Ultra-central Collisions Research Articles

Probing collectivity in heavy-ion collisions with fluctuations of the pT spectrum

Event-by-event fluctuations in the initial stages of ultrarelativistic nucleus-nucleus collisions depend little on rapidity. The hydrodynamic expansion which occurs in later stages then gives rise to correlations among outgoing particles which depend weakly on their relative rapidity. Azimuthal correlations, through which anisotropic flow (vn(pT)) is defined, have been the most studied. Here we study a new observable introduced in 2020 by Schenke, Shen and Teaney and dubbed v0(pT), which quantifies the relative change in the pT spectrum induced by a fluctuation. We describe how it can be measured. Using hydrodynamic simulations, we make quantitative predictions for v0(pT) of charged and identified hadrons. We then discuss how v0(pT) relates to two phenomena which have been measured: The increase of the mean transverse momentum in ultracentral collisions, and the event-by-event fluctuations of the transverse momentum per particle [pT]. We show that v0(pT) determines the dependence of these quantities on the pT cuts implemented in the analysis. We quantitatively explain the rise of σpT observed by ATLAS as the upper pT-cut is increased from 2 to 5 GeV/c.

Probing configuration of α clusters with spectator particles in relativistic heavy-ion collisions

We propose to use spectator particle yield ratios to probe the configuration of α clusters in 12C and 16O by their ultracentral collisions at RHIC and LHC energies. The idea is illustrated based on initial density distributions with various α-cluster configurations generated by a microscopic cluster model, and without α clusters from mean-field calculations. The multifragmentation of the spectator matter produces more spectator light nuclei including α clusters in collisions of nuclei with chain structure of α clusters, compared to those of nuclei with a more compact structure. The yield ratio of free spectator neutrons to spectator particles with mass-to-charge ratio A/Z=2 scaled by their masses can be practically measured by the zero-degree calorimeter (ZDC) at RHIC and LHC, serving as a clean probe free from modeling the complicated dynamics at midrapidities.

Transverse momentum fluctuation in ultra-central Pb+Pb collision at the LHC

The ATLAS collaboration has recently observed that the variance of the transverse momentum per particle ([pt]), when measured as a function of the collision multiplicity (Nch) in Pb+Pb collisions, decreases by a factor 2 for the largest values of Nch, corresponding to ultra-central collisions. We show that this phenomenon is naturally explained by invoking impact parameter (b) fluctuations, which contribute to the variance, and gradually disappear in ultracentral collisions. It implies that Nch and [pt] are strongly correlated at fixed b, which is explained by the local thermalization of the QGP medium.

ATLAS measurement of mean momentum fluctuations and correlations with the flow in Xe+Xe and Pb+Pb collisions

The thermal fluctuations in the QGP medium formed in heavy ion collisions present themselves as event-wise mean transverse momentum ([pT]) fluctuations in the final state. Recent studies have shown that the fluctuations are sensitive to radial flow, random thermal motion, and nuclear deformation. They can provide constraints on the extent of thermalization of the QGP droplet. Recently, correlations of [pT] with flow harmonic coefficients (vn) also gained interest, as they were found to be sensitive primarily to the initial state fluctuations. This talk presents precise measurements of up to 3rd order [pT] cumulants as a function of multiplicity and centrality with an emphasis on ultra-central collisions. These results have strong implications for understanding the impacts of the initial condition, medium thermalization, and medium properties on final state [pT] fluctuations.

Hydrodynamic fluctuations and ultra-central flow puzzle in heavy-ion collisions

One of the long-standing problems in the field of high-energy heavy-ion collisions is that the dynamical models based on viscous hydrodynamics fail to describe the experimental elliptic flow v2 and the triangular flow v3 simultaneously in ultra-central collisions. The problem, known as the ultra-central flow puzzle, is specifically that hydrodynamics-based models predict the flow ratio of the two-particle cumulant method v2{2}/v3{2}>1 while v2{2}/v3{2}∼1 in the experimental data. In this Letter, we focus on the effects of hydrodynamic fluctuations during the space-time evolution of the QGP fluid on the flow observables in the ultra-central collisions. Using the (3+1)-dimensional integrated dynamical model which includes relativistic fluctuating hydrodynamics, we analyze the anisotropic flow coefficients vn{2} in 0–0.2% central Pb+Pb collisions at sNN=2.76TeV. We find that the hydrodynamic fluctuations decrease the model overestimate of v2{2}/v3{2} from the experimental data by about 19% within the present setup of η/s=1/2π. This means that the hydrodynamic fluctuations qualitatively have an effect to improve the situation for the puzzle, but the effect of the hydrodynamic fluctuations alone is quantitatively insufficient to resolve the puzzle. The decrease of the ratio largely depends on the shear viscosity η/s, which calls for future comprehensive analyses with, for example, a realistic temperature-dependent viscosity.

