Medium modification of pion production in low-energy $\mathrm{Au}+\mathrm{Au}$ collisions

There is a major mismatch between the charged-pion yields in $\mathrm{Au}+\mathrm{Au}$ collisions at low energies calculated by various transport models and the experimental measured values from the HADES Collaboration. In this work, reasonable improvements on the equation of state, in-medium modification of cross sections, and the influence of the nuclear potential for $\mathrm{\Delta }$ resonances will be investigated in the framework of the GiBUU transport model. As a result, we demonstrate that theoretical calculations can indeed describe the charged-pion yields measured by HADES for $\mathrm{Au}+\mathrm{Au}$ collisions rather well, but that a mismatch then remains between calculations and data for the yields of neutral pions extracted from dileptons within the same experiment.

Figure 1

The binding energy per nucleon and the effective mass as a function of nuclear density for various EOS's [13, 14, 21]. The red band in the plot of the binding energies shows the reference from astrophysical constraints [16].

Figure 2

Particle numbers of nucleons, delta's, and pions over time (note the different scales for different particle multiplicities on the $y$ axis, and the offset in that for the nucleons).

Figure 3

Central baryon density in units of the nuclear density ${\rho }_0=0.16{\mathrm{fm}}^{-3}$ throughout the collision. The vertical line at $t=12\mathrm{fm}/c$ corresponds to the moment of overlap of both nuclei, thus the moment of maximum density.

Figure 4

Comparison of net collision rates for $NN\to N\mathrm{\Delta }$, $NN\to NN\pi$, $NN\to NR$, and $NN\to \mathrm{\Delta }\mathrm{\Delta }$ without (default) and with in-medium modifications.

Figure 5

Proton rapidity spectra without (default) and with in-medium modifications (see text) for beam energies of $0.4A\mathrm{Ge}\mathrm{V}$ (top) and $1.5A\mathrm{Ge}\mathrm{V}$ (bottom) compared to the experimental data from Ref. [18].

Figure 6

Side flow obtained with the EOS by Liu et al. [14] with or without in-medium modifications for beam energies of $0.4A\mathrm{Ge}\mathrm{V}$ (left) and $1.5A\mathrm{Ge}\mathrm{V}$ (right) compared to the experimental data from Ref. [18]. MUL and ERAT are the two prescriptions used by FOPI to determine the impact parameter.

Figure 7

Same as in Fig. 6, but with NL2 by Lang et al. [13] used for the EOS instead.

Figure 8

transverse-momentum spectra of negatively (top) and positively (bottom) charged pions compared to FOPI data at $1.5A\mathrm{Ge}\mathrm{V}$ [19] for the Liu EOS with and without in-medium modifications. The data points shown as empty circles for momenta below $100\mathrm{MeV}$ were not measured but extrapolated.

Figure 9

Rapidity spectra of negatively (top) and positively (bottom) charged pions for the Liu EOS with and without in-medium modifications compared to the experimental data from HADES in Ref. [1].

Figure 10

Rapidity spectra of charged pions, upper (lower) set for ${\pi }^{-}$ (${\pi }^{+}$), without in-medium modifications (default) compared to separately only either introducing the $m^{*}/m$ suppression or the modified $\mathrm{\Delta }$ potential, together with their combined effect (solid red) as in Fig. 9.

Figure 11

Same as in Fig. 10, but with NL2 by Lang et al. [13] used for the EOS instead.

Figure 12

transverse-momentum spectra of negatively (top) and positively (bottom) charged pions for the Liu EOS with and without in-medium modifications (see text) compared to the experimental data from HADES in Ref. [1].

Figure 13

Integrated charged-pion multiplicities for both types of in-medium modifications (with Liu EOS) over the expected numbers of participants for the various centrality cuts [33] compared to the experimental data from Fig. 7 in Ref. [1].

Figure 14

The ratio of calculated multiplicities of ${\pi }^0$ over the average $({\pi }^{+}+{\pi }^{-})/2$ as function of centrality [33].

Figure 15

Invariant-mass spectra of dielectrons for the Liu EOS with and without in-medium modifications of the cross sections compared to data from Ref. [20]. No in-medium broadening of the $\rho$ resonance or $pn$ bremsstrahlungs corrections were included as in Ref. [9], to isolate the effects of an in-medium suppressed pion production here. The insert zooms in on the ${\pi }^0$-Dalitz region using a linear scale for the plot range.