\boldmath{$\Upsilon$} and \boldmath{$\eta_b$} mass shifts in nuclear matter

TL;DR

This paper estimates the in-medium mass shifts of bottomonium and bottomonium-like mesons in nuclear matter, revealing differences in their interaction strengths with nuclear matter compared to charmonium, using effective Lagrangians and meson loop calculations.

Contribution

It provides the first detailed comparison of bottomonium and charmonium mass shifts in nuclear matter, highlighting differences in their interaction strengths.

Findings

Upsilon mass shift: -16 to -22 MeV at saturation density.

Eta_b mass shift: -75 to -82 MeV at saturation density.

Significant difference between bottomonium and charmonium interactions with nuclear matter.

Abstract

We estimate the $\Upsilon$, $\eta_b$ and $B^*$ meson mass shifts in symmetric nuclear matter. The interest is, whether the strengths of the bottomonium-(nuclear matter) and charmonium-(nuclear matter) interactions are similar or different. This is because, each ($J/\Psi,\Upsilon$) and ($\eta_c,\eta_b$) meson group is usually assumed to have very similar properties based on the heavy charm and bottom quark masses. The estimate for the $\Upsilon$ is made using an SU(5) effective Lagrangian and the anomalous coupling one, by studying the $BB$, $BB^*$, and $B^*B^*$ meson loop contributions for the self-energy. As for the $\eta_b$, we include the $BB^*$ and $B^*B^*$ meson loop contributions in the self-energy. The in-medium masses of the $B$ and $B^*$ mesons appearing in the self-energy are calculated by the quark-meson coupling model. An analysis on the $BB$, $BB^*$, and $B^*B^*$ meson loops in the $\Upsilon$ mass shift is made by comparing with the corresponding $DD, DD^*$, and $D^*D^*$ meson loops for the $J/\Psi$ mass shift. Our prediction for the $\eta_b$ mass shift is made including only the lowest order $BB^*$ meson loop. The $\Upsilon$ mass shift, with including only the $BB$ loop, is predicted to be -16 to -22 MeV at the nuclear matter saturation density using the $\Upsilon BB$ coupling constant determined by the vector meson dominance model with the experimental data, while the $\eta_b$ mass shift is predicted to be -75 to -82 MeV with the SU(5) universal coupling constant determined by the $\Upsilon BB$ coupling constant. Our results show an appreciable difference between the bottomonium-(nuclear matter) and charmonium-(nuclear matter) interaction strengths. We also study the $\Upsilon$ and $\eta_b$ mass shifts in a heavy quark (heavy meson) symmetry limit.