$\Upsilon$ and $\eta_{b}$ mass shifts in nuclear matter and the nucleus bound states

TL;DR

This paper estimates the mass shifts of bottomonium states in nuclear matter, finding they can form bound states with nuclei and highlighting differences between bottomonium and charmonium interactions.

Contribution

First estimation of $$ and $_b$ meson mass shifts in nuclear matter using an SU(5) effective Lagrangian and quark-meson coupling model, revealing interaction strength differences.

Findings

Both $$ and $_b$ can form bound states with nuclei.

Significant difference in interaction strengths between bottomonium and charmonium.

Mass shifts depend on form factor choices and are studied in heavy quark symmetry limit.

Abstract

The $\Upsilon$ and $\eta_b$ as well as $B^*$ meson mass shifts (scalar potentials) are estimated for the first time in symmetric nuclear matter. The main interest is, whether or not the strengths of the bottomonium-nuclear matter and charmonium-nuclear matter interactions are similar or very different, in the range of a few tens of MeV at the nuclear matter saturation density. This is because, each ($\Upsilon,J/\Psi$) 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 density, by studying the $BB$, $BB^*$, and $B^*B^*$ meson loop contributions for the self-energy in free space and in nuclear medium. As a result, only the $BB$ meson loop contribution is included as our minimal prediction. As for the $\eta_b$, is included only the $BB^*$ meson loop contribution in the self-energy, to be consistent with the minimal prediction for the $\Upsilon$. The in-medium masses of the $B$ and $B^{*}$ mesons appearing in the self-energy loops are calculated by the quark-meson coupling model. Form factors are used to regularize the loop integrals with a wide range of the cutoff mass values. The results suggest that both $\Upsilon$ and $\eta_b$ should form bound states with a variety of nuclei considered in this study, for which the $\Upsilon$-nucleus and $\eta_b$-nucleus bound state energies are calculated. The results also show an appreciable difference between the bottomonium-nuclear matter and charmonium-nuclear matter interaction strengths. Are also studied the $\Upsilon$ and $\eta_b$ mass shifts in a heavy quark (heavy meson) symmetry limit. In addition, an initial study was done to investigate the influence of the choice of the form factor on our predictions.