dorsal/arxiv
View SchemaUsing chiral perturbation theory to extract the neutron-neutron scattering length from pi- d -> n n gamma
| Authors | A. Gardestig, D. R. Phillips |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0501049 |
| URL | https://arxiv.org/abs/nucl-th/0501049 |
| DOI | 10.1103/PhysRevC.73.014002 |
| Journal | Phys.Rev.C73:014002,2006 |
Abstract
The reaction pi- d -> n n gamma is calculated in chiral perturbation theory so as to facilitate an extraction of the neutron-neutron scattering length (a_nn). We include all diagrams up to O(Q^3). This includes loop effects in the elementary pi- p -> gamma n amplitude and two-body diagrams, both of which were ignored in previous calculations. We find that the chiral expansion for the ratio of the quasi-free (QF) to final-state-interaction (FSI) peaks in the final-state neutron spectrum converges well. Our third-order calculation of the full spectrum is already accurate to better than 5%. Extracting a_nn from the shape of the entire pi- d -> n n gamma spectrum using our calculation in its present stage would thus be possible at the +-0.8 fm level. A fit to the FSI peak only would allow an extraction of a_nn with a theoretical uncertainty of +-0.2 fm. The effects that contribute to these error bars are investigated. The uncertainty in the $nn$ rescattering wave function dominates. This suggests that the quoted theoretical error of +-0.3 fm for the most recent pi- d -> n n gamma measurement may be optimistic. The possibility of constraining the nn rescattering wave function used in our calculation more tightly--and thus reducing the error--is briefly discussed.
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"abstract": "The reaction pi- d -\u003e n n gamma is calculated in chiral perturbation theory\nso as to facilitate an extraction of the neutron-neutron scattering length\n(a_nn). We include all diagrams up to O(Q^3). This includes loop effects in the\nelementary pi- p -\u003e gamma n amplitude and two-body diagrams, both of which were\nignored in previous calculations. We find that the chiral expansion for the\nratio of the quasi-free (QF) to final-state-interaction (FSI) peaks in the\nfinal-state neutron spectrum converges well. Our third-order calculation of the\nfull spectrum is already accurate to better than 5%. Extracting a_nn from the\nshape of the entire pi- d -\u003e n n gamma spectrum using our calculation in its\npresent stage would thus be possible at the +-0.8 fm level. A fit to the FSI\npeak only would allow an extraction of a_nn with a theoretical uncertainty of\n+-0.2 fm. The effects that contribute to these error bars are investigated. The\nuncertainty in the $nn$ rescattering wave function dominates. This suggests\nthat the quoted theoretical error of +-0.3 fm for the most recent pi- d -\u003e n n\ngamma measurement may be optimistic. The possibility of constraining the nn\nrescattering wave function used in our calculation more tightly--and thus\nreducing the error--is briefly discussed.",
"arxiv_id": "nucl-th/0501049",
"authors": [
"A. Gardestig",
"D. R. Phillips"
],
"categories": [
"nucl-th",
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],
"doi": "10.1103/PhysRevC.73.014002",
"journal_ref": "Phys.Rev.C73:014002,2006",
"title": "Using chiral perturbation theory to extract the neutron-neutron scattering length from pi- d -\u003e n n gamma",
"url": "https://arxiv.org/abs/nucl-th/0501049"
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