Figure 1

The mass parameter $m_{\omega }^2$ defined in Eq. (3) and averaged within the Borel window as a function of the baryon density for ${\kappa }_N=4$ and $c_4=0$ (solid curve). Note that the parameter $m_{\omega }^2$ coincides only in zero-width approximation with the $\omega$ pole mass squared; in general it is a normalized moment of $\mathrm{Im}{\Pi }^{\omega }$ to be calculated from data or models. The sum rule Eq. (4) is evaluated as described in the text with appropriately adjusted ${\kappa }_0$. Inclusion of $c_4^{(0)}=\mathcal{O}(\pm {10}^{-3}){\mathrm{GeV}}^8$ requires a readjustment of ${\kappa }_0$ in the range $1\cdots 5$ to $m_{\omega }^{(0)2}$. A simultaneous change of ${\kappa }_N$ in the order of 20% is needed to recover the same density dependence as given by the solid curve at small values of $n$. The effect of a $c_4^{(1)}$ term is exhibited, too ($c_4^{(1)}=\pm {10}^{-5}{n}_0^{-1}{\mathrm{GeV}}^8$, dashed curves; $c_4^{(1)}=\pm 5\times {10}^{-5}{n}_0^{-1}{\mathrm{GeV}}^8$, dotted curves; the upper (lower) curves are for negative (positive) signs.Reuse & Permissions