Strong Coupling of the Multi-Partial-Wave Meson Isotriplet

The algebraic formulation of strong coupling is applied to the strong coupling of the ${\mathrm{SU}}_2$-symmetric model in which all the partial waves of the $\pi$ mesons are included. The strong-coupling group is a semidirect product of the ${\mathrm{SU}}_2\otimes {\mathrm{SU}}_2$ internal symmetry group and an Abelian group which is generated by an infinite number of commuting generators corresponding to the vertices of the $\pi$ mesons in different orbital angular momentum states. A physically interesting irreducible representation of the group is obtained which consists of a series of irreducible representations of the $P$-wave strong-coupling group. The Regge recurrences of isobars appear in this series. Each degenerate multiplet of isobars is specified by three quantum numbers—spin $s$, isospin $i$, and an additional quantum number $v$—which satisfy the angular momentum triangular relation. The following form of mass formula is obtained: $M(s,i,v)=M_0+m_0\mathrm{}\left[x\right(x-1\mathrm{}\left)s\right(s+1\mathrm{})+(1-x\left)i\right(i+1\mathrm{})+xv(v+1\mathrm{}\left)\right]$.