Abstract
In this paper we have solved the nonrelativistic form of the Lippmann-Schwinger equation in the momentum-helicity space by inserting a spin-dependent quark-antiquark potential model numerically. To this end, we have used the momentum-helicity basis states for describing a nonrelativistic reduction of one-gluon exchange potential. Then we have calculated the mass spectrum of the charmonium ψcc¯, and finally we have compared the results with the other theoretical results and experimental data.
Highlights
During the past years, several models and methodological approaches based on solving the relativistic and nonrelativistic form of the Schrodinger or Lippmann-Schwinger equation have been developed for studying the light and heavy mesons in the coordinate and momentum spaces, respectively.Recently, the three-dimensional approach based on momentum-helicity basis states for studding the nucleonnucleon scattering and deuteron state has been developed [1, 2]
We extend this approach to particle physics problems by solving the nonrelativistic form of the Lippmann-Schwinger equation to obtain the mass spectrum of the heavy mesons using the nonrelativistic quark-antiquark interaction in terms of a linear confinement, a Coulomb, and various spindependent pieces
We have used the nonrelativistic form of the LippmannSchwinger equation in the momentum-helicity representation to study the charmonium as a heavy meson
Summary
Several models and methodological approaches based on solving the relativistic and nonrelativistic form of the Schrodinger or Lippmann-Schwinger equation have been developed for studying the light and heavy mesons in the coordinate and momentum spaces, respectively. The three-dimensional approach based on momentum-helicity basis states for studding the nucleonnucleon scattering and deuteron state has been developed [1, 2] We extend this approach to particle physics problems by solving the nonrelativistic form of the Lippmann-Schwinger equation to obtain the mass spectrum of the heavy mesons using the nonrelativistic quark-antiquark interaction in terms of a linear confinement, a Coulomb, and various spindependent pieces. We have used the nonrelativistic form of the LippmannSchwinger equation in the momentum-helicity representation to study the charmonium as a heavy meson For this purpose, we have used a nonrelativistic quark-antiquark potential based on one-gluon exchange in the momentumhelicity representation.
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