Mass and the E1 decay rate of the singlet P state of charmonium

We calculate the hyperfine splitting of the P states of charmonium using the perturbative QCD hyperfine interaction to order αs2, in an improved quasistatic approximation whereby the quark-antiquark scattering amplitude is expanded in powers of p2/p02 instead of p2/m2 and terms of up to first order in p2/p02 are kept. We evaluated the hyperfine splitting using the wave functions obtained from the unperturbed Hamiltonian of Gupta, Radford, and Suchyta. We find the splitting ΔMP=Mc.o.g.3PJ-M1P1 to be -0.63 MeV. Our result is very similar to the result of Halzen, Olson, Olsson, and Stong who find ΔMP=-0.7±0.2 MeV, using various potential models. It also confirms the recent published experimental result on ΔMP. We also note that if we had used the improved quasistatic approximation of Gupta to extract the hyperfine interaction from the q bar q scattering amplitude to order αs2 in QCD, we would have obtained entirely different results for the P-wave hyperfine splitting in charmonium. We also calculate the electric dipole decay rate of the process 1 1P1→1 1S0+γ and find it to be about 630 keV for charmonium