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

TL;DR

This paper investigates the spectrum and wave functions of the $B_c$ meson system by solving the Salpeter equation, classifying states into three categories based on parity and analyzing their partial wave compositions and mixing angles.

Contribution

It provides a detailed classification of $B_c$ states into three categories and calculates their wave functions and mixing angles using a relativistic framework.

Findings

Identifies three categories of $J^P$ states in the $B_c$ system.

Calculates mixing angles for ${}^1P_1-{}^3P_1$ states.

Analyzes partial wave components of various $J^P$ states.

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 ${}^1S_0$ dominant state with a small amount of $P$ wave and ${}^3P_0$ 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 ${}^3S_1$ dominant state with a small amount of $P$ and $D$ waves, and the other is the ${}^3D_1$ 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 ${}^1P_1-{}^3P_1$ mixing states, and the corresponding mixing angles are calculated by using the relativistic wave functions.