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 $\mathrm{fm}∕c$ 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 reproduces 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 $Q_{\mathrm{inv}}$.

Figure 1

Balance functions for charged pion pairs as measured by the STAR Collaboration. For each charged pion, there is an enhanced probability of finding an extra charged pion of the opposite sign within a unit of rapidity. The peripheral data are well reproduced by the HIJING model, which can be considered as being caused by overlapping independent $pp$ collisions.

Figure 2

The mean widths of ${\pi }^{+}{\pi }^{-}$ balance functions as measured by STAR. For small impact parameters $b$, the balance function becomes narrower, qualitatively consistent with expectations for a quark-gluon plasma. For peripheral collisions, the width matches predictions from HIJING.

Figure 3

${\pi }^{+}{\pi }^{-}$ balance functions for RQMD are shown for both $pp$ and $\mathrm{Au}+\mathrm{Au}$ collisions assuming a perfect detector. In contrast to the experimental results of [2], the balance function is slightly broader for central $\mathrm{Au}+\mathrm{Au}$ collisions.

Figure 4

Balance functions for HIJING with and without the hadronic cascade GROMIT are shown as a function of the rapidity difference in the upper panel and as a function of $Q_{\mathrm{inv}}$ in the lower panel. These results have incorporated the STAR acceptance, but not the efficiency. The incorporation of the cascade leads to a slightly broadened balance function when analyzed as a function of $\mathrm{\Delta }y$ and a narrower balance function when analyzed as a function of $Q_{\mathrm{inv}}$. This apparent contradiction derives from the failure of HIJING∕GROMIT to correctly describe the dependence of $⟨p_t⟩$ as a function of centrality.

Figure 5

Balance function results for a pion gas (dotted lines) and for a resonance gas (dashed lines) are shown for the canonical thermal blast-wave model. Resonances clearly narrow the balance function when plotted against $Q_{\mathrm{inv}}$ (upper panel) but have little effect on the balance function when plotted as a function of the rapidity difference (lower panel). Balance functions corrected for interpair correlations (solid lines) again differ when plotted as a function of $Q_{\mathrm{inv}}$. The additional distortion arises from the effects of Coulomb interaction, symmetrization, and a more sophisticated treatment of the strong interaction.

Figure 6

Balance functions from $200A\mathrm{GeV}$ $\mathrm{Au}+\mathrm{Au}$ collisions measured by STAR are compared to the canonical blast-wave model described in the text. The model should set a lower bound for the width of a balance function provided the particles are emitted thermally. The remarkable agreement with the data suggests that charge conservation remains highly localized at breakup.