Study of the Zb (10610) and Zb (10650) states through $B\\bar{B}^*$ and $B^*\\bar{B}^*$ interactions using local hidden gauge approach

Abstract

We have studied the $B\\bar{B}^*$ and $B^*\\bar{B}^*$ interactions for isospin I = 1 using the Local Hidden gauge approach. Since both interactions via one light meson exchange are not allowed by Okubo-Zweig-Iizuka (OZI) rule, we investigated the contributions for those interactions coming from two pions, interacting and noninteracting among themselves, and also due to the heavy vector meson exchange, in which the OZI rule no longer holds. From the amplitudes calculated by these mechanism, we determine an effective potential which is used as a kernel of the Bethe-Salpeter equation. Our goal is look for poles in the T-matrix in attemp to relate them with the charged Zb(10610) and Zb(10650) states observed by Belle Collaboration. For the $B\\bar{B}^*$ interaction, we find a loosely bound state with the mass in the range 10587–10601 MeV, which is close to the experimental value observed by Belle Collaboration. For the $B^*\\bar{B}^*$ case, we find a cusp at 10650 MeV.