Assessing the ultracentral flow puzzle in hydrodynamic modeling of heavy-ion collisions

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. 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.

Free spectator nucleons in ultracentral relativistic heavy-ion collisions as a probe of neutron skin

Besides the yield ratio of free spectator neutrons produced in ultracentral $^{96}\mathrm{Zr}$+$^{96}\mathrm{Zr}$ to $^{96}\mathrm{Ru}$+$^{96}\mathrm{Ru}$ collisions [Liu et al., Phys. Lett. B 834, 137441 (2022)], we propose that the yield ratio ${N}_{n}/{N}_{p}$ of free spectator neutrons to protons in a single collision system at the BNL Relativistic Heavy Ion Collider or the CERN Large Hadron Collider can be a more sensitive probe of the neutron-skin thickness $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$ and the slope parameter $L$ of the symmetry energy. The idea is demonstrated based on the proton and neutron density distributions of colliding nuclei obtained from Skyrme-Hartree-Fock-Bogolyubov calculations, and on a Glauber model that provides information of spectator matter. The final spectator particles are produced from direct emission, clusterization by a minimum spanning tree algorithm or a Wigner function approach, and deexcitation of heavy clusters by gemini. A larger $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$ associated with a larger $L$ value increases the isospin asymmetry of spectator matter and thus leads to a larger ${N}_{n}/{N}_{p}$, especially in ultracentral collisions where the multiplicity of free nucleons are free from the uncertainties of cluster formation and deexcitation. We have further shown that the double ratio of ${N}_{n}/{N}_{p}$ in isobaric collision systems or in collisions by isotopes helps to cancel the detecting efficiency for protons. Effects from nuclear deformation and electromagnetic excitation are studied, and they are found to be subdominant compared to the expected sensitivity to $\mathrm{\ensuremath{\Delta}}{r}_{\mathrm{np}}$.

Peeling away neutron skin in ultracentral collisions of relativistic nuclei

In heavy nuclei the ratio between local densities of neutrons and protons increases towards the nuclear periphery. The excess of neutrons is known as the neutron skin (NS) with a subtle difference ($<0.5$~fm) between the r.m.s radii of the distributions of neutrons and protons. We show that the presence of NS in $^{208}$Pb leads to extra spectator neutrons in ultracentral $^{208}$Pb--$^{208}$Pb collisions at the CERN SPS and LHC. The yields of spectator neutrons and protons were calculated within a new version of Abrasion-Ablation Monte Carlo for Colliders model (AAMCC-MST) taking into account NS and pre-equilibrium clustering of spectator matter. While the average numbers of spectator neutrons and protons in ultracentral collisions vary insignificantly, the cross sections of emission of certain numbers of spectator neutrons in events with 0,1,...5 spectator protons are changed by 50--250\%, depending on the thickness of NS. These cross sections are less sensitive to other parameters in calculations, and their measurements in the ALICE experiment at the LHC will make it possible to restrict the existing variety of neutron density parameterizations in $^{208}$Pb.

Probing neutron-skin thickness with free spectator neutrons in ultracentral high-energy isobaric collisions

We show that the yield ratio of free spectator neutrons produced in high-energy 96Zr+96Zr to 96Ru+96Ru collisions is a clean probe of the neutron-skin thickness of colliding nuclei and the slope parameter L of the symmetry energy. The idea is demonstrated based on the proton and neutron density distributions via a state-of-the-art Skyrme-Hartree-Fock-Bogolyubov calculation. Among spectator nucleons given by the Glauber model, free spectator neutrons include those from direct production that survive from clusterization as well as those from deexcitation of heavy clusters described by the popular GEMINI model. More free neutrons are produced in collisions of 96Zr nucleus due to its larger neutron skin, compared to those produced in collisions of 96Ru nucleus with a smaller neutron skin. The difference of the free spectator neutron yield is further increased with the increasing difference of the neutron-skin thickness between 96Zr and 96Ru with a larger L value, and the increase in ultracentral collisions is particularly insensitive to model details and experimental uncertainties. Since the production of free spectator neutrons is not affected by the complicated dynamics in the mid-rapidity region, the ratio of their multiplicities in ultracentral isobaric collisions is a robust observable for constraining the neutron skin and L value.

