Critical point fluctuations: Finite size and global charge conservation effects
Roman V. Poberezhnyuk, Oleh Savchuk, Mark I. Gorenstein, Volodymyr Vovchenko, Kirill Taradiy, Viktor V. Begun, Leonid Satarov, Jan Steinheimer, Horst Stoecker
We investigate simultaneous effects of finite system size and global charge conservation on thermal fluctuations in the vicinity of a critical point. For that we consider a finite interacting system which exchanges particles with a finite reservoir (thermostat), comprising a statistical ensemble that is distinct from the common canonical and grand canonical ensembles. As a particular example the van der Waals model is used. The global charge conservation effects strongly influence the cumulants of particle number distribution when the system size is comparable to that of the reservoir. If the system size is large enough to capture all the physics associated with the interactions, the global charge conservation effects can be accurately described and corrected for analytically, within a recently developed subensemble acceptance method. The finite size effects start to play a significant role when the correlation length grows large due to proximity of the critical point or when the system is small enough to be comparable to an eigenvolume of an individual particle. We discuss our results in the context of fluctuation measurements in heavy-ion collisions.
The exact charge conservation significantly impacts multiplicity fluctuations. The result depends strongly on the part of the system charge carried by the particles of interest. Along with the expected suppression of fluctuations for large systems, charge conservation may lead to negative skewness or kurtosis for small systems.
We investigate the effect of the global charge conservation on the cumulants of conserved charges observed in relativistic heavy ion collisions in a finite rapidity window, $Δη$, with a special emphasis on the time evolution of fluctuations in the hadronic medium. It is argued that the experimental result of the net-electric charge fluctuation observed by ALICE does not receive effects from the global charge conservation, because of the finite diffusion distance of charged particles in the hadronic stage. We emphasize that the magnitude of the effect of the global charge conservation can be es…
We revisit the problem of particlization of a QCD fluid into hadrons and resonances at the end of the fluid dynamical stage in relativistic heavy-ion collisions in a context of fluctuation measurements. The existing methods sample an ideal hadron resonance gas, therefore, they do not capture the non-Poissonian nature of the grand-canonical fluctuations, expected due to QCD dynamics such as the chiral transition or QCD critical point. We address the issue by partitioning the particlization hypersurface into locally grand-canonical fireballs populating the space-time rapidity axis that are const…
We analyze the behavior of cumulants of conserved charges in a subvolume of a thermal system with exact global conservation laws by extending a recently developed subensemble acceptance method (SAM) [V. Vovchenko et al., arXiv:2003.13905] to multiple conserved charges. Explicit expressions for all diagonal and off-diagonal cumulants up to sixth order that relate them to the grand canonical susceptibilities are obtained. The derivation is presented for an arbitrary equation of state with an arbitrary number of different conserved charges. The global conservation effects cancel out in any ratio …
We introduce the subensemble acceptance method 2.0 (SAM-2.0) -- a procedure to correct cumulants of a random number distribution inside a subsystem for the effect of exact global conservation of a conserved quantity to which this number is correlated, with applications to measurements of event-by-event fluctuations in heavy-ion collisions. The method expresses the corrected cumulants in terms of the cumulants inside and outside the subsystem that are not subject to the exact conservation. The derivation assumes that all probability distributions associated with the cumulants are peaked at the …
Subensemble is a type of statistical ensemble which is the generalization of grand canonical and canonical ensembles. The subensemble acceptance method (SAM) provides general formulas to correct the cumulants of distributions in heavy-ion collisions for the global conservation of all QCD charges. The method is applicable for an arbitrary equation of state and sufficiently large systems, such as those created in central collisions of heavy ions. The new fluctuation measures insensitive to global conservation effects are presented. The main results are illustrated in the hadron resonance gas and…
If photon mass is not exactly zero, though arbitrary small, electric charge would not be conserved in interaction of charged particles with black holes. Manifestations of such mechanism of electric charge non-conservation are discussed.
General constraints on fluid velocity divergences for particles in quark matter are derived from baryon number conservation and enforced electric charge neutrality. A new oscillation pattern in three-flavor normal quark matter satisfying these conditions is found and its bulk viscosity is calculated. The result may have astrophysical implication for maximum rotation frequencies of compact stars.
