Analysis of pseudoscalar and scalar $D$ mesons and charmonium decay width in hot magnetized asymmetric nuclear matter

In this paper, we calculate the mass shift and decay constant of isospin-averaged pseudoscalar $(D^{+},D^0)$ and scalar $(D_0^{+},D_0^0)$ mesons by the magnetic-field-induced quark and gluon condensates at finite density and temperature of asymmetric nuclear matter. We have calculated the in-medium chiral condensates from the chiral $\mathrm{SU}\left(3\right)$ mean-field model and subsequently used these condensates in QCD sum rules to calculate the effective mass and decay constant of $D$ mesons. Consideration of external magnetic-field effects in hot and dense nuclear matter lead to appreciable modification in the masses and decay constants of $D$ mesons. Furthermore, we also studied the effective decay width of higher charmonium states $[\psi \left(3686\right),\psi \left(3770\right),{{\chi }_c}_0\left(3414\right),{{\chi }_c}_2\left(3556\right)]$ as a by-product by using the ${}^3\mathrm{P}_0$ model, which can have an important impact on the yield of $J/\psi$ mesons. The results of the present work will be helpful to understand the experimental observables of heavy-ion colliders which aim to produce matter at finite density and moderate temperature.

Figure 1

The light quark condensates $({\langle \overline{u}u\rangle }_{{\rho }_N}$ and ${\langle \overline{d}d\rangle }_{{\rho }_N})$ and gluon condensate ${〈\frac{{\alpha }_s}{\pi }{G}_{\mu \nu }^a{G^a}^{\mu \nu }〉}_{{\rho }_N}$ (denoted by $G_{{\rho }_N})$ is plotted for symmetric nuclear matter $(\eta =0)$ as a function of magnetic field $eB$ under different conditions of medium.

Figure 2

The light quark condensates $({\langle \overline{u}u\rangle }_{{\rho }_N}$ and ${\langle \overline{d}d\rangle }_{{\rho }_N})$ and gluon condensate ${〈\frac{{\alpha }_s}{\pi }{G}_{\mu \nu }^a{G^a}^{\mu \nu }〉}_{{\rho }_N}$ (denoted by $G_{{\rho }_N})$ is plotted for asymmetric nuclear matter $(\eta \ne 0)$ as a function of magnetic field $eB$ under different conditions of medium.

Figure 3

Comparison of quark ${\langle \overline{q}q\rangle }_{{\rho }_N}$ and gluon condensates ${〈\frac{{\alpha }_s}{\pi }{G}_{\mu \nu }^a{G}^{a\mu \nu }〉}_{{\rho }_N}$ (denoted by $G_{{\rho }_N})$ calculated in the chiral SU(3) model and in the linear density approximation.

Figure 4

The effective masses of protons and neutrons are plotted for symmetric and asymmetric nuclear matter as a function of magnetic field $eB$ under different conditions of medium.

Figure 5

The effective mass of pseudoscalar $D^{+}$ (charged) and $D^0$ (uncharged) mesons is plotted as a function of magnetic field $eB$ under different conditions of medium.

Figure 6

The shift in decay constant of pseudoscalar $D^{+}$ (charged) and $D^0$ (uncharged) mesons is plotted as a function of magnetic field $eB$ under different conditions of medium.

Figure 7

The effective mass of scalar $D_0^{+}$ (charged) and $D_0^0$ (uncharged) mesons is plotted as a function of magnetic field $eB$ under different conditions of medium.

Figure 8

The shift in decay constant of scalar $D_0^{+}$ (charged) and $D_0^0$ (uncharged) mesons is plotted as a function of magnetic field $eB$ under different conditions of medium.

Figure 9

The effective decay width of the charmonium state $\psi \left(3686\right)$ decaying into $D\overline{D}$ pairs is plotted as a function of magnetic field $eB$ under different conditions of medium.

Figure 10

The effective decay width of the charmonium state $\psi \left(3770\right)$ decaying into $D\overline{D}$ pairs is plotted as a function of magnetic field $eB$ under different conditions of medium.