Revealing baryon number fluctuations from proton number fluctuations in relativistic heavy ion collisions

Abstract

Baryon number cumulants are invaluable tools to diagnose the primordial stage of heavy ion collisions if they can be measured. In experiments, however, proton number cumulants have been measured as substitutes. In fact, proton number fluctuations are further modified in the hadron phase and are different from those of the baryon number. We show that the isospin distribution of nucleons at kinetic freeze-out is binomial and factorized. This leads to formulas that express the baryon number cumulants solely in terms of proton number fluctuations, which are experimentally observable.PACS numbers: 12.38. Mh, 25.75.Nq, 24.60.Ky The order of the phase transition of quantum chromodynamics (QCD) at nonzero temperature (T ) is believed to change from crossover [1] to first order at a nonzero baryon chemical potential (µ B ). The existence of the QCD critical point is thus expected in the phase diagram on the T -µ B plane [2]. Experiments to explore the phase structure at nonzero µ B , especially the existence of the critical point, are now ongoing in the energy scan program at the Relativistic Heavy Ion Collider (RHIC) [3,4], and will also be performed in future facilities [5,6]. Much attention has also been paid to this problem from numerical experiments on the lattice [1,7]. The establishment of the QCD phase structure at nonzero µ B is an important issue, not only to deepen our knowledge of the matter described by QCD, but also to gain understanding of a wide array of topics in physics which share the concepts of phase transitions and techniques to treat strongly correlated many-body systems.Fluctuations, which are experimentally measured by event-by-event analyses in heavy ion collisions, are promising observables to probe the properties of created fireballs [8], as their behaviors are sensitive to the state of the matter. For example, because of the singularity at the critical point, fluctuations of various physical quantities, including skewness and kurtosis, behave anomalously near the critical point [9][10][11]. One can also argue that ratios between the cumulants of conserved charges are sensitive to the magnitudes of the charge carried by the quasiparticles composing the system, and hence they behave differently in the hadronic and quark-gluon phases [12][13][14]. Recently, it was also pointed out that some higher-order cumulants of conserved charges change signs around the phase boundary of QCD, which would serve as clear experimental signatures to determine the location of the matter in the phase diagram [15][16][17].Among the fluctuation observables, those of conserved charges can reflect fluctuations produced in earlier stages during the time evolution of fireballs, than non-conserved ones [18]. This is because the variation of a conserved charge in a volume is achieved only through diffusion, which makes the relaxation to equilibrium slower. In fact, it is argued that if the rapidity range of a detector is taken to be sufficiently large, whereas the range should be kept narrow enough so that the rest of ...

Relation between baryon number fluctuations and experimentally observed proton number fluctuations in relativistic heavy ion collisions

“…[25], the authors of the present paper have argued that, whereas the baryon number cumulants are not the direct experimental observables as discussed above, they can be determined in experiments by only using the experimentally measured proton number fluctuations for √ s NN 10GeV. The key idea is that isospins of nucleons in the final state are almost completely randomized and uncorrelated, because of reactions of nucleons with thermal pions in the hadronic stage, as will be elucidated in Sec.…”

“…The main purpose of the present paper is to elaborate the discussion in Ref. [25] with some extensions. In Ref.…”

“…The procedures of the manipulations and discussions omitted in Ref. [25] are also addressed in detail.…”

“…In Ref. [25] the formulas are derived only for isospin symmetric medium. In the present study we extend them to incorporate cases with nonzero isospin densities.…”

Fluctuations of conserved charges in relativistic heavy ion collisions: An introduction

“…2 [28]. It, however, should be remembered that the net-proton number is not a conserved charge and different from net-baryon number [98,99]. In fact, it is shown in Refs.…”