Longitudinal structure of the quark-gluon plasma from differently shaped nuclei

Technical Summary: Longitudinal Structure of the Quark–Gluon Plasma from Differently Shaped Nuclei

Problem Statement
Ultrarelativistic collisions of atomic nuclei create a quark–gluon plasma (QGP) that behaves as a near-perfect fluid. While the transverse geometry of the QGP and the intrinsic deformations of nuclei have been successfully imaged via anisotropic flow, the longitudinal structure of the QGP along the beam direction remains poorly understood. The primary obstacle is "nonflow" correlations—short-range effects arising from jet fragmentation and resonance decays—which dominate the two-particle correlation signal at small relative pseudorapidity ($|\Delta\eta| \lesssim 1\text{--}2$). These nonflow correlations mask the genuine long-range flow decorrelation signal. Existing methods, such as the ratio observable $r_n(\eta)$, attempt to mitigate nonflow by using reference particles at large rapidity, but these provide only indirect, biased information and fail to recover the full longitudinal decorrelation map $R_n(\eta_1, \eta_2)$.

Methodology
The authors propose a novel strategy to isolate the genuine longitudinal flow structure by exploiting differences in nuclear shape. The core hypothesis is that while nonflow correlations and fluctuation-driven flow components are nearly identical for nuclei of similar mass, the flow component induced by nuclear deformation differs significantly.

1. System Selection: The study compares collisions of nuclei with similar mass numbers but distinct quadrupole deformations ($\beta$). Specifically, the authors simulate head-on collisions of prolate-deformed $^{238}\text{U}$ ($\beta \approx 0.28$) and nearly spherical $^{197}\text{Au}$ ($\beta \approx -0.14$) at $\sqrt{s_{NN}} = 193$ and $200$ GeV, respectively, using the AMPT transport model.
2. Decomposition of Flow: The elliptic flow vector $V_2(\eta)$ is decomposed into a spherical baseline component ($V_{2,sp}$, arising from random nucleon fluctuations) and a deformation-induced component ($V_{2,\beta}$). These components are statistically uncorrelated.
3. Nonflow Removal via Subtraction: The two-particle correlation coefficient $V_{2\Delta}$ is expressed as the sum of the spherical baseline, the deformation term, and nonflow contamination ($\delta_{nf}$). By comparing the correlations of the two systems and applying a multiplicity-scaled subtraction (Eq. 7), the spherical baseline and the nonflow contributions cancel out. This leaves the pure deformation-driven correlation $V_{2\Delta,\beta}$.
4. Reconstruction of the Map: The genuine decorrelation map $R_{2,\beta}(\eta_1, \eta_2)$ is extracted from the difference signal. The authors validate that the longitudinal profile of the deformation-induced flow is identical to that of the spherical baseline, allowing the full longitudinal structure to be recovered.

Key Results

• Recovery of the Full Decorrelation Map: The subtraction method successfully isolates the longitudinal flow decorrelation over the full pseudorapidity range, free from nonflow contamination. The resulting map $R_{2,\beta}(\eta_1, \eta_2)$ reveals a highly non-linear rapidity dependence that cannot be captured by conventional observables.
• Universality of Longitudinal Profiles: The study demonstrates that the longitudinal decorrelation profile is universal; it is identical for both the fluctuation-driven (spherical) and deformation-driven components. This confirms that nuclear deformation changes the magnitude of the flow but not its longitudinal structure.
• Bias in Standard Measurements: The paper quantifies a significant bias in standard flow measurements using the three-subevent method. The bias factor $B_2$ deviates from unity (reaching $\sim 15\%$ for mid-rapidity particles with $\eta_{ref} \approx 4$) because correlation losses across successive rapidity intervals do not simply add up. This contradicts the common assumption that $r_2(\eta)$ directly measures the true decorrelation $R_2(\eta, -\eta)$.
• Non-Additive Decorrelation: The extracted map shows that the decorrelation structure is "super-additive" (consistent with a power-law form $p > 1$), implying that the sources of correlation (e.g., QCD strings) have a finite longitudinal extent. This structure causes the standard ratio observable $r_2(\eta)$ to overestimate the decorrelation in certain kinematic regions.

Significance and Claims
The paper claims that nuclear shape serves as a tool for the 3D imaging of the QGP and the quantum fluctuations of nuclear wavefunctions. By reversing the traditional approach—using nuclear shape to image the plasma rather than using the plasma to image the nucleus—the authors provide the first established method to recover the full longitudinal structure of the QGP.

The significance of this work lies in two main areas:

1. Initial State Constraints: The nonflow-free decorrelation maps provide direct constraints on the rapidity profile of energy deposition, the evolution of quark and gluon distributions, and the quantum fluctuations of the nuclear wavefunction.
2. Experimental Calibration: The study reveals that previous flow measurements, particularly in small systems (e.g., $p/d/^{3}\text{He}+\text{Au}$) and for higher-order harmonics ($v_3$), have been subject to unquantified biases due to longitudinal decorrelations. The proposed method allows for the calculation of bias factors for any specific experimental acceptance, enabling a consistent comparison of results from different detectors and collision systems.

The authors note that the necessary system pairs (e.g., $^{238}\text{U}+^{238}\text{U}$ vs. $^{197}\text{Au}+^{197}\text{Au}$, or $^{96}\text{Ru}+^{96}\text{Ru}$ vs. $^{96}\text{Zr}+^{96}\text{Zr}$) have already been recorded at RHIC and the LHC, making this strategy immediately applicable to existing data.