dorsal/arxiv
View SchemaConvolution approach to the piNN system
| Authors | B. Blankleider, A. N. Kvinikhidze |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9402011 |
| URL | https://arxiv.org/abs/nucl-th/9402011 |
| Journal | Few Body Syst.Suppl.7:294-308,1994 |
Abstract
The unitary NN-piNN model contains a serious theoretical flaw: unitarity is obtained at the price of having to use an effective piNN coupling constant that is smaller than the experimental one. This is but one aspect of a more general renormalization problem whose origin lies in the truncation of Hilbert space used to derive the equations. Here we present a new theoretical approach to the piNN problem where unitary equations are obtained without having to truncate Hilbert space. Indeed, the only approximation made is the neglect of connected three-body forces. As all possible dressings of one-particle propagators and vertices are retained in our model, we overcome the renormalization problems inherent in previous piNN theories. The key element of our derivation is the use of convolution integrals that have enabled us to sum all the possible disconnected time-ordered graphs. We also discuss how the convolution method can be extended to sum all the time orderings of a connected graph. This has enabled us to calculate the fully dressed NN one pion exchange potential. We show how such a calculation can be used to estimate the size of the connected three-body forces neglected in the new piNN equations. Early indications are that such forces may be negligible.
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"abstract": "The unitary NN-piNN model contains a serious theoretical flaw: unitarity is\nobtained at the price of having to use an effective piNN coupling constant that\nis smaller than the experimental one. This is but one aspect of a more general\nrenormalization problem whose origin lies in the truncation of Hilbert space\nused to derive the equations. Here we present a new theoretical approach to the\npiNN problem where unitary equations are obtained without having to truncate\nHilbert space. Indeed, the only approximation made is the neglect of connected\nthree-body forces. As all possible dressings of one-particle propagators and\nvertices are retained in our model, we overcome the renormalization problems\ninherent in previous piNN theories. The key element of our derivation is the\nuse of convolution integrals that have enabled us to sum all the possible\ndisconnected time-ordered graphs. We also discuss how the convolution method\ncan be extended to sum all the time orderings of a connected graph. This has\nenabled us to calculate the fully dressed NN one pion exchange potential. We\nshow how such a calculation can be used to estimate the size of the connected\nthree-body forces neglected in the new piNN equations. Early indications are\nthat such forces may be negligible.",
"arxiv_id": "nucl-th/9402011",
"authors": [
"B. Blankleider",
"A. N. Kvinikhidze"
],
"categories": [
"nucl-th"
],
"journal_ref": "Few Body Syst.Suppl.7:294-308,1994",
"title": "Convolution approach to the piNN system",
"url": "https://arxiv.org/abs/nucl-th/9402011"
},
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