Heavy vector and axial-vector mesons in hot and dense asymmetric strange hadronic matter

We calculate the effects of finite density and temperature of isospin asymmetric strange hadronic matter, for different strangeness fractions, on the in-medium properties of vector $\left(D^{*},D_s^{*},B^{*},B_s^{*}\right)$ and axial-vector $\left(D_1,D_{1s},B_1,B_{1s}\right)$ mesons, using the chiral hadronic SU(3) model and QCD sum rules. We focus on the evaluation of in-medium mass-shift and shift in decay constant of above vector and axial-vector mesons. In the quantum chromodynamics sum rule approach, the properties, e.g., the masses and decay constants of vector and axial-vector mesons are written in terms of quark and gluon condensates. These quark and gluon condensates are evaluated in the present work within the chiral SU(3) model, through the medium modification of scalar-isoscalar fields $\sigma$ and $\zeta$, the scalar-isovector field $\delta$, and the scalar dilaton field $\chi$, in the strange hadronic medium which includes both nucleons as well as hyperons. As we shall see in detail, the masses and decay constants of heavy vector and axial-vector mesons are affected significantly from isospin asymmetry and the strangeness fraction of the medium, and these modifications may influence the experimental observables produced in heavy-ion collision experiments. The results of present investigations of in-medium properties of vector and axial-vector mesons at finite density and temperature of strange hadronic medium may be helpful for understanding the experimental data from heavy-ion collision experiments in particular for the compressed baryonic matter (CBM) experiment of the FAIR facility at GSI, Germany.

Figure 1

In the above figure, (a)–(c) show the variation of ratio of the in-medium value to the vacuum value of scalar fields, $\sigma /{\sigma }_0, \zeta /{\zeta }_0$, and $\chi /{\chi }_0$ as a function of baryonic density, ${\rho }_B$ (in units of nuclear saturation density, ${\rho }_0$). In (d) we have shown the scalar-isovector field $\delta$ as a function of density of medium. We show the results at temperatures $T$ = 0 and 100 MeV. For each value of temperature, the results are plotted for isospin asymmetry parameters $I$ = 0 and 0.5, and the strangeness fractions $f_s$ =0 and 0.5.

Figure 2

In the above figure, we plot the ratio of in-medium quark condensate to vacuum condensate, as a function of baryonic density ${\rho }_B$ (in units of nuclear saturation density, ${\rho }_0$). We compare the results at isospin asymmetric parameters $I$ = 0 and 0.5. For each value of isospin asymmetry parameter $I$, the results are shown for strangeness fractions $f_s$ =0 and 0.5 and temperatures $T=0$ and 100 MeV.

Figure 3

In the above figure, we plot the ratio of in-medium scalar gluon condensate to the vacuum value of gluon condensate, as a function of baryonic density ${\rho }_B$ (in units of nuclear saturation density ${\rho }_0$). We compare the results at isospin asymmetric parameters $I$ = 0 and 0.5. For each value of isospin asymmetry parameter $I$, the results are shown for strangeness fractions $f_s=0$ and 0.5 and temperatures $T=0$ and 100 MeV. In the $y$ axis, $G=〈\frac{{\alpha }_s}{\pi }{G}_{\mu \nu }^a{G}^{\mu \nu a}〉$ and $G_0$ denotes the expectation value of gluon condensate for zero density and temperature.

Figure 4

In the above figure, the variation of mass shift of vector mesons $D^{*}$ ($D^{*+}$ and $D^{*0}$) and $B^{*}$ ($B^{*+}$ and $B^{*0}$) is shown as a function of the squared Borel mass parameter $M^2$. We compare the results at temperatures $T$ = 0 and $T=100$ MeV. For each value of temperature, the results are shown for isospin asymmetric parameters $I$ = 0 and 0.5 and the strangeness fractions $f_s$ = 0 and 0.5.

Figure 5

In the above figure, the variation of shift in the decay constant of vector mesons $D^{*}$ ($D^{*+}$ and $D^{*0}$) and $B^{*}$ ($B^{*+}$ and $B^{*0}$), is shown as a function of squared Borel mass parameter $M^2$. We compare the results at temperatures $T$ = 0 and $T=100$ MeV. For each value of temperature, the results are shown for isospin asymmetric parameters $I$ = 0 and 0.5, and the strangeness fractions $f_s$ = 0 and 0.5.

Figure 6

In the above figure, the variation of shift in mass and the decay constant of strange vector mesons $D_s^{*}$ and $B_s^{*}$ is shown as a function of squared Borel mass parameter $M^2$. We show the results at temperatures $T=0$ and $T=100$ MeV. For each value of temperature, the results are shown for isospin asymmetry parameter $I$ = 0 and 0.5, and the strangeness fractions $f_s$ = 0 and 0.5.

Figure 7

In the above figure, the variation of mass shift of axial-vector mesons, $D_1$ ($D_1^{+}$ and $D_1^0)$ and $B_1$ ($B_1^{+}$ and $B_1^0)$, is shown as a function of squared Borel mass parameter $M^2$. We compare the results at temperatures $T$ = 0 and $T=100$ MeV. For each value of temperature, the results are shown for isospin asymmetric parameters $I$ = 0 and 0.5 and the strangeness fractions $f_s$ = 0 and 0.5.

Figure 8

In the above figure, the variation of shift in decay constant of axial-vector mesons, $D_1$ ($D_1^{+}$ and $D_1^0)$ and $B_1$ ($B_1^{+}$ and $B_1^0)$, is shown as a function of squared Borel mass parameter $M^2$. We compare the results at temperatures $T$ = 0 and $T=100$ MeV. For each value of temperature, the results are shown for isospin asymmetric parameters $I$ = 0 and 0.5 and the strangeness fractions $f_s$ = 0 and 0.5.

Figure 9

In the above figure, the variation of shift in mass and decay constant of strange axial-vector mesons $D_{1s}$ and $B_{1s}$, is shown as a function of squared Borel mass parameter $M^2$. We show the results at temperatures $T=0$ and $T=100$ MeV. For each value of temperature, the results are shown for isospin asymmetry parameter $I$ = 0 and 0.5, and the strangeness fractions $f_s$ = 0 and 0.5.