$D$ meson mass increase by restoration of chiral symmetry in nuclear matter

Spectral functions of the pseudoscalar $D$ meson in the nuclear medium are analyzed using QCD sum rules and the maximum entropy method. This approach enables us to extract the spectral functions without any phenomenological assumption, and thus to visualize in-medium modification of the spectral functions directly. It is found that the reduction of the chiral condensates of dimension 3 and 5 causes the masses of both $D^{+}$ and $D^{-}$ mesons to grow gradually at finite density. Additionally, we construct charge-conjugate-projected sum rules and find a $D^{+}–D^{-}$ mass splitting of about $-15$ MeV at nuclear saturation density.

Figure 1

Schematic picture of spectral function contributions in ${\mathrm{\Pi }}^{\mathrm{even}}\left(q_0^2\right)$ and $q_0{\mathrm{\Pi }}^{\mathrm{odd}}\left(q_0^2\right)$ of the $D^{+}$ correlator. The factor $1/2$ on the right-hand side is omitted for simplicity. Spectral functions of the old-fashioned correlator include only spectra in the positive energy region.

Figure 2

Spectral function extracted with MEM from the $D^{\pm }$ meson sum rule in vacuum. The definition of the error bar at the peak is given in Ref. [49].

Figure 3

Default model dependence of spectral function extracted with MEM from the $D^{\pm }$ meson sum rule in vacuum. Solid and dashed lines denote spectral functions extracted with MEM and input default models, respectively.

Figure 4

Spectral functions extracted with MEM from $D^{\pm }$ meson sum rules in nuclear matter. (a) $D^{+}$ meson. (b) $D^{-}$ meson. ${\rho }_0=0.0013\left[{\mathrm{GeV}}^3\right]$ is the nuclear saturation density.

Figure 5

Density dependence of $D^{\pm }$ meson peak positions. Dashed lines and shaded areas correspond to errors from uncertainties of in-medium condensates.

Figure 6

Sigma term dependence of $D$ meson mass shifts at nuclear saturation density ${\rho }_0$. Dashed lines and shaded areas correspond to errors from uncertainties of in-medium condensates excluding the error of ${\sigma }_{\pi N}$.

Figure 7

Artificial heavy quark mass dependence of $D$ meson mass shifts at nuclear saturation density ${\rho }_0$. (a) Dependencies of individual $D^{+}$ and $D^{-}$ mass shifts. (b) Dependence of mass splitting between $D^{+}$ and $D^{-}$, namely the values of $m^{-}(m_h,\rho ={\rho }_0)-m^{+}(m_h,\rho ={\rho }_0)$.