Spectral function of the ${\eta }^{\prime }$ meson in nuclear medium based on phenomenological models

Abstract

The in-medium modification of the spectral function of the ${\eta }^{\prime }$ meson with and without the spatial momentum is studied with the $T\rho$ approximation by employing two phenomenological models for the ${\eta }^{\prime }N$ scattering; one is called coupled channels model and the other the $N(1895)$-dominance model. In the former model, the ${\eta }^{\prime }N$ scattering amplitude is calculated in the unitarized coupled-channel approach involving the ${\eta }^{\prime }N$ channel, while in the latter model the ${\eta }^{\prime }N$ scattering process is dominated by the $N(1895)$ resonance with the spin and parity $J^P=1/2^{-}$. In the \com{coupled channels model}, one single peak of the in-medium ${\eta }^{\prime }$ mode appears in the spectral function and the peak position shifts to higher energies along with the increase of the nuclear density reflecting the repulsive ${\eta }^{\prime }N$ scattering length of the unitarized coupled-channel amplitude. On the other hand, two branches related to the ${\eta }^{\prime }$ and $N(1895)$-hole modes appear in the $N(1895)$-dominance model. In both models, the shift of the peak position and the width in the spectral function are a few tens of MeV at the normal nuclear density for the ${\eta }^{\prime }$ meson at rest in the nuclear medium. Once the spatial momentum is turned on, the peak positions in the spectral function approach the energies without the nuclear medium effect. Particularly, in the $N(1895)$-dominance model, the peak strength of the $N(1895)$-hole mode gets smaller with the finite momentum and the spectral function comes to have one single peak.

16 pages, 14 figures. Typos are corrected

References in corpus (14)

• η- and η'-mesic nuclei and U_A(1) anomaly at finite density
• Pseudoscalar neutral mesons in hot and dense matter
• Feasibility Study of Observing eta' Mesic Nuclei with (p,d) Reaction
• Determination of the eta'-proton scattering length in free space
• Measurement of excitation spectra in the ${}^{12}$C$(p,d)$ reaction near the ${\eta }^{\prime }$ emission threshold
• Strong evidence for nucleon resonances near 1900\,MeV
• Level crossing of particle-hole and mesonic modes in eta mesic nuclei
• Formation of eta-mesic nuclei by (pi,N) reaction and N^*(1535) in medium
• Determination of the real part of the η'-Nb optical potential
• Momentum dependence of the imaginary part of the $\omega$- and ${\eta }^{\prime }$-nucleus optical potential
• The role of $N^{\ast }(1535)$ in ${\eta }^{\prime }$ production
• Search for ${\eta }^{\prime }$ bound nuclei in the ${}^{12}\mathrm{C}(\gamma ,p)$ reaction with simultaneous detection of decay products
• Formation spectra of light kaonic nuclei by in-flight ($\bar{K},N$) reactions with chiral unitary amplitude
• $N^{\ast }\to N{\eta }^{\prime }$ decays from photoproduction of ${\eta }^{\prime }$-mesons off protons