https://doi.org/10.1140/epja/s10050-021-00569-7
Regular Article - Theoretical Physics
and 
mass shifts in nuclear matter
1
Laboratório de Física Teórica e Computacional, Universidade Cidade de São Paulo (UNICID), 01506-000, São Paulo, SP, Brazil
2
Departamento de Física, Universidad de Sonora, Boulevard Luis Encinas J. y Rosales, Colonia Centro, 83000, Hermosillo, Sonora, Mexico
3
Universidade Cruzeiro do Sul, 01506-000, São Paulo, SP, Brazil
c kazuo.tsushima@gmail.com, kazuo.tsushima@cruzirodosul.edu.br
Received:
24
March
2021
Accepted:
13
August
2021
Published online:
25
August
2021
By extending the previous works that two of the present authors were involved, we estimate for the first time the and as well as 
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 few tens of MeV at the nuclear matter saturation density. This is because, each (
) and (
) meson group is usually assumed to have very similar properties based on the heavy charm and bottom quark masses. The estimate for the is made using an SU(5) effective Lagrangian density and the anomalous coupling one, by studying the BB, 
, and 
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 , to be complete, we include the and meson loop contributions in the self-energy for the analysis. The in-medium masses of the B and 
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, 
, and 
meson loop contributions for the mass shift is made by comparing with the respectively corresponding 
, and 
meson loop contributions for the 
mass shift. Based on the analysis for the , our prediction for the mass shift is made on the same footing as that for the , namely including only the lowest order meson loop. The mass shift is predicted to be 
to 
MeV at the nuclear matter saturation density with the cutoff mass values in the range of 2000–6000 MeV using the 
coupling constant determined by the vector meson dominance model with the experimental data, while the mass shift is predicted to be 
to 
MeV with the SU(5) universal coupling constant determined by the 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 and 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 and 
mass shifts. For the 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, 
to 
MeV for , 
to 
MeV for , and 
to 
MeV for with a broken SU(5) symmetry, where the corresponding charm sector ones are, 
to 
for , 
to 
for , and 
to 
for with a broken SU(4) symmetry.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
