算子乘积展开在核势短程行为中的应用
Application of the operator product expansion to the short distance behavior of nuclear potentials
摘要：
通过微扰计算QCD中6夸克算符的反常维数，研究了由Bethe-Salpeter波函数定义的核子-核子（NN）势的短程行为。由于QCD的渐近自由性，单圈计算给出了零距离极限下势的某些精确结果。特别地，在短距离$r$处的S态中心NN势的函数形式被预测为比$r^{-2}$稍弱。另一方面，由于反常维谱的有趣性质，单靠微扰的考虑不能确定这种势在短距离下是排斥的还是吸引的。一个粗略的估计表明，在短距离上的力是排斥力，正如在格点量子色动力学中的数值结果一样。张量势也有类似的行为。
英文摘要：
We investigate the short distance behavior of nucleon-nucleon (NN) potentials defined through Bethe-Salpeter wave functions, by perturbatively calculating anomalous dimensions of 6-quark operators in QCD. Thanks to the asymptotic freedom of QCD, 1-loop computations give certain exact results for the potentials in the zero distance limit. In particular the functional form of the S-state central NN potential at short distance $r$ is predicted to be a little weaker than $r^{-2}$. On the other hand, due to the intriguing character of the anomalous dimension spectrum, perturbative considerations alone can not determine whether this potential is repulsive or attractive at short distances. A crude estimation suggests that the force at short distance is repulsive, as found numerically in lattice QCD. A similar behavior is found for the tensor potential.
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