Dynamical Calculations of Pseudoscalar and Axial-Vector Meson Parameters Using the Relativistic Lippmann-Schwinger Equation
J. Boguta, H. W. Wyld · Physical Review · 1969
A multichannel dynamical calculation of pseudoscalar and axial-vector meson parameters is performed using the relativistic Lippmann-Schwinger equation. The channel considered is $\mathrm{PV}\ensuremath{\rightarrow}\mathrm{PV}$. The potential is computed using the usual Feynman rules and the resulting equations are solved on a computer. The cutoff is fixed by adjusting the output mass of one resonance or bound state or the output width to the experimental value. For ${J}^{P}={0}^{\ensuremath{-}}$ we fix ${m}_{K}=496$ MeV and obtain as output ${m}_{\ensuremath{\pi}}=135$ MeV, ${m}_{\ensuremath{\eta}}=587$ MeV. For ${J}^{P}={1}^{+}$, we fix ${\ensuremath{\Gamma}}_{B}=114$ MeV and obtain as output ${m}_{B}=1060$ MeV, ${m}_{{{K}_{c}}^{*}}=1310$ MeV, ${\ensuremath{\Gamma}}_{{{K}_{c}}^{*}}=87$ MeV, ${m}_{H}=975$ MeV, ${\ensuremath{\Gamma}}_{H}=50$ MeV, ${m}_{{H}^{\ensuremath{'}}}=1400$ MeV, ${\ensuremath{\Gamma}}_{{H}^{\ensuremath{'}}}=43$ MeV. Furthermore, if we fix ${m}_{{A}_{1}}=1080$ MeV, we obtain ${\ensuremath{\Gamma}}_{{A}_{1}}=110$ MeV, ${m}_{D}=1370$ MeV as a bound state.