A helicity amplitude analysis for the processes ψ ( 3686 ) → γ χ c J → γ p p ¯ is performed. The joint angular distributions for these processes are obtained, which allows a proper estimation of the detection efficiency using helicity amplitude information. The helicity amplitudes parameters for χ c 1 , 2 → p p ¯ are also obtained using measured α values for the first time. In addition, the sensitivities of measurements of the helicity amplitudes parameters for these processes are discussed based on the MC simulation.