More about the Wilsonian analysis on the pionless NEFT

Abstract

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.

39 pages, 5 figures, the final version

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Cited by in corpus (9)

• Modern Theory of Nuclear Forces
• Nuclear effective field theory: status and perspectives
• Effective field theory description of halo nuclei
• Scattering Models for Ultracold Atoms
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• Pions are neither perturbative nor nonperturbative: Wilsonian renormalization group analysis of nuclear effective field theory including pions
• Effective field theory for shallow P-wave states
• New fixed points of the renormalisation group for two-body scattering
• 'Running' under tight constraints in pionless effective field theory