论文标题
$^3 p_j $ charmonium to $ dd，dd^*，d^*d^*$的衰减宽度和相应的质量转移$^3 p_j $ charmonium
Decay widthes of $^3 P_J$ charmonium to $DD,DD^*,D^*D^*$ and corresponding mass shifts of $^3 P_J$ charmonium
论文作者
论文摘要
在这项工作中，我们计算过程的幅度$ c \ bar c（{^3p_j}）\ rightarrow dd，dd^*，d^*d^*\ rightArrow c \ rightArrow c \ bar c（{^^3p_j}）$以非质量扩张的领先顺序。 The imaginary parts of the amplitudes are corresponding to the branch decay widthes of the charmonium $c\bar c({^3P_J}) \rightarrow DD,DD^*, D^*D^*$ and the real parts are corresponding to the mass shifts of the charmonium $c\bar c({^3P_J})$ due to these decay channels.在吸收纯真实并包括紫外线差异的多项式贡献之后，分支衰减宽度与相应质量移位之间的比率仅取决于质量中心能量。我们发现衰减宽度和$^3p_2 $状态的质量变化在领先顺序中零。当$^3p_0，{^3p_1} $状态的分支衰减宽度与质量变化之间的比率大于5时，质量中心能量高于$ dd，dd^*，d^*d^*$ threshold。质量转移对质量中心能量的依赖性是不平凡的，尤其是当质量中心能量低于阈值时。分析结果可以直接扩展到$ b $ quark行业。
In this work, we calculate the amplitudes of the processes $c\bar c({^3P_J}) \rightarrow DD,DD^*, D^*D^* \rightarrow c\bar c({^3P_J})$ in the leading order of the nonrelativistic expansion. The imaginary parts of the amplitudes are corresponding to the branch decay widthes of the charmonium $c\bar c({^3P_J}) \rightarrow DD,DD^*, D^*D^*$ and the real parts are corresponding to the mass shifts of the charmonium $c\bar c({^3P_J})$ due to these decay channels. After absorbing the polynomial contributions which are pure real and include the UV divergences, the ratios between the branch decay widthes and the corresponding mass shifts are only dependent on the center-of-mass energy. We find the decay widthes and the mass shifts of the $^3P_2$ states are exact zero in the leading order. The ratios between the branch decay widthes and the mass shifts for the $^3P_0, {^3P_1}$ states are larger than 5 when the center-of-mass energy is above the $DD,DD^*, D^*D^*$ threshold. The dependence of the mass shifts on the center-of-mass energy is nontrivial especially when the center-of-mass energy is below the threshold. The analytic results can be extended to the $b$ quark sector directly.
