Initial Baryon Stopping and Angular Momentum in Heavy-Ion Collisions

TL;DR

The paper addresses how initial orbital angular momentum in noncentral heavy-ion collisions is deposited into the early fireball and how baryon stopping shapes the angular-momentum distribution across rapidity. It introduces Glauber+, an extended Glauber framework that computes rapidity distributions of net baryon number and angular momentum by incorporating a rapidity-loss mechanism via an elasticity parameter $e$ and fluctuations drawn from a logit-normal distribution $f(e)$. Calibrating to net-proton data, the authors derive an energy-dependent average stopping $\bar{e}(Y_{ m beam}) = 0.2075 + 0.0500 Y_{ m beam}$ and predict that the angular-momentum per produced charged particle at mid-rapidity peaks near $5$ GeV, with $J_y/B$ increasing with beam energy. Overall, Glauber+ provides a practical framework to constrain initial conditions for spin polarization studies and serves as a basis for Monte Carlo simulations connecting early angular momentum to final-state polarization signals.

Abstract

Noncentral heavy-ion collisions create fireballs with large initial orbital angular momentum that is expected to induce strong vorticity in the hot bulk fluid and generate global spin polarization of the produced particles. As the collision beam energy $\sqrt{s_{\rm NN}}$ decreases to approach the two-nucleon-mass threshold, this initial angular momentum approaches zero. One may thus expect that the observed global spin polarization should reach a maximum and then drop to zero as increased stopping competes with decreased initial momentum. Recent experimental measurements, however, appear to show a continual rise of hyperon polarization even down to $\sqrt{s_{\rm NN}} =$ 2.42 GeV, suggesting a peak very near threshold which is difficult to interpret and calls for a better understanding of angular momentum initial conditions, especially at low energy. Here, we develop a new Glauber-based initial state model ("Glauber+") to investigate the initial distribution of angular momentum with respect to rapidity as well as the dependence of this distribution on initial baryon stopping across a wide range of collisional beam energy. We estimate that the angular momentum per produced final charged particle at mid-rapidity peaks around 5 GeV, which may present a potential challenge to an interpretation of the spin polarization measurements near threshold as being a consequence of the initial angular momentum of the colliding system.

Figures (10)

• Figure 1: Rapidity distribution of baryon number $dB / dY$ versus rapidity $Y$, for a variety of selected parameter values.
• Figure 2: Rapidity distribution of angular momentum $dJ_y / dY$ versus rapidity $Y$, for a variety of selected parameter values.
• Figure 3: (a) The extracted optimal $\bar{e}$ values at several beam energies where STAR measurements are available. A linear fit of this dependence is shown as the straight line. See text for details. (b) The corresponding average rapidity loss $\langle Y_{\rm loss} \rangle = (1 - \bar{e}) Y_{\rm beam}$, computed with $\bar{e}$ from the fit in (a).
• Figure 4: The triply-differential baryon number density $d^3B / dxdydY$ (in $\textrm{fm}^{-2}$) evaluated at $y = 0$ for a few choices of $\sqrt{s_{\rm NN}}$ and $b$. Calibrated $\bar{e}$ values are used, and $\sigma = 1.0$. Note the reflection symmetry of the density with respect to $(x, Y)$.
• Figure 5: The net baryon number $B$ in mid-rapidity $|Y| < 1$ versus centrality at different beam energies $\sqrt{s_{\rm NN}}$. Note that some of the lowest energies produce visually indistinguishable curves here.