Light vector meson masses in strange hadronic matter: A QCD sum rule approach

In the present work, the properties of the light vector mesons ($\rho ,\omega$, and $\varphi$) in strange hadronic matter are studied using the QCD sum rule approach. The in-medium masses of the vector mesons are calculated from the modifications of the light quark condensates and the gluon condensates in the hadronic medium. The light quark condensates in the hadronic matter are obtained from the values of the nonstrange and strange scalar fields of the explicit chiral symmetry breaking term in a chiral SU(3) model. The in-medium gluon condensate is calculated through the medium modification of a scalar dilaton field, which is introduced into the chiral SU(3) model to simulate the scale symmetry breaking of QCD. The mass of the $\omega$ meson is observed to have initially a drop with increase in density and then a rise due to the scattering with the baryons. The mass of the $\rho$ meson is seen to drop with density due to decrease of the light quark condensates in the medium. The effects of isospin asymmetry and strangeness of the medium on the masses of the vector mesons are also studied in the present work. The $\varphi$ meson is observed to have marginal drop in its mass in the nuclear medium. However, the strangeness of the medium is seen to lead to an appreciable increase in its mass arising due to scattering with the hyperons.

Figure 1

The quark condensates ${(-m_q\langle \overline{q}q\rangle )}^{1/4} \left(q=u,d\right)$ and ${(-m_s\langle \overline{s}s\rangle )}^{1/4}$, in units of MeV, are plotted as functions of density for isospin asymmetric hadronic matter (for $f_s=0$, 0.3 and 0.5) in (b) and (d), and compared with the isospin symmetric case, shown in (a) and (c).

Figure 2

The quantity ${\langle \frac{{\alpha }_s}{\pi }{G^a}_{\mu \nu }{G^a}^{\mu \nu }\rangle }^{1/4}$ in MeV plotted as a function of the baryon density in units of the nuclear matter saturation density. This is plotted for isospin asymmetric hadronic matter (for strangeness fraction, $f_s=0$, 0.3, 0.5 and isospin asymmetric parameter, $\eta =0.5$) in (b) and compared with the symmetric matter $\left(\eta =0\right)$ in (a).

Figure 3

The mass of $\omega$ meson plotted as a function of the baryon density in units of nuclear saturation density, for the isospin asymmetric strange hadronic matter (for strangeness fraction, $f_s=0$, 0.3, 0.5, and isospin asymmetric parameter, $\eta =0.5$) in (b) and compared with the symmetric matter $\left(\eta =0\right)$ shown in (a).

Figure 4

The mass of $\rho$ meson plotted as a function of the baryon density in units of nuclear saturation density, for the isospin asymmetric strange hadronic matter (for strangeness fraction, $f_s=0$, 0.3, 0.5, and isospin asymmetric parameter, $\eta =0.5$) in (b) and compared with the symmetric matter $\left(\eta =0\right)$ shown in (a).

Figure 5

The mass of $\varphi$ meson plotted as a function of the baryon density in units of nuclear saturation density, for the isospin asymmetric strange hadronic matter (for strangeness fraction, $f_s=0$, 0.3, 0.5, and isospin asymmetric parameter, $\eta =0.5$) in subplot (b) and compared with the symmetric matter $\left(\eta =0\right)$ shown in (a).

Figure 6

The density dependence of ${s^{*}}_0^V$ for the vector mesons $(\omega ,\rho$, and $\varphi )$ in the strange hadronic matter is shown for the isospin symmetric $\left(\eta =0\right)$ and isospin asymmetric (with $\eta =0.5$) cases for values of $f_s=0$, 0.3, and 0.5.

Figure 7

The density dependence of $F_V^{*}$ for the vector mesons ($\omega ,\rho$, and $\varphi$) in the strange hadronic matter is shown for the isospin symmetric $\left(\eta =0\right)$ and isospin asymmetric (with $\eta =0.5$) cases for values of $f_s=0$, 0.3, and 0.5.

Figure 8

The density dependence of the four quark condensate for the cases of the $\omega ,\rho$, and $\varphi$ mesons is shown for the isospin symmetric $\left(\eta =0\right)$ and asymmetric (with $\eta =0.5$) hadronic matter for the values of the strangeness fraction, $f_s=0$, 0.3, and 0.5.