The mass spectrum and wave functions of the $B_c$ system

Abstract

The spectrum and relativistic wave functions of $B_c$ system are investigated via solving the complete Salpeter equation. Emphases are put on the study of the partial waves of each $J^P$ state. Our study shows that there are three categories of $J^P$ states. The first category contains $0^{-}$ and $0^{+}$ states, which are ${}^1{S}_0$ dominant state with a small amount of $P$ wave and ${}^3{P}_0$ dominant state with a small amount of $S$ wave, respectively. The second category includes the natural parity states, such as $1^{-}$, $2^{+}$, $3^{-}$, etc. Taking the $1^{-}$ state as an example, we study it in two cases. One is the ${}^3{S}_1$ dominant state with a small amount of $P$ and $D$ waves, and the other is the ${}^3{D}_1$ dominant state but contains a large amount of $S$ and $P$ wave components. The third category includes the unnatural parity states, such as $1^{+}$, $2^{-}$, $3^{+}$, etc. For the $1^{+}$ spectrum, the states are grouped into pairs with different radial quantum numbers. Each pair contains two ${}^1{P}_1-{}^3{P}_1$ mixing states, and the corresponding mixing angles are calculated by using the relativistic wave functions.

26 pages, 1 table, 8 figures

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