Quarkonium Bound States and Coupling to Hadrons

Coupling constants and transition potentials for hadronic decay modes of a meson

“…The matrix elements n ′ |V | n are those given in [5]. For the lowest lying q q systems n ′ is linearly related to n. The curves are determined with expression (31) for the five three-meson vertices of Table (2). The upper curve (blue) corresponds to the pseudoscalar vertices with (vector, vector) and (pseudoscalar, vector) the middle curve (violet) to the pseudoscalar vertex with (vector, positive-C-parity axial vector), the lower curve (red) to the pseudoscalar vertices with (pseudoscalar, scalar) and (vector, negative-Cparity axial vector).…”

“…Figure 5: Transition potentials for the decay of vector mesons (r and V (r) are dimensionless). The curves are determined with expression (31) for the nine three-meson vertices of Table (2). The curves, from the curve with the highest maximum to the curve with the lowest maximum, represent the vector vertices with respectively (vector, vector in P wave, total spin S = 2), (pseudoscalar, vector), (vector, positive-C-parity axial vector), (scalar, vector), (pseudoscalar, pseudoscalar), (pseudoscalar, positive-C-parity axial vector) and (vector, negative-C-parity axial vector), (pseudoscalar, negative-Cparity axial vector), (vector, vector in P wave, total spin S = 0).…”

“…In this paper we will calculate explicitly the matrix elements for the decay processes: meson → meson + meson (Sects. 2,3,4). Of course, the Clebsch-Gordannery is straightforward, but it is useful to have the complete formulas written somewhere.…”

“…In several publications [1][2][3][4] it is discussed that hadronic decay cannot be ignored in hadron models. As a consequence it is essential for the description of mesons (and baryons) to know the allowed decay modes and their relative strengths.…”

“…Figure6: Transition potentials for the decay of scalar mesons (r and V (r) are dimensionless). The curves are determined with expression (31) for the eleven three-meson vertices of Table(2). The curves, from the curve with the highest maximum to the curve with the lowest maximum, represent the scalar vertices with respectively (vector, vector in D wave, total spin S = 2), (pseudoscalar, positive-C-parity axial vector) and (vector, negative-C-parity axial vector), (pseudoscalar, pseudoscalar), (vector, vector (angular excitation)), (pseudoscalar, pseudoscalar (radial excitation)) and (negative-C-parity axial vector, negative-C-parity axial vector), (scalar, scalar), (vector, vector in S wave, total spin S = 0), (vector, vector (radial excitation)), (positive-C-parity axial vector, positive-C-parity axial vector).…”