Pions are neither perturbative nor nonperturbative: Wilsonian renormalization-group analysis of nuclear effective field theory including pions
Pions are neither perturbative nor nonperturbative: Wilsonian renormalization-group analysis of nuclear effective field theory including pions
复制标题
DOI：
10.1103/physrevc.83.034002
复制
发表时间：
2010-12
影响因子：
3.1
通讯作者：
K. Harada;H. Kubo;Y. Yamamoto
中科院分区：
文献类型：
--
作者：
K. Harada;H. Kubo;Y. Yamamoto
从威尔逊重整化群的观点出发，研究了双核子扇区中包含π介子的核有效场论。π介子交换在浮动截止尺度{λ}处被截断，短距离部分根据重整化的一般原理被表示为接触相互作用。我们推导了算子空间中非相对论近似首阶的非微扰重整化群方程，直至包含O（p{sup 2}），并找到了{sup 1}S{sub 0}和{sup 3}S{sub 1}-{sup 3}D{sub 1}通道中的非平凡不动点，这些不动点与无π NEFT中的不动点相同。标度尺寸，这决定了功率计数，接触相互作用在非平凡的固定点也确定与那些在pionless NEFT。我们强调的重要性，分离的π交换成短距离和长距离的部分，因为前者的一部分是非微扰的，而后者是微扰的。
Nuclear effective field theory (NEFT) including pions in the two-nucleon sector is examined from the Wilsonian renormalization group point of view. The pion exchange is cut off at the floating cutoff scale, {Lambda}, with the short-distance part being represented as contact interactions in accordance with the general principle of renormalization. We derive the nonperturbative renormalization group equations in the leading order of the nonrelativistic approximation in the operator space up to including O(p{sup 2}), and find the nontrivial fixed points in the {sup 1}S{sub 0} and {sup 3}S{sub 1}-{sup 3}D{sub 1} channels which are identified with those in the pionless NEFT. The scaling dimensions, which determine the power counting, of the contact interactions at the nontrivial fixed points are also identified with those in the pionless NEFT. We emphasize the importance of the separation of the pion exchange into the short-distance and the long-distance parts, since a part of the former is nonperturbative while the latter is perturbative.