dorsal/arxiv
View SchemaTesting Low Energy Theorems in Nucleon-Nucleon Scattering
| Authors | Thomas D. Cohen, James M. Hansen |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9901065 |
| URL | https://arxiv.org/abs/nucl-th/9901065 |
| DOI | 10.1103/PhysRevC.59.3047 |
| Journal | Phys.Rev. C59 (1999) 3047-3051 |
Abstract
Low energy theorems have been derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading nontrivial order in an expansion based $Q$ counting, a scheme in which both $m_\pi$ and $1/a$ (where $a$ is the scattering length) are treated as small mass scales. Previous tests of these theorems based on coefficients extracted from scattering data indicate a pattern of gross violations which suggested serious problems for the perturbative treatment of pions implicit in $Q$ counting. We discuss the possibility that uncertainties associated with extracting the coefficients from the scattering data make such tests invalid. Here we show that errors in the s-wave phase shift extractions are sufficiently small to test direct test predictions from $Q$ counting at next to leading order. In particular we show that there exist low energy theorems for the sum of all terms in the effective range expansion beyond the first two which allow for precise tests. These low energy theorems fail badly which suggests that pionic aspects of $Q$ counting are not under control.
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"abstract": "Low energy theorems have been derived for the coefficients of the effective\nrange expansion in s-wave nucleon-nucleon scattering valid to leading\nnontrivial order in an expansion based $Q$ counting, a scheme in which both\n$m_\\pi$ and $1/a$ (where $a$ is the scattering length) are treated as small\nmass scales. Previous tests of these theorems based on coefficients extracted\nfrom scattering data indicate a pattern of gross violations which suggested\nserious problems for the perturbative treatment of pions implicit in $Q$\ncounting. We discuss the possibility that uncertainties associated with\nextracting the coefficients from the scattering data make such tests invalid.\nHere we show that errors in the s-wave phase shift extractions are sufficiently\nsmall to test direct test predictions from $Q$ counting at next to leading\norder. In particular we show that there exist low energy theorems for the sum\nof all terms in the effective range expansion beyond the first two which allow\nfor precise tests. These low energy theorems fail badly which suggests that\npionic aspects of $Q$ counting are not under control.",
"arxiv_id": "nucl-th/9901065",
"authors": [
"Thomas D. Cohen",
"James M. Hansen"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.59.3047",
"journal_ref": "Phys.Rev. C59 (1999) 3047-3051",
"title": "Testing Low Energy Theorems in Nucleon-Nucleon Scattering",
"url": "https://arxiv.org/abs/nucl-th/9901065"
},
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