Approaches based on viscous hydrodynamics for the hot and dense stage and hadronic transport for the final dilute rescattering stage are successfully applied to the dynamic description of heavy ion reactions at high beam energies. One crucial step in such hybrid approaches is the so called particlization, the transition between the hydrodynamic description to microscopic degrees of freedom. For this purpose, individual particles are sampled on the Cooper-Frye hypersurface. In this work, 4 different realizations of sampling algorithms are compared, where three of them incorporate global conserv…
A non-local field theory which breaks discrete symmetries, including C, P, CP, and CPT, but preserves Lorentz symmetry, is presented. We demonstrate that at one-loop level the masses for particle and antiparticle remain equal due to Lorentz symmetry only. An inequality of masses implies breaking of the Lorentz invariance and non-conservation of the usually conserved charges.
We point out that the variance of net-baryon distribution normalized by the Skellam distribution baseline, $κ_2[B-\bar{B}]/\langle B+\bar{B}\rangle$, is sensitive to the possible modification of (anti)baryon yields due to $B\bar{B}$ annihilation in the hadronic phase. The corresponding measurements can thus place stringent limits on the magnitude of the $B\bar{B}$ annihilation and its inverse reaction. We perform Monte Carlo simulations of the hadronic phase in Pb-Pb collisions at the LHC via the recently developed subensemble sampler + UrQMD afterburner and show that the effect survives in ne…
A modification of the Skellam and Poisson distributions is proposed for subsystems when the constraints imposed by the charge conservation law in the complete system are taken into account. Such distributions can be applied, for example, for an analysis of the fluctuations of baryon and net baryon numbers in certain pseudo-rapidity interval in $A+A$ and $p+p$ collisions with high multiplicities. The presented modified Skellam, Poisson and Gaussian distributions can be utilized also in various branches of science, when one studies the fluctuations of the two variables related to a subsystem, as…
Charged multiplicity distribution in a pseudo-rapidity window is formulated under the assumption that the charge conservation is satisfied in the full phase space. At first, we analyze measured charged particle multiplicity distributions in pseudo-rapidity windows in LHC by CMS and ALICE collaborations with the two probability distributions. One is the convolution of negative binomial and Poisson distributions, and the other is the Glauber-Lachs formula. Each distribution is considered as an analogy of the quantum optics. Next, we analyze the data with the double GL formulae for $|η|<2.4$ at 7…
The effect of nuclear interactions on measurable net-proton number fluctuations in heavy ion collisions at the SIS18/GSI accelerator is investigated. The state of the art UrQMD model including interaction potentials is employed. It is found that the nuclear forces enhance the baryon number cumulants, as predicted from grand canonical thermodynamical models. The effect however is smeared out for proton number fluctuations due to iso-spin randomization and global baryon number conservation, which decreases the cumulant ratios. For a rapidity acceptance window larger than $Δy> 0.4$ the effects of…
It is conjectured that dark matter (DM) was produced before inflation from neutral particles present after the Big Bang and survived inflation due to a specific coupling with gravitation, while the charged particles existing after the Big Bang disappeared during inflation in a process of charge non-conservation. Ordinary matter was produced at a later stage at a lower temperature following a symmetry restoring phase transition. In this way the non-luminous character of dark matter and the existence of two types of matter, ordinary and dark, get a natural explanation. Because of the high temper…
We consider the string theory origin of R-charge conservation laws in heterotic orbifold compactifications, deriving the corresponding string coupling selection rule for factorizable and non-factorizable orbifolds, with prime ordered and non-prime ordered point groups. R-charge conservation arises due to symmetries among the worldsheet instantons that can mediate the couplings. Among our results is a previously missed non-trivial contribution to the conserved R-charges from the Gamma-phases in non-prime orbifolds, which weakens the R-charge selection rule. Symmetries among the worldsheet insta…
Unveiling QCD Criticality with Cross-Rapidity Net-Baryon Cumulants
Universität Heidelberg（海德堡大学）；GSI Helmholtzzentrum für Schwerionenforschung（GSI重离子研究中心）；Tsinghua University（清华大学）；University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
A brief overview of the recent developments concerning theoretical description of event-by-event fluctuations in heavy-ion collisions is presented, with an emphasis on the role of exact conservation laws and calculations based on relativistic hydrodynamics.
