Dilepton production in nucleus-nucleus collisions at top CERN Super Proton Synchrotron energy of 158$A$ GeV within the parton-hadron-string dynamics transport approach

Dilepton production in $\mathrm{In}+\mathrm{In}$ collisions at 158$A$ GeV is studied within the microscopic parton-hadron-string dynamics (PHSD) transport approach that incorporates explicit partonic degrees of freedom and dynamical hadronization as well as the more familiar hadronic dynamics in the final reaction stages. A comparison to the data of the NA60 Collaboration shows that the measured dilepton yield is well described by including the collisional broadening of vector mesons, while simultaneously accounting for the electromagnetic radiation of the strongly coupled quark-gluon plasma (sQGP) via off-shell quark-antiquark annihilation, quark annihilation with additional gluon bremsstrahlung, and the gluon-Compton scattering mechanisms. In particular, the spectra in the intermediate mass range (1 GeV $⩽M⩽2.5$ GeV) are dominated by quark-antiquark annihilation in the nonperturbative QGP. Also, the observed softening of the transverse mass spectra at intermediate masses (1 GeV $⩽M⩽2.5$ GeV) is approximately reproduced. Furthermore, for dileptons of low masses ($M<0.6$ GeV), we find a sizable contribution from the quark annihilation with additional gluon bremsstrahlung, thus providing another possible window for probing the properties of the sQGP.

Figure 1

The number of $q+\overline{q}$ (a) and $q+g$ (b) collisions, in which a dilepton pair is produced, in a central $\mathrm{In}+\mathrm{In}$ reaction at an incident energy of 158$A$ GeV versus the masses of the (quasiparticle) quark and antiquark as resulting from PHSD.

Figure 2

Number of parton collisions per event in a central $\mathrm{In}+\mathrm{In}$ reaction at an incident energy of 158$A$ GeV versus the invariant energy $\sqrt{s}$ of the elementary partonic collision as simulated in PHSD. The number of $q+\overline{q}$ collisions is given by the solid (red) line while that of $q+g$ collisions is given by the dashed (blue) line.

Figure 3

Diagrams contributing to dilepton production from the QGP: (a) Drell-Yan mechanism, (b) gluon-Compton scattering (GCS), (c) vertex correction, and (d) gluon bremsstrahlung (NLODY), where virtual photons (wavy lines) split into lepton pairs, spiral lines denote gluons, and arrows denote quarks. In each diagram the time runs from left to right.

Figure 4

Diagrams contributing to dilepton production by virtual quasiparticles in addition to those presented in Fig. 3. First three diagrams: The decay of a virtual quark. The last two diagrams: The decay of a virtual gluon. Virtual photons (wavy lines) split into lepton pairs, spiral lines denote gluons, and arrows denote quarks.

Figure 5

(a) Cross sections for the reactions $e^{+}{e}^{-}\to \pi +\rho$ (a) and $e^{+}{e}^{-}\to \pi +\omega$ (b) in our model versus the experimental data. Panel (c) gives the measured cross section of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\pi }^0$ reaction versus the sum of the model cross sections for $e^{+}{e}^{-}\to \pi +\omega$, $e^{+}{e}^{-}\to \pi +a_1$, and $e^{+}{e}^{-}\to \rho +\rho$.

Figure 6

Rates of dileptons created in $q+\overline{q}$ and $\pi +\pi$ annihilations within a thermalized gas of quarks with temperature $T_{\mathrm{QGP}}$ and pions with temperature $T_{\pi }$. (a) $T_{\mathrm{QGP}}=250$ MeV, $T_{\pi }=150$ MeV; (b) $T_{\mathrm{QGP}}=T_{\pi }=190$ MeV.

Figure 7

The HSD results for the mass differential dilepton spectra from $\mathrm{In}+\mathrm{In}$ collisions at 158$A$ GeV in comparison to the excess mass spectrum from the NA60 Collaboration [11]. The actual NA60 acceptance filter and mass resolution have been incorporated [79]. The solid lines show the HSD results for a scenario including the collisional broadening of the $\rho$ meson whereas the dashed lines correspond to calculations with “free” $\rho$ spectral functions for reference. The dash-dotted lines represent the HSD calculations for the dropping mass $+$ collisional broadening model. The wide (light blue) bands represent the PHSD results incorporating direct dilepton radiation from the QGP in addition to a broadened $\rho$ meson.

Figure 8

Acceptance-corrected mass spectra of excess dimuons from $\mathrm{In}+\mathrm{In}$ at 158$A$ GeV integrated over $p_T$ in $0.2<p_T<2.4$ GeV from PHSD compared to the data of the NA60 Collaboration [81]. The dash-dotted line shows the dilepton yield from the in-medium $\rho$ with a broadened spectral function, the dashed line presents the yield from the $q+\overline{q}$ annihilation, the dash-dot-dot line gives the contribution of the gluon bremsstrahlung process ($q\overline{q}\to g{l}^{+}{l}^{-}$), and the solid line is the sum of all contributions. For the description of the other lines, which correspond to the nondominant channels, please refer to the figure legend.

Figure 9

Dilepton radiation from $\rho$ mesons of different origins in PHSD from central $\mathrm{In}+\mathrm{In}$ collisions at 158$A$ GeV compared to the contributions from the 4$\pi$ processes ($a_1+\pi$, $\pi +\omega$, and $\rho +\rho$). The direct $\rho$ mesons produced in mesonic and baryonic strings are given by the dashed line and the thermal $\rho$ mesons produced in $\pi +\pi$ annihilations are given by the dash-dotted line. The contributions of the $4\pi$ processes are shown by the lines with symbols: the $\pi +a_1\to l^{+}{l}^{-}$ process is displayed by the line with stars, the $\pi +w\to l^{+}{l}^{-}$ process by the line with squares, and the $\rho +\rho \to l^{+}{l}^{-}$ process by the line with circles.

Figure 10

Mass spectra of excess dimuons from $\mathrm{In}+\mathrm{In}$ at 158$A$ GeV for $0.2<p_T<2.4$ GeV and $3<\eta <4.2$ from PHSD for different centrality bins. The dash-dotted, dashed, and solid lines show, respectively, the dilepton yield from the in-medium $\rho$ meson with a broadened spectral function, the dilepton yield from the $q+\overline{q}$ annihilation, and the sum of them.

Figure 11

Number of charged particles as a function of the impact parameter from HSD (solid lines) and PHSD (dash-dot lines) integrated over rapidity (upper lines) and within the pseudorapidity acceptance window of the NA60 experiment (lower lines). The vertical dashed lines indicate the different centrality classes.

Figure 12

Acceptance-corrected mass spectra of excess dimuons from $\mathrm{In}+\mathrm{In}$ collisions at 158$A$ GeV for different transverse-momentum bins from PHSD compared to the data of the NA60 Collaboration [11, 81]. The dash-dot, dash-dot-dot, and solid lines show, respectively, the dilepton yield from the in-medium $\rho$ meson with a broadened spectral function, the dilepton yield from $q+\overline{q}$, and the sum of them.

Figure 13

Transverse mass spectra of dileptons for $\mathrm{In}+\mathrm{In}$ at 158$A$ GeV in PHSD compared to the data of the NA60 Collaboration [11, 81].

Figure 14

The inverse slope parameter $T_{\mathrm{eff}}$ of the dimuon yield from In $+$ In at 158$A$ GeV as a function of the dimuon invariant mass in PHSD compared to the data of the NA60 Collaboration [11, 81].