Υ and ηb mass shifts in nuclear matter

By extending the previous works that two of the present authors were involved, we estimate for the first time the Upsilon and eta(b) as well as B* meson mass shifts (scalar potentials) in symmetric nuclear matter. The main interest is, whether the strengths of the bottomonium-(nuclear matter) and charmonium-(nuclear matter) interactions are similar or very different, in the range of a fewtens of Me V at the nuclear matter saturation density. 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 density and the anomalous coupling one, 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, we include only the BB meson loop contribution as our prediction. As for the eta(b), to be complete, we include the BB* and B*B* meson loop contributions in the self-energy for the analysis. 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. A detailed analysis on the BB, BB*, and B*B* meson loop contributions for the. mass shift is made by comparing with the respectively corresponding DD, DD*, and D*D* meson loop contributions for the J/Psi mass shift. Based on the analysis for the Upsilon, our prediction for the eta(b) mass shift is made on the same footing as that for the Upsilon, namely including only the lowest order BB* meson loop. The Upsilon mass shift is predicted to be -16 to -22 MeV at the nuclear matter saturation density with the cutoff mass values in the range of 2000-6000 MeV 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 for the same range of the cutoff mass values. 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, namely, by calculating their mass shifts using the same coupling constant value as that was used to estimate the J/Psi and eta(c) mass shifts. For the eta(b) mass shift an SU(5) symmetry breaking case is also studied in this limit. Our predictions for these cases at nuclear matter saturation density are, -6 to -9 MeV for Upsilon, -31 to -38 MeV for eta(b), and -8 to -11 MeV for eta(b) with a broken SU(5) symmetry, where the corresponding charm sector ones are, -5 to -21 for J/Psi, -49 to -87 for eta(c), and -17 to -51 for eta(c) with a broken SU(4) symmetry.

Automated summary

This study estimates the mass shifts of Upsilon, eta(b), and B* mesons in symmetric nuclear matter, and examines the different interactions strengths between bottomonium and charmonium. The results show a significant difference in the interaction strengths between bottomonium and charmonium.