dorsal/arxiv
View SchemaRegularization, Renormalization and Range: The Nucleon-Nucleon Interaction from Effective Field Theory
| Authors | Thomas D. Cohen |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9606044 |
| URL | https://arxiv.org/abs/nucl-th/9606044 |
| DOI | 10.1103/PhysRevC.55.67 |
| Journal | Phys.Rev.C55:67-72,1997 |
Abstract
Regularization and renormalization is discussed in the context of low-energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by treating them as having a finite range. The low energy physical observables should be insensitive to this range provided that the range is of a similar or greater scale than that of the interaction. Alternative schemes, such as dimensional regularization, lead to paradoxical conclusions such as the impossibility of repulsive interactions for truly low energy effective theories where all of the exchange particles are integrated out. This difficulty arises because a nonrelativistic field theory with repulsive contact interactions is trivial in the sense that the $S$ matrix is unity and the renormalized coupling constant zero. Possible consequences of low energy attraction are also discussed. It is argued that in the case of large or small scattering lengths, the region of validity of effective field theory expansion is much larger if the contact interactions are given a finite range from the beginning.
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"abstract": "Regularization and renormalization is discussed in the context of low-energy\neffective field theory treatments of two or more heavy particles (such as\nnucleons). It is desirable to regulate the contact interactions from the outset\nby treating them as having a finite range. The low energy physical observables\nshould be insensitive to this range provided that the range is of a similar or\ngreater scale than that of the interaction. Alternative schemes, such as\ndimensional regularization, lead to paradoxical conclusions such as the\nimpossibility of repulsive interactions for truly low energy effective theories\nwhere all of the exchange particles are integrated out. This difficulty arises\nbecause a nonrelativistic field theory with repulsive contact interactions is\ntrivial in the sense that the $S$ matrix is unity and the renormalized coupling\nconstant zero. Possible consequences of low energy attraction are also\ndiscussed. It is argued that in the case of large or small scattering lengths,\nthe region of validity of effective field theory expansion is much larger if\nthe contact interactions are given a finite range from the beginning.",
"arxiv_id": "nucl-th/9606044",
"authors": [
"Thomas D. Cohen"
],
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"doi": "10.1103/PhysRevC.55.67",
"journal_ref": "Phys.Rev.C55:67-72,1997",
"title": "Regularization, Renormalization and Range: The Nucleon-Nucleon Interaction from Effective Field Theory",
"url": "https://arxiv.org/abs/nucl-th/9606044"
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