Finite Size Vertex Correction to the Strong Decay of η_c and χ_c States and a Determination of α_s(m_c)

Abstract：

In previous calculations of the strong decay of a charmonium,the first-order momentum dependence of the quark propagator is kept. It was found that the finite-size vertex correction to the Γ(J/ψ→3g) process is large. In this paper we calculate the two-gluon decay widths of η_c,χ_c0 and χ_c2 by including the full momentum dependence of the quark propagator. Comparing to the zero-order calculation we find that the finite-size vertex correction factor to the two-gluon decay widths of η_c is 1.32,and for the two gluon decays of χ_c0 and χ_c2,the vertex correction factors are 1.45 and 1.26, respectively. With the corrected decay widths Γ(η_c→2g) we extract the value as α_s(m_c)=0.28±0.05 which agrees with that calculated from the Γ(J/ψ→3g) process with the same correction. The finite-size vertex correction to the process Γ(η_c→3g) is not as large as that to the process Γ(J/ψ→3g).