Study of the timelike electromagnetic form factors of the c

In this paper, the reaction of electron-positron annihilation into c^+c^- is investigated. The c^+c^- scattering amplitudes are obtained by solving the Lippmann-Schwinger equation. The contact, annihilation, and two pseudoscalar-exchange potentials are taken into account in the spirit of the chiral effective field theory. The amplitudes of e^+e^- c^+c^- are constructed by the distorted wave Born approximation method, with the final state interactions of the c^+c^- re-scattering implemented. By fitting to the experimental data, the unknown couplings are fixed, and high-quality solutions are obtained. With these amplitudes, the individual electromagnetic form factors in the timelike region, GE^c, GM^c, and their ratio, GE^c/GM^c, are extracted. Both modulus and phases are predicted. These individual electromagnetic form factors reveal new insights into the properties of the c. The separated contributions of the Born term, contact, annihilation, as well as the two pseudoscalar exchange potentials to the electromagnetic form factors are isolated. It is found that the Born term dominates the whole energy region. The contact term plays a crucial role in the enhancement near the threshold, and the annihilation term is essential in generating the fluctuation of the electromagnetic form factors.