Particlization of an interacting hadron resonance gas with global conservation laws for event-by-event fluctuations in heavy-ion collisions
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Analytic formulas to calculate statistical uncertainties of v n { 2 k } harmonics extracted from the Q cumulants are presented. The Q cumulants are multivariate polynomial functions of the weighted means of 2m-particle azimuthal correlations, $\langle\langle 2 m \rangle\rangle$. Variances and covariances of the $\langle\langle 2 m \rangle\rangle$ are included in the analytic formulas of the uncertainties that can be calculated simultaneously with the calculations of the v n { 2 k } harmonics. The calculations are performed using a simple toy model, which roughly simulates elliptic flow azimuthal anisotropy with magnitudes around 0.05. The results are compared with the results obtained by the many data subsets, and by the bootstrapping method. The first one is a common way of estimation of the statistical uncertainties of the v n { 2 k } harmonics in a real experiment. In order to increase precision in the measurement of the v n { 2 k } harmonics, a large number of 15 000 subsets and the same number of the resampling in the bootstrap method is used. Unlike the other ways of the analytic calculation of the v n { 2 k } statistical uncertainties, our proposal that includes the use of squared weights in the calculation of both the variances and covariances, gives the best agreement with the results obtained from the subsets and bootstrap method. Additionally, a recurrence equation between Q cumulants of any order is also presented.
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In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flows v n are linearly related to the strengths of the multipole shape of the distribution of nucleons in the transverse plane, ε n : v n ∝ε n . The ε n , for n=1, 2, 3, 4, are sensitive to the shapes of the colliding ions, characterized by the quadrupole β 2 , octupole β 3 , and hexadecapole β 4 deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, $\langleε^{2}_{n}\rangle$ = $a^{'}_{n} + b^{'}_{n}β^{2}_{n}$, for events in a fixed centrality. The $\langleε^{2}_{1}\rangle$ has a contribution from β 3 and β 4 , and $\langleε^{2}_{3}\rangle$ from β 4 . In ultracentral collisions, there are little cross contributions between β 2 and ε 3 and between β 3 and ε 2 , but clear cross contributions are present in noncentral collisions. Additionally, $\langleε^{2}_{n}\rangle$ are insensitive to nonaxial shape parameters such as the triaxiality. This is good news because the measurements of v 2 , v 3 , and v 4 can be used to constrain simultaneously the β 2 , β 3 , and β 4 values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical $a^{'}_{n}$, to obtain a simple equation that relates the β n of the two species. Finally, this opens up the possibility to map the shape of the atomic nuclei at a timescale (<10 –24 s) much shorter than probed by low-energy nuclear structure physics (<10 –21 s), which ultimately may provide information complementary to that obtained in the nuclear structure experiments.
The initial state is one of the greatest uncertainties in heavy-ion collisions. A model-agnostic approach is taken in the phenomenological Trento framework which constrains parameters using Bayesian analysis. However, the color-glass condensate (CGC) effective theory predicts initial energy densities that lie outside the recent Bayesian analyses due, in part, to the assumption in Trento of event-by-event multiplicity fluctuations following a Γ distribution. We compare the Trento-preferred √T A T B scaling to CGC-like T A T B scaling coupled with log-normal fluctuations in AuAu and dAu collisions and find there is a significant impact on the multiplicity distributions and on the eccentricities, which may affect the extraction of viscosity in small systems.
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Measurements from the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC) can be used to study the properties of quark-gluon plasma. Systematic constraints on these properties must combine measurements from different collision systems and methodically account for experimental and theoretical uncertainties. Such studies require a vast number of costly numerical simulations. While computationally inexpensive surrogate models (“emulators”) can be used to efficiently approximate the predictions of heavy ion simulations across a broad range of model parameters, training a reliable emulator remains a computationally expensive task. We use transfer learning to map the parameter dependencies of one model emulator onto another, leveraging similarities between different simulations of heavy ion collisions. By limiting the need for large numbers of simulations to only one of the emulators, this technique reduces the numerical cost of comprehensive uncertainty quantification when studying multiple collision systems and exploring different models.
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Here we present high-precision measurements of elliptic, triangular, and quadrangular flow v 2 , v 3 , and v 4 , respectively, at midrapidity for identified hadrons π, p, K, φ, K s , Λ as a function of centrality and transverse momentum in Au+Au collisions at the center-of-mass energy √ s NN = 200 GeV. We observe similar v n trends between light and strange mesons which indicates that the heavier strange quarks flow as strongly as the lighter up and down quarks. The number-of-constituent-quark scaling for v 2 , v 3 , and v 4 is found to hold within statistical uncertainty for 0–10%, 10–40%, and 40–80% collision centrality intervals. The results are compared to several viscous hydrodynamic calculations with varying initial conditions, and could serve as an additional constraint to the development of hydrodynamic models.
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High-energy heavy-ion collisions contain enormous angular momentum, |$\vec{𝐽}$|, which is 𝑂(10 3 –10 6 ℏ) in the range of collision energy, $\sqrt{s_{NN}}$, spanned experimentally by the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). Here, a fraction of $\vec{𝐽}$ is transferred to the overlapping collision region, which is indispensable for measuring observables such as vorticity-driven hadron spin alignment with $\hat{𝐽}$. Experiments estimate the orientation of $\hat{𝐽}$ of the participant nucleons within the collision overlap region, $\hat{𝐽}$ part , by using that of the forward- and backward-going spectating nucleons $\hat{𝐽}$ spec . Using two models, we study the decorrelation between $\hat{𝐽}$ part and $\hat{𝐽}$ spec , driven both by angular-momentum conservation and event-by-event fluctuations, as well as by the decorrelation between the orientation of the elliptic overlap region and the $\hat{𝐽}$ part . $\sqrt{s_{NN}}$-dependent decorrelation is observed in both of these cases and is large enough to be an important corrective factor used when experimentally observing phenomena driven by $\vec{𝐽}$.
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An outstanding problem in heavy-ion collisions is the inability for models to accurately describe ultra-central experimental flow data, despite that being precisely the regime where a hydrodynamic description should be most applicable. Here, we reassess the status of this puzzle by computing the flow in ultra-central collisions obtained from multiple recent Bayesian models that were tuned to various observables in different collision systems at typical centralities. While central data can now be described with better accuracy than in previous calculations, tension with experimental observation remains and worsens as one goes to ultra-central collisions. Tuning the model parameters cannot remove this tension without destroying the fit at other centralities. As such, new elements are likely needed in the standard modeling of heavy-ion collisions.