We argue that the charge fractionalization in quarks has a hidden topological character related to a broken ${\cal Z}_2$ symmetry between integer-charged bare quarks and leptons. The mechanism is a tunneling process occurring in time between standard field configurations of a pure gauge form with different topological winding numbers associated with integer-charged bare quarks in the far past and future. This transition, which nonperturbatively normalizes local bare charges with a universal accumulated value, corresponds to a specific topologically nontrivial configuration of the weak gauge fi…
In some models with infinite extra dimensions, gauge fields are localized on a brane by gravity. A generic property of these models is the existence of arbitrarily light bulk modes of charged fields. This property may lead to interesting low-energy effects such as electric charge non-conservation on the brane (decay of electron to nothing). One may worry that light charged Kaluza--Klein modes would lead to unacceptable phenomenology due to their copious production in, e.g., electron-positron annihilation and/or their contribution to QED observables like anomalous magnetic moments. We argue, ho…
The effect of inverse magnetic catalysis (IMC) has been observed on the conserved charge fluctuations and the correlations along the chemical freeze-out curve in a hadron resonance gas model. The fluctuations and the correlations have been compared with and without charge conservations. The charge conservation plays an important role in the calculation of the fluctuations at nonzero magnetic field and for the fluctuations in the strange charge at zero magnetic field. The charge conservation diminishes the correlations $χ_{BS}$ and $χ_{QB}$, but enhances the correlation $χ_{QS}$. The baryonic f…
We present a sampling method for the transition from relativistic hydrodynamics to particle transport, commonly referred to as particlization, which preserves the local event-by-event conservation of energy, momentum, baryon number, strangeness, and electric charge. The proposed method is essential for studying fluctuations and correlations by means of stochastic hydrodynamics. It is also useful for studying small systems. The method is based on Metropolis sampling applied to particles within distinct patches of the hypersurface, where hydrodynamics and kinetic evolutions are matched.
We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) time-like vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperatu…
The production of hadrons in relativistic heavy ion collisions is studied using a statistical ensemble with thermal and chemical equilibrium. Special attention is given to exact conservation laws, i.e. certain charges are treated canonically instead of using the usual grand canonical approach. For small systems, the exact conservation of baryon number, strangeness and electric charge is to be taken into account. We have derived compact, analytical expressions for particle abundances in such ensemble. As an application, the change in $K/π$ ratios in AGS experiments with different interaction sy…
In the context of quantum field theory (QFT), we compute the amplitudes of weak interaction processes such as $ W^{+} \rightarrow e^{+} + ν_{e}$ and $ W^{+} \rightarrow e^{+} + ν_μ$ by using different representations of flavor states for mixed neutrinos. Analyzing the short time limit of the above amplitudes, we find that the neutrino states defined in QFT as eigenstates of the flavor charges lead to results consistent with lepton charge conservation. On the contrary, the Pontecorvo flavor states produce a violation of lepton charge in the vertex, which is in contrast with what expected at tre…
Variable speed of light (VSL) theories generically lead to large violations of charge conservation that can be written in terms of a dimensionless parameter $λ$. It is shown that the motion of the Earth with respect to the Sun could lead to a seasonal variation for the SAGE and GALLEX-GNO experiments and analyzing the reported counting rates for these experiments, a very stringent bound $λ\le 2 \times 10^{-19} $ is obtained, some $10^9$ times smaller than previous ones. Furthermore, a bound on the lifetime of the $\null^{71}{\rm Ga} \to \null^{71} {\rm Ge}$ charge-nonconserving decay in VSL th…
We argue that global charges, such as baryon or lepton number, are not conserved in theories with the Standard Model fields localized on the brane which propagates in higher-dimensional space-time. The global-charge non-conservation is due to quantum fluctuations of the brane surface. These fluctuations create "baby branes" that can capture some global charges and carry them away into the bulk of higher-dimensional space. Such processes are exponentially suppressed at low-energies, but can be significant at high enough temperatures or energies. These effects can lead to a new, intrinsically hi…