Phenomenological study on correlation between flow harmonics and mean transverse momentum in nuclear collisions

To assess the properties of the quark-gluon plasma formed in nuclear collisions, the Pearson correlation coefficient between flow harmonics and mean transverse momentum, \rho\left(v_{n}^{2},\left[p_{\mathrm{T}}\right]\right)ρ(vn2,[pT]), reflecting the overlapped geometry of colliding atomic nuclei, is measured. \rho\left(v_{2}^{2},\left[p_{\mathrm{T}}\right]\right)ρ(v22,[pT]) was found to be particularly sensitive to the quadrupole deformation of the nuclei. We study the influence of the nuclear quadrupole deformation on \rho\left(v_{n}^{2},\left[p_{\mathrm{T}}\right]\right)ρ(vn2,[pT]) in Au+Au and U+U collisions at RHIC energy using AMPT transport model, and show that the \rho\left(v_{2}^{2},\left[p_{\mathrm{T}}\right]\right)ρ(v22,[pT]) is reduced by the quadrupole deformation \beta_2β2 and turns to change sign in ultra-central collisions (UCC).

Probing nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in heavy ion collisions

In heavy ion collisions, elliptic flow $v_2$ and radial flow, characterized by event-wise average transverse momentum $[p_{\mathrm{T}}]$, are related to the shape and size of the overlap region, which are sensitive to the shape of colliding atomic nuclei. The Pearson correlation coefficient between $v_2$ and $[p_{\mathrm{T}}]$, $\rho_2$, was found to be particularly sensitive to the quadrupole deformation parameter $\beta$ that is traditionally measured in low energy experiments. Built on earlier insight that the prolate deformation $\beta>0$ reduces the $\rho_2$ in ultra-central collisions (UCC), we show that the prolate deformation $\beta<0$ enhances the value of $\rho_2$. As $\beta>0$ and $\beta<0$ are the two extremes of triaxiality, the strength and sign of $v_2^2-[p_{\mathrm{T}}]$ correlation can be used to provide valuable information on the triaxiality of the nucleus. Our study provide further arguments for using the hydrodynamic flow as a precision tool to directly image the deformation of the atomic nuclei at extremely short time scale ($<10^{-24}$s).

Shape of atomic nuclei in heavy ion collisions

In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flow $v_n$ are linearly related to the strength of the multi-pole shape of the distribution of nucleons in the transverse plane $\varepsilon_n$, $v_n\propto \varepsilon_n$. The $\varepsilon_n$, for $n=1,2,3,4$, are sensitive to the shape of the colliding ions, characterized by the quadrupole $\beta_2$, octupole $\beta_3$ and hexadecapole $\beta_4$ deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, $\langle\varepsilon_n^2\rangle = a_n'+b_n'\beta_n^2$, for events in a fixed centrality. The $\langle\varepsilon_1^2\rangle$ has a contribution from $\beta_3$ and $\beta_4$, and $\langle\varepsilon_3^2\rangle$ from $\beta_4$. In the ultra-central collisions, there are little cross contributions between $\beta_2$ and $\varepsilon_3$ and between $\beta_3$ and $\varepsilon_2$, but clear cross contributions are present in non-central collisions. Additionally, $\langle\varepsilon_n^2\rangle$ are insensitive to non-axial 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 $\beta_2$, $\beta_3$, and $\beta_4$ values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical $a_n'$, to obtain simple equation that relates the $\beta_n$ of the two species. 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 those obtained in the nuclear structure experiments.

Flow and centrality fluctuations from ATLAS

Results of multi-particle cumulants for harmonic flow coefficients νn are obtained in sNN=5.02TeV Pb+Pb collisions with the ATLAS detector at the Large Hadron Collider. The cumulant ratios νn{4}/νn{2} for n = 2, 3 and 4 and ν2{6}/ν2{4} show centrality-dependent behavior compatible with eccentricity fluctuations. However, significant dependences on transverse momentum are observed, suggesting that flow fluctuations may also arise from final-state interactions. The flow cumulants are also found to depend on the resolution of the quantity used to define event centrality: poorer centrality resolution tends to increase the value of ν2{2} and changes the sign of ν2{4} and ν3{4} in ultra-central collisions. These results shed light on the contributions of flow fluctuations from the initial state and the final state, as well as on the influences of centrality fluctuations.

