dorsal/arxiv
View SchemaMore about the Wilsonian analysis on the pionless NEFT
| Authors | Koji Harada, Hirofumi Kubo, Atsushi Ninomiya |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0702074 |
| URL | https://arxiv.org/abs/nucl-th/0702074 |
| DOI | 10.1142/S0217751X09044528 |
| Journal | Int.J.Mod.Phys.A24:3191-3225,2009 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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.
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"abstract": "We extend our Wilsonian renormalization group (RG) analysis on the pionless\nnuclear effective theory (NEFT) in the two-nucleon sector in two ways; on the\none hand, (1) we enlarge the space of operators up to including those of\n$\\mathcal{O}(p^4)$ in the $S$ waves, and, on the other hand, (2) we consider\nthe RG flows in higher partial waves ($P$ and $D$ waves). In the larger space\ncalculations, we find, in addition to nontrivial fixed points, two ``fixed\nlines\u0027\u0027 and a ``fixed surface\u0027\u0027 which are related to marginal operators. In the\nhigher partial wave calculations, we find similar phase structures to that of\nthe $S$ waves, but there are \\textit{two} relevant directions in the $P$ waves\nat the nontrivial fixed points and \\textit{three} in the $D$ waves. We explain\nthe physical meaning of the $P$-wave phase structure by explicitly calculating\nthe low-energy scattering amplitude. We also discuss the relation between the\nLegendre flow equation which we employ and the RG equation by Birse, McGovern,\nand Richardson, and possible implementation of Power Divergence Subtraction\n(PDS) in higher partial waves.",
"arxiv_id": "nucl-th/0702074",
"authors": [
"Koji Harada",
"Hirofumi Kubo",
"Atsushi Ninomiya"
],
"categories": [
"nucl-th",
"hep-ph"
],
"doi": "10.1142/S0217751X09044528",
"journal_ref": "Int.J.Mod.Phys.A24:3191-3225,2009",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "More about the Wilsonian analysis on the pionless NEFT",
"url": "https://arxiv.org/abs/nucl-th/0702074"
},
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