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We estimate the $\Upsilon$, $\eta_b$ and $B^*$ meson mass shifts in symmetricnuclear matter. The interest is, whether the strengths of thebottomonium-(nuclear matter) and charmonium-(nuclear matter) interactions aresimilar or different. This is because, each ($J/\Psi,\Upsilon$) and($\eta_c,\eta_b$) meson group is usually assumed to have very similarproperties based on the heavy charm and bottom quark masses. The estimate forthe $\Upsilon$ is made using an SU(5) effective Lagrangian and the anomalouscoupling one, by studying the $BB$, $BB^*$, and $B^*B^*$ meson loopcontributions 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 massesof the $B$ and $B^*$ mesons appearing in the self-energy are calculated by thequark-meson coupling model. An analysis on the $BB$, $BB^*$, and $B^*B^*$ mesonloops 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. Ourprediction 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 saturationdensity using the $\Upsilon BB$ coupling constant determined by the vectormeson dominance model with the experimental data, while the $\eta_b$ mass shiftis predicted to be -75 to -82 MeV with the SU(5) universal coupling constantdetermined by the $\Upsilon BB$ coupling constant. Our results show anappreciable difference between the bottomonium-(nuclear matter) andcharmonium-(nuclear matter) interaction strengths. We also study the $\Upsilon$and $\eta_b$ mass shifts in a heavy quark (heavy meson) symmetry limit.

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