Charge Balance Function Research Articles

Charge Conservation and the Shape of the Ridge of Two-Particle Correlations in Relativistic Heavy-Ion Collisions

We demonstrate that, in the framework of the event-by-event hydrodynamics followed by statistical hadronization, the proper charge conservation in the mechanism of hadron production provides the crucial nonflow component and leads to agreement with the two-dimensional two-particle correlation data in relative azimuthal angle and pseudorapidity at soft transverse momenta (p(T)<2 GeV). The falloff of the same-side ridge in relative pseudorapidity follows from the fact that a pair of particles with balanced charges is emitted from the same fluid element, whose collective velocity collimates the momenta of the pair. We reproduce basic experimental features of the two-dimensional correlation function, such as the dependence on the relative charge and centrality, as well as the related charge balance functions and the harmonic flow coefficients as functions of the relative pseudorapidity.

General charge balance functions: A tool for studying the chemical evolution of the quark-gluon plasma

In the canonical picture of the evolution of the quark-gluon plasma during a high-energy heavy-ion collision, quarks are produced in two waves. The first is during the first fm/c of the collision, when gluons thermalize into the QGP. After a roughly isentropic expansion that roughly conserves the number of quarks, a second wave ensues at hadronization, 5-10 fm/c into the collision. Since each hadron contains at least two quarks, the majority of quark production occurs at this later time. For each quark produced in a heavy-ion collision, an anti-quark of the same flavor is created at the same point in space-time. Charge balance functions identify, on a statistical basis, the location of balancing charges for a given hadron, and given the picture above one expects the distribution in relative rapidity of balancing charges to be characterized by two scales. After first demonstrating how charge balance functions can be created using any pair of hadronic states, it will be shown how one can identify and study both processes of quark production. By considering balance functions of several hadronic species, and by performing illustrative calculations, this class of measurement appears to hold the prospect of providing the field's most stringent insight into the chemical evolution of the QGP.

The study of longitudinal properties of the charge balance function

The charge balance function is studied in Au + Au collisions at \(\surd \overline {s_{NN} } \) GeV using the STAR detector at the Relativistic Heavy-Ion Collider. Within the acceptance of the STAR TPC, it is found that the balance function is independent of the position of pseudorapidity windows with equal-size. It is also demonstrated for the first time at RHIC that the balance function divided by a scaling factor related to pseudorapidity is independent of the width and position of the pseudorapidity window. Moreover, Such a scaled balance function is further found to exist in the subset of particles with the same restricted transverse-momentum range.

Statistical model analysis of the charge balance function at RHIC

The balance functions have been computed for charged particle pairs and charged pion pairs in a hydrodynamics-motivated thermal model with resonances. These balance functions are presented in terms of the relative pseudorapidity Δη, the relative rapidity Δy and the relative azimuthal angle Δϕ. With suitably parameterized thermal freeze-out temperature and transverse flow velocity, the values of the model-calculated balance function are generally lower than those from the most central Au + Au collisions, while the widths of the model calculated balance function are fairly close to those from central Au + Au collisions. The dependence of the balance function on the position of the pseudorapidity window is also studied.

Longitudinal scaling property of the charge balance function in [formula omitted] collisions at [formula omitted

We present measurements of the charge balance function, from the charged particles, for diverse pseudorapidity and transverse momentum ranges in Au+Au collisions at sNN=200 GeV using the STAR detector at RHIC. We observe that the balance function is boost-invariant within the pseudorapidity coverage [−1.3,1.3]. The balance function properly scaled by the width of the observed pseudorapidity window does not depend on the position or size of the pseudorapidity window. This scaling property also holds for particles in different transverse momentum ranges. In addition, we find that the width of the balance function decreases monotonically with increasing transverse momentum for all centrality classes.

Longitudinal boost invariance of the charge balance function in hadron-hadron and nucleus-nucleus collisions

Using Monte Carlo generators of the PYTHIA model for hadron-hadron collisions and a multiphase transport (AMPT) model for nucleus-nucleus collisions, the longitudinal boost invariance of charge balance function and its transverse-momentum dependence are carefully studied. It shows that the charge balance function is boost invariant in both $p+p$ and $\mathrm{Au}+\mathrm{Au}$ collisions in these two models, consistent with experimental data. The balance function properly scaled by the width of the pseudorapidity window is independent of the position or the size of the window and is corresponding to the balance function of the whole pseudorapidity range. This longitudinal property of balance function also holds for particles in small transverse-momentum ranges in the PYTHIA and the AMPT default models, but is violated in the AMPT with string melting. The physical origin of the results is discussed.

