${\mathrm{K̄}}^{*}$ mesons in dense matter

We study the properties of ${\mathrm{K̄}}^{*}$ mesons in nuclear matter using a unitary approach in coupled channels within the framework of the local hidden gauge formalism and incorporating the $\mathrm{K̄}\pi$ decay channel in matter. The in-medium ${\mathrm{K̄}}^{*}N$ interaction accounts for Pauli blocking effects and incorporates the ${\mathrm{K̄}}^{*}$ self-energy in a self-consistent manner. We also obtain the ${\mathrm{K̄}}^{*}$ (off-shell) spectral function and analyze its behavior at finite density and momentum. At a normal nuclear matter density, the ${\mathrm{K̄}}^{*}$ meson feels a moderately attractive potential, while the ${\mathrm{K̄}}^{*}$ width becomes five times larger than in free space. We estimate the transparency ratio of the $\gamma A\to K^{+}{K}^{*-}{A}^{\prime }$ reaction, which we propose as a feasible scenario at the present facilities to detect changes in the properties of the ${\mathrm{K̄}}^{*}$ meson in nuclear medium.

Figure 1

The $\mathrm{K̄}$ propagator renormalized to allow its decay into $\mathrm{K̄}\pi$, in the free space (left) and in the medium (right), including the self-energies of the $\mathrm{K̄}$ and $\pi$ mesons.

Figure 2

Self-energy diagrams at first order in the nuclear density contributing to the decay of the ${\mathrm{K̄}}^{*}$ meson in the medium.

Figure 3

Imaginary part of the ${\mathrm{K̄}}^{*}$ self-energy at zero momentum, coming from the $\mathrm{K̄}\pi$ decay mode in dense matter at normal saturation density ${\rho }_0$. Different approaches are studied: (i) calculation in free space, (ii) including the $\pi$ self-energy, (iii) including the $\pi$ and $\mathrm{K̄}$ self-energies, and (iv) including the $\pi$ dressing with vertex corrections and the $\mathrm{K̄}$ self-energy.

Figure 4

Real and imaginary parts of the ${\mathrm{K̄}}^{*}N\to {\mathrm{K̄}}^{*}N$ amplitude as a function of the center-of-mass energy $P_0$ for a fixed total momentum $\left|\mathrm{P⃗}\right|=0$. Two new states are generated dynamically: ($I=0$) $\Lambda (1783)$ and ($I=1$) $\Sigma (1830).$

Figure 5

Real and imaginary parts of the ${\mathrm{K̄}}^{*}$ self-energy as functions of the meson energy $q^0$ for zero momentum and normal saturation density ${\rho }_0$ showing the different contributions: (i) self-consistent calculation of the ${\mathrm{K̄}}^{*}N$ interaction (dashed lines), (ii) self-energy coming from ${\mathrm{K̄}}^{*}\to \mathrm{K̄}\pi$ decay (dot-dashed lines), and (iii) combined self-energy from both sources (solid lines).

Figure 6

The ${\mathrm{K̄}}^{*}$ self-energy as a function of the meson energy $q^0$ for different momenta and densities.

Figure 7

The ${\mathrm{K̄}}^{*}$ spectral function as a function of the meson energy $q^0$ for different densities and zero momentum.

Figure 8

Diagrams of contributions to (a) the pseudoscalar-baryon or (b) the vector-baryon interaction via exchange of a vector meson.

Figure 9

Transparency ratio.