Hadronic transitions andP11states of heavy quarkonia

Stimulated by both new experimental data and theoretical interest, the properties of the spin-singlet P state ${(}^1$ $P_1$) in the cc¯ and bb¯ system have been reexamined in the framework of the QCD multipole expansion. We have estimated various rates for producing ψ(1 ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$) and Υ(1 ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$) in hadronic transitions, and for producing ψ(1 ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$) in pp¯ annihilation. The ππ mass spectrum in the transition Υ’ ’→Υ(1 ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$)ππ has been computed, and the two pions peak at low masses. An interesting approximation proposed by Voloshin and Zakharov is explored further in conjunction with the axial anomaly to relate many isospin-violating ${\pi }^0$ transitions involving ${}_{}{}^1{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$ to the known rate of ψ’→J/ψ ${\pi }^0$. The rates for ψ’→ψ (1 ${}_{}{}^1{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$)${\mathrm{\pi }}^0$ and ψ(1 ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$)→J/ψ ${\pi }^0$ are found to be large. The implications are discussed.