Multichannel Bootstrap Calculation of the Vector-Meson Parameters Using a Relativistic Lippmann-Schwinger Equation

Abstract

A multichannel bootstrap calculation of the vector mesons is performed, using a relativistic Lippmann-Schwinger equation. The vector mesons are obtained as resonances in the scattering of pseudoscalar mesons by pseudoscalar mesons, the potential between the two pseudoscalar mesons being taken as that due to vector-meson exchange. The on-shell potential is calculated using the usual Feynman rules, assuming that the coupling constants satisfy $\mathrm{SU}\left(3\right)\mathrm{}$. Input parameters are taken from experiment. The potential is extra-polated off-shell, and the resulting Schrödinger equations are solved exactly. We take the input $\rho$-meson width ${{\Gamma }_{\rho }}^{\mathrm{in}}$ to be 105 MeV, and the cutoff is so chosen that the output mass is equal to the input mass. With this choice of parameters, we obtain the following results: ${{\Gamma }_{\rho }}^{\mathrm{out}}=134\mathrm{}$ MeV, ${{\Gamma }_K}^{*\mathrm{out}}=51\mathrm{}$ MeV, ${m_K}^{*\mathrm{out}}=933\mathrm{}$ MeV, ${{\Gamma }_{\varphi }}^{\mathrm{out}}=2.4\mathrm{}$ MeV, ${m_{\varphi }}^{\mathrm{out}}=1009\mathrm{}$ MeV.