Two-particle azimuthal angle correlations and azimuthal charge balance function in relativistic heavy ion collisions

The two-particle azimuthal angle correlation (TPAC) and azimuthal charge balance function (ACBF) are used to study the anisotropic expansion in relativistic heavy ion collisions. It is demonstrated by the relativistic quantum molecular dynamics (RQMD) model and a multi-phase transport (AMPT) model that the small-angle correlation in TPAC indeed presents anisotropic expansion, and the large-angle (or back-to-back) correlation is mainly due to global momentum conservations. The AMPT model reproduces the observed TPAC, but the RQMD model fails to reproduce the strong correlations in both small and large azimuthal angles. The width of ACBF from RQMD and AMPT models decreases from peripheral to central collisions, consistent with experimental data, but in contrast to the expectation from thermal model calculations. The ACBF is insensitive to anisotropic expansion. It is a probe for the mechanism of hadronization, similar to the charge balance function in rapidity.

ON THE RELATION BETWEEN THE WIDTH OF CHARGE BALANCE FUNCTION AND HADRONIZATION TIME IN RELATIVISTIC HEAVY ION COLLISION

A Monte Carlo study on the charge balance function in high energy hadron-hadron and relativistic heavy ion collisions are carried out using the Monte Carlo generators PYTHIA and AMPT, respectively. A strong dependence of the width of balance function on multiplicity is found in both cases. Using the mean parton-freeze-out time of a heavy-ion-collision event as the characteristic hadronization time for the event, it is found that for a fixed multiplicity interval the width of balance function is consistent with being independent of hadronization time.

PSEUDORAPIDITY AND TRANSVERSE MOMENTUM DEPENDENCE OF CHARGE BALANCE IN Au−Au COLLISIONS AT $\sqrt{s_{NN}} = 200\, {\rm GeV}$

The charge balance function (BF) is studied in Au − Au collisions at [Formula: see text] using the STAR detector. It is observed that within the acceptance (−1.3 &lt; η &lt; 1.3) of STAR Time Projection Chamber (TPC), the BF is independent of the position of the windows of same size, showing that BF is boost-invariant in the TPC accepted region. It is found that the BF measured in an observed window η w , B(δη|η w ), divided by [Formula: see text] is independent of the size and position of the observed window η w . These properties of BF hold for different transverse momenta and the width of BF decreases with the increasing of the latter. The result supports the delayed-hadronization scenario in thermal models.

Two-charge-particle azimuthal correlations and the azimuthal balance function in RQMD and AMPT

Two-charge-particle azimuthal correlations (TCPAC) and the azimuthal charge balance function (ACBF) are compared with anisotropic flow by using transport models, RQMD and AMPT. In these two models, TCPAC has the same centrality dependence as anisotropic flow. The momentum conservation contributes only back-to-back correlations in TCPAC, which are well separated from small angle correlations caused by anisotropic transverse momentum distribution, while the centrality dependence of ACBF is different from those of anisotropic flow and TCPAC. This indicates that ACBF cannot be used as another presentation of anisotropic flow, as expected from thermal models.

RAPIDITY DEPENDENCE OF CHARGE FLUCTUATIONS AND CORRELATIONS IN HADRONIC AND NUCLEAR COLLISIONS

Size and position of rapidity window dependence of charge fluctuations and correlations are studied by PYTHIA and RQMD models for hadron–hadron and nucleus–nucleus collisions respectively. The results show that all the measures for charge fluctuations and correlations depend on the size of central rapidity windows and most of them depend on the position of the rapidity windows, which is not expected. Only charge balance function in hadron–hadron collisions is independent of the position of rapidity window, i.e. boost-invariant, in consistent with corresponding experimental data, while charge fluctuations measured by D(Q) is not boost-invariant in contrast to the experimental data. The measures for three kind of charge correlations (R++, R--, R+-) show a good account for the behavior of charge correlations and global charge conservation in longitudinal phase space in both PYTHIA and RQMD.

Narrowing of the charge balance function and hadronization time in relativistic heavy-ion collisions

The width of charge balance function in high energy hadron-hadron and relativistic heavy-ion collisions are studied using the Monte Carlo generators PYTHIA and AMPT, respectively. The narrowing of balance function as the increase of multiplicity is found in both cases. The mean parton-freeze-out time of a heavy-ion collision event is used as the characteristic hadronization time for the event. It turns out that for a fixed multiplicity interval the width of balance function is consistent with being independent of hadronization time.

