Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2007-02-23
Int.J.Mod.Phys.A24:3191-3225,2009
Physics
Nuclear Physics
Nuclear Theory
39 pages, 5 figures, the final version
Scientific paper
10.1142/S0217751X09044528
We extend our Wilsonian renormalization group (RG) analysis on the pionless nuclear effective theory (NEFT) in the two-nucleon sector in two ways; on the one hand, (1) we enlarge the space of operators up to including those of $\mathcal{O}(p^4)$ in the $S$ waves, and, on the other hand, (2) we consider the RG flows in higher partial waves ($P$ and $D$ waves). In the larger space calculations, we find, in addition to nontrivial fixed points, two ``fixed lines'' and a ``fixed surface'' which are related to marginal operators. In the higher partial wave calculations, we find similar phase structures to that of the $S$ waves, but there are \textit{two} relevant directions in the $P$ waves at the nontrivial fixed points and \textit{three} in the $D$ waves. We explain the physical meaning of the $P$-wave phase structure by explicitly calculating the low-energy scattering amplitude. We also discuss the relation between the Legendre flow equation which we employ and the RG equation by Birse, McGovern, and Richardson, and possible implementation of Power Divergence Subtraction (PDS) in higher partial waves.
Harada Koji
Kubo Hirofumi
Ninomiya Atsushi
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