η_c和χ_c强衰变的有限顶角修正及α_s(m_c)的确定

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

计算了ηc 和 χc 两胶子衰变宽度的有限顶角展开的修正 .通过数值计算 ,得到ηc,χc0 和 χc2 的零程近似的修正因子分别为 :γ =1 .3 2 ,1 .45和 1 .2 6,利用衰变宽度Γ( ηc→ 2g)抽出强耦合参数αs(mc) =0 .2 8± 0 .0 5,这个值与Γ(J/ ψ→ 3g)强衰变的顶角修正得到的结果一致 .而Γ( ηc→ 2g)的有限顶角修正没有Γ(J/ ψ→ 3g)大 .

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).