Boost invariance and multiplicity dependence of the charge balance function in π+p and K+p collisions at s=22 GeV

Boost invariance and multiplicity dependence of the charge balance function are studied in $\pi^{+}\rp$ and $\rK^{+}\rp$ collisions at 250 GeV/$c$ incident beam momentum. Charge balance, as well as charge fluctuations, are found to be boost invariant over the whole rapidity region, but both depend on the size of the rapidity window. It is also found that the balance function becomes narrower with increasing multiplicity, consistent with the narrowing of the balance function when centrality and/or system size increase, as observed in current relativistic heavy ion experiments.

Rapidity, azimuthal, and multiplicity dependence of mean transverse momentum and transverse momentum correlations inπ+pandK+pcollisions ins=22 GeV

Rapidity, azimuthal and multiplicity dependence of mean transverse momentum and transverse momentum correlations of charged particles is studied in ${\ensuremath{\pi}}^{+}\mathrm{p}$ and ${\mathrm{K}}^{+}\mathrm{p}$ collisions at $250\text{ }\text{ }\mathrm{GeV}/c$ incident beam momentum. For the first time, it is found that the rapidity dependence of the two-particle transverse momentum correlation is different from that of the mean transverse momentum, but both have similar multiplicity dependence. In particular, the transverse momentum correlations are boost invariant. This is similar to the recently found boost invariance of the charge balance function. A strong azimuthal dependence of the transverse momentum correlations originates from the constraint of energy-momentum conservation. The results are compared with those from the PYTHIA Monte Carlo generator. The similarities to and differences with the results from current heavy ion experiments are discussed.

Balance of baryon number in the quark coalescence model

The charge and baryon balance functions are studied in the coalescence hadronization mechanism of quark–gluon plasma. Assuming that in the plasma phase the qq¯ pairs form uncorrelated clusters whose decay is also uncorrelated, one can understand the observed small width of the charge balance function in the Gaussian approximation. The coalescence model predicts even smaller width of the baryon–antibaryon balance function: σBB¯/σ+−=2/3.

The balance function in azimuthal angle is a measure of the transverse flow

The charge or barion number balance function in the relative azimuthal angle of a pair of particles emitted in ultrarelativistic heavy-ion collisions is studied. The π+π− and pp¯ balance functions are computed using thermal models with two different set of parameters, corresponding to a large freeze-out temperature and a moderate transverse flow or a small temperature and a large transverse flow. The single-particle spectra including pions from resonance decays are similar for the two scenarios, on the other hand the azimuthal balance function is very different and could serve as an independent measure of the transverse flow at the freeze-out.

Bringing the Balance Function into Focus

Charge balance functions provide important insight concerning hadronization and charge transport in heavy ion collisions at RHIC. Unfortunately, this observable is clouded by several effects. One of these effects is resonance production. Here, we present a simple thermal model where resonance production is included via a Monte Carlo technique based on the canonical ensemble. Resonance production is not found to have a large effect on the width.

Statistical and dynamic models of charge balance functions

Charge balance functions, which identify balancing particle-antiparticle pairs on a statistical basis, have been shown to be sensitive to whether hadronization is delayed by several fm/c in relativistic heavy ion collisions. Results from two classes of models are presented here, microscopic hadronic models and thermal models. The microscopic models give results which are contrary to recently published pi+pi- balance functions from the STAR collaboration, whereas the thermal model roughly reproduce the experimental results. This suggests that charge conservation is local at breakup, which is in line with expectations for a delayed hadronization. Predictions are also presented for balance functions binned as a function of Q_inv.

Removing distortions from charge balance functions

Charge balance functions provide insight into critical issues concerning hadronization and transport in heavy-ion collisions by statistically isolating charge/anti-charge pairs which are correlated by charge conservation. However, distortions from residual interactions and unbalanced charges cloud the observable. Within the context of simple models, the significance of these effects is studied by constructing balance functions in both relative rapidity and invariant relative momentum. Methods are presented for eliminating or accounting for these distortions.

Correlations and fluctuations, a summary of Quark Matter 2002

Results for correlations and fluctuations presented at Quark Matter 2002 are summarized. These results include Hanbury-Brown Twiss interferometry of a wide variety of species, large scale fluctuations and correlations in p t and multiplicity, and charge fluctuations and charge balance functions.