Ultracentral Collisions of Small and Deformed Systems at RHIC

We study a range of collision systems involving deformed ions and compare the elliptic and triangular flow harmonics produced in a hydrodynamics scenario versus a color glass condensate (CGC) scenario. For the hydrodynamics scenario, we generate initial conditions using TRENTO and work within a linear response approximation to obtain the final flow harmonics. For the CGC scenario, we use the explicit calculation of two-gluon correlations taken in the high-pT “(semi)dilute-(semi)dilute” regime to express the flow harmonics in terms of the density profile of the collision. We consider ultracentral collisions of deformed ions as a testbed for these comparisons because the difference between tip-on-tip and side-on-side collisions modifies the multiplicity dependence in both scenarios, even at zero impact parameter. We find significant qualitative differences in the multiplicity dependence obtained in the initial conditions+hydrodynamics scenario and the CGC scenario, allowing these collisions of deformed ions to be used as a powerful discriminator between models. We also find that sub-nucleonic fluctuations have a systematic effect on the elliptic and triangular flow harmonics which are most discriminating in 0–1% ultracentral symmetric collisions of small deformed ions and in 0–10% d197Au collisions. The collision systems we consider are 238U238U, d197Au, 9Be197Au, 9Be9Be, 3He3He, and 3He197Au.

Possible octupole deformation of Pb208 and the ultracentral v2 to v3 puzzle

Recent measurements have established the sensitivity of ultracentral heavy-ion collisions to the deformation parameters of non-spherical nuclei. In the case of ${}^{ 129}$Xe collisions, a quadrupole deformation of the nuclear profile led to an enhancement of elliptic flow in the most central collisions. In ${}^{ 208}$Pb collisions a discrepancy exists in similar centralities, where either elliptic flow is over-predicted or triangular flow is under-predicted by hydrodynamic models; this is known as the $v_2$-to-$v_3$ puzzle in ultracentral collisions. Motivated by low-energy nuclear structure calculations, we consider the possibility that $^{208}$Pb nuclei could have a pear shape deformation (octupole), which has the effect of increasing triangular flow in central PbPb collisions. Using the recent data from ALICE and ATLAS, we revisit the $v_2$-to-$v_3$ puzzle in ultracentral collisions, including new constraints from recent measurements of the triangular cumulant ratio $v_3\left\{4\right\}/v_3\left\{2\right\}$ and comparing two different hydrodynamic models. We find that, while an octupole deformation would slightly improve the ratio between $v_2$ and $v_3$, it is at the expense of a significantly worse triangular flow cumulant ratio. In fact, the latter observable prefers no octupole deformation, with $\beta_3\lesssim 0.0375$ for ${}^{ 208}$Pb, and is therefore consistent with the expectation for a doubly-magic nucleus even at top collider energies. The $v_2$-to-$v_3$ puzzle remains a challenge for hydrodynamic models.

Centrality fluctuations and decorrelations in heavy-ion collisions in a Glauber model

The centrality or the number of initial-state sources $V$ of the system produced in heavy ion collision is a concept that is not uniquely defined and subject to significant theoretical and experimental uncertainties. We argue that a more robust connection between the initial-state sources with final-state multiplicity could be established from the event-by-event multiplicity correlation between two subevents separated in pseudorapidity, $N_a$ vs $N_b$. This correlation is sensitive to two main types of centrality fluctuations (CF): 1) particle production for each source $p(n)$ which smears the relation between $V$ and $N_a$ used for experimental centrality, and 2) decorrelations between the sources in the two subevents $V_b$ and $V_a$. The CF is analyzed in terms of cumulants of $V_b$ and $N_b$ as a function of $N_a$, i.e. experimental centrality is defined with $N_a$. We found that the mean values $\langle V_b\rangle_{N_a}$ and $\langle N_b\rangle_{N_a}$ increase linearly with $N_a$ in mid-central collisions, but flatten out in ultra-central collisions. Such non-linear behavior is sensitive to the centrality resolution of $N_a$. In the presence of centrality decorrelations, the scaled variances $\langle(\delta V_b)^2\rangle/\langle V_b\rangle$ and $\langle(\delta N_b)^2\rangle/\langle N_b\rangle$ are found to decrease linearly with $N_a$ in mid-central collisions, while the $p(n)$ leads to another sharp decrease in the ultra-central region. The higher-order cumulants of $V_b$ and $N_b$ show interesting but rather complex behaviors which deserve further studies. Our results suggest that one can use the cumulants of the two-dimensional multiplicity correlation, especially the mean and variance, to constrain the particle production mechanism as well as the longitudinal fluctuations of the initial-state sources.

