Properties of open and hidden charm mesons in light quark matter

In this work we study the implications of light quark pionic matter at finite temperatures on the properties of open and hidden charm mesons. Meson-meson interactions are described by means of a chiral unitary approach accounting for coupled-channel effects. The in-medium Lippmann-Schwinger equations, which consider the change in self-energy that the mesons acquire from interacting with the surrounding pionic matter, are solved self-consistently, and the spectral functions of the mesons in the hot pion bath are obtained. It is observed that the charmed mesons develop a quite substantial pion induced width, being several tens of MeV at a temperature of 150 MeV. The $J/\psi$ meson stays narrow, but its pionic width at 150 MeV, found to be around 0.1 MeV, is already larger than its vacuum width.

Figure 1

Feynman diagrams representing (a) the Lippmann-Schwinger equation for the meson-pion interaction at finite temperature, (b) the resulting self-energy from closing the pion line, (c) the in-medium meson-meson interaction obtained with dressed propagators, and (d) the resulting meson self-energy, which needs to be obtained self-consistently.

Figure 2

Cross sections for $J/\psi \pi \to X$ employing (a) the nonunitarized amplitudes and (b) the unitarized ones.

Figure 3

Imaginary part of the meson-meson loop as a function of the energy $p^0$ at temperatures $T=50$, 100, and 150 MeV and $\vec{p}=0$. (a) $D\pi$, (b) $D^{*}\pi$, (c) $J/\psi \pi$, and (d) $D{D}^{*}$. Vertical dashed lines correspond to $\mid m_1-m_2\mid$ and $m_1+m_2$. Inset in (d): The $T=0$ case (dot-dashed line) is shown for reference.

Figure 4

Imaginary part of the unitarized amplitude as a function of the energy $p^0$ at temperatures $T=50$, 100, and 150 MeV and $\vec{p}=0$. (a) $D\pi \to D\pi$, (b) $D^{*}\pi \to D^{*}\pi$, (c) $J/\psi \pi \to J/\psi \pi$, and (d) $D{D}^{*}\to D{D}^{*}$. Dashed vertical lines correspond to $\mid m_1-m_2\mid$ and $m_1+m_2$ in (a) and (b) and to $m_{J/\psi }+m_{\pi }$, $m_{{\eta }_c}+m_{\rho }$, and $m_D+m_{D^{*}}$ in (c) and (d).

Figure 5

Imaginary part of the pion induced self-energy as a function of the energy $p^0$ at temperatures $T=50$, 100, and 150 MeV and $\vec{p}=0$. (a) $D$, (b) $D^{*}$, and (c) $J/\psi$. Vertical lines in (a) and (b) indicate $p^0=m_{D^{(*)}}$ and $p^0=m_{D^{(*)}}+2m_{\pi }$, whereas those in (c) mark $m_{J/\psi }$, $m_{J/\psi }+2m_{\pi }$, and $m_D+m_{D^{*}}+m_{\pi }$.

Figure 6

Meson spectral function as a function of the energy $p^0$ at temperatures $T=50$, 100, and 150 MeV and $\vec{p}=0$. (a) $D$, (b) $D^{*}$, (c) $J/\psi$, and (d) $J/\psi$ on a logarithmic scale.

Figure 7

Pion induced width as a function of the temperature at the meson mass and $\vec{p}=0$. (a) $D$, (b) $D^{*}$, and (c) $J/\psi$. To illustrate the process of achieving self-consistent results we show this for different iterations $n$. Further details are given in the text.