). This corresponds to an enrichment factor of approximately 11 times over the raw data fraction.
  • Tip–tip selection: Achieves a purity of 0.573 (NLEFT) and 0.540 (PGCM), corresponding to an enrichment factor of roughly 4.5.
• Linear vs. Non-linear: The authors note that while the distributions exhibit some overlap and potential non-linear structures, a linear separator provides a transparent baseline. Attempts to use machine learning approaches did not yield a significant increase in purity over the linear method.

Significance
The paper demonstrates that the orientation of deformed nuclei leaves measurable imprints on the initial collision geometry, even when accounting for event-by-event fluctuations and the smearing effects of hydrodynamic evolution. By utilizing the correlation between eccentricity and transverse compactness, it is possible to construct event samples enriched in specific geometric configurations (body–body or tip–tip). This capability allows for a more direct experimental probe of the many-body interactions and ground-state geometries predicted by advanced low-energy nuclear theories like NLEFT and PGCM. The work establishes that these geometry-sensitive observables provide complementary information, validating the use of multidifferential selections to constrain nuclear structure parameters in high-energy collisions.