Resonance decay dynamics and their effects on $p_T$ spectra of pions in heavy-ion collisions

The influence of resonance decay dynamics on the momentum spectra of pions in heavy-ion collisions is examined. Taking the decay processes $\omega \to 3\pi$ and $\rho \to 2\pi$ as examples, I demonstrate how the resonance width and details of decay dynamics (via the decay matrix element) can modify the physical observables. The latter effect is commonly neglected in statistical models. To remedy the situation, a theoretical framework for incorporating hadron dynamics into the analysis is formulated, which can be straightforwardly extended to describe general $N$-body decays.

Figure 1

Differential phase space function $\mathrm{dPS}$ calculated by Eq. (4) for the decay $\omega \to 3\pi$. Solid line corresponds to calculation with the full matrix element (19) while dashed line corresponds to result from the isotropic approximation.

Figure 2

The midrapidity (a) and rapidity-integrated (b) $p_T$ spectra of decay pions from $\omega$-meson decay [static source, $T=120$ MeV at ${\mu }_{\omega }=0\mathrm{MeV}\left(\mathrm{black}\right),100\mathrm{MeV}\left(\mathrm{blue}\right)$], calculated for full decay matrix element in Eq. (19) and for the isotropic case. Also shown (as points) are the corresponding results (at ${\mu }_{\omega }=0$) including the width of the $\omega$ meson via the $S$-matrix approach from Eq. (32), for the case of physical resonance width and the case in which the width is scaled up 10 times.

Figure 3

Generalized phase shift function $\mathcal{Q}$ (a) and the effective spectral function $B$ (b) computed from Eq. (30) for the model amplitude (29). The results are shown for the case of physical resonance width and the case in which the width is scaled up 10 times.

Figure 4

The midrapidity (a) and rapidity-integrated (b) $p_T$ spectra of decay pions from $\rho$-meson decay (static source, $T=120$ MeV). The $S$-matrix treatment of $\rho$ meson is discussed in Refs. [35, 36]. The low-$p_T$ enhancement from $B\left(M\right)$ is clearly visible.