Fluctuations of anisotropic flow in Pb+Pb collisions at sqrt{{mathrm{s}}_{mathrm{NN}}} = 5.02 TeV with the ATLAS detector

Multi-particle azimuthal cumulants are measured as a function of centrality and transverse momentum using 470 μb−1 of Pb+Pb collisions at sqrt{s_{mathrm{NN}}} = 5.02 TeV with the ATLAS detector at the LHC. These cumulants provide information on the event-by-event fluctuations of harmonic flow coefficients vn and correlated fluctuations between two harmonics vn and vm. For the first time, a non-zero four-particle cumulant is observed for dipolar flow, v1. The four-particle cumulants for elliptic flow, v2, and triangular flow, v3, exhibit a strong centrality dependence and change sign in ultra-central collisions. This sign change is consistent with significant non-Gaussian fluctuations in v2 and v3. The four-particle cumulant for quadrangular flow, v4, is found to change sign in mid-central collisions. Correlations between two harmonics are studied with three- and four-particle mixed-harmonic cumulants, which indicate an anti-correlation between v2 and v3, and a positive correlation between v2 and v4. These correlations decrease in strength towards central collisions and either approach zero or change sign in ultra-central collisions. To investigate the possible flow fluctuations arising from intrinsic centrality or volume fluctuations, the results are compared between two different event classes used for centrality definitions. In peripheral and mid-central collisions where the cumulant signals are large, only small differences are observed. In ultra-central collisions, the differences are much larger and transverse momentum dependent. These results provide new information to disentangle flow fluctuations from the initial and final states, as well as new insights on the influence of centrality fluctuations.

Correlations in the Initial Conditions of Heavy-Ion Collisions

Ultracentral collisions of heavy nuclei, in which the impact parameter is nearly zero, are especially sensitive to the details of the initial state model and the microscopic mechanism for collective flow. In a hydrodynamic “flow” picture, the final state momentum correlations are a direct response to the fluctuating initial geometry, although models of the initial geometry differ widely. Alternatively, dynamical mechanisms based in the color glass condensate (CGC) formalism can naturally lead to many-body correlations with very different systematics. Here we present a calculation of event-by-event elliptic flow in both the hydrodynamic and CGC paradigms and show that they can be qualitatively distinguished in ultracentral collisions of deformed nuclei. Specifically, the multiplicity dependence in such collisions is qualitatively opposite, with the CGC correlations increasing with multiplicity while the hydrodynamic correlations decrease. The consistency of the latter with experimental data on UU collisions appears to rule out a CGC-mediated explanation. We find that these qualitative features also persist in small deformed systems and can therefore be a valuable test of the microscopic physics in that regime. The authors acknowledge support from the US-DOE Nuclear Science Grant No. DE-SC0019175, and the Alfred P. Sloan Foundation, and the Zuckerman STEM Leadership Program.

Non-linear flow modes of identified particles in Pb–Pb collisions at [formula omitted] with the ALICE detector

The non-linear flow modes, v4,22, v5,32 and v6,33 as a function of transverse momentum (pT) have been measured for the first time in Pb–Pb collisions at sNN=5.02TeV for identified particles, i.e. charged pions, kaons and (anti-)protons. These observables probe the contribution of the second and third initial anisotropy coefficients to the higher order flow harmonics. Interestingly, all the characteristic features observed in previous pT-differential as well as pT-integrated measurements (e.g. v2 and v3) for various particle species are present in these measurements, i.e. increase of magnitude with increasing centrality percentile, a mass ordering in the low pT region and a particle type grouping in the intermediate pT region. The results cover 0–1% (ultra-central collisions), 10–20% (mid-central collisions) and 40–50% (mid-peripheral collisions) centrality intervals and allow to test models that attempt to describe initial conditions and the mode-coupling of different harmonics.

Flow fluctuations in Pb+Pb collisions at [formula omitted] with the ATLAS detector

Measurements of four-particle cumulants cn{4} for n=1,2,3,4 are presented using 470μb−1 of Pb+Pb collisions at sNN=5.02TeV with the ATLAS detector at the LHC. These cumulants provide information on the event-by-event fluctuations of single harmonics p(vn). For the first time, a negative c1{4} is observed. The c4{4} is found to be negative in central collisions but changes sign around 20–25% centrality. This behavior is consistent with a nonlinear contribution to v4 that is proportional to v22. c2{4} and c3{4} are calculated using two reference event classes in order to investigate the influence of volume fluctuations. Over most of the centrality range, c2{4} and c3{4} are found to be negative, while in the ultra-central collisions, c2{4} changes sign and becomes positive, suggesting a deviation from Gaussian behavior in the event-by-event fluctuation of v2. The magnitudes of the sign change are also found to be dependent of the event class definition.