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Title: Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves

Abstract

We extend our subtractive-renormalization method to evaluate the {sup 1}S{sub 0} and {sup 3}S{sub 1}-{sup 3}D{sub 1} NN-scattering phase shifts up to next-to-next-to-leading order (NNLO) in chiral effective theory. We show that, if energy-dependent contact terms are employed in the NN potential, the {sup 1}S{sub 0} phase shift can be obtained by carrying out two subtractions on the Lippmann-Schwinger equation. These subtractions use knowledge of the the scattering length and the {sup 1}S{sub 0} phase shift at a specific energy to eliminate the low-energy constants in the contact interaction from the scattering equation. For the J=1 coupled channel, a similar renormalization can be achieved by three subtractions that employ knowledge of the {sup 3}S{sub 1}scattering length, the {sup 3}S{sub 1} phase shift at a specific energy, and the {sup 3}S{sub 1}-{sup 3}D{sub 1} generalized scattering length. In both channels a similar method can be applied to a potential with momentum-dependent contact terms, except that in that case one of the subtractions must be replaced by a fit to one piece of experimental data. This method allows the use of arbitrarily high cutoffs in the Lippmann-Schwinger equation. We examine the NNLO S-wave phase shifts for cutoffs as large as 19 GeVmore » and show that the presence of linear energy dependence in the NN potential creates spurious poles in the scattering amplitude. In consequence the results are in conflict with empirical data over appreciable portions of the considered cutoff range. We also identify problems with the use of cutoffs greater than 1 GeV when momentum-dependent contact interactions are employed. These problems are ameliorated, but not eliminated, by the use of spectral-function regularization for the two-pion exchange part of the NN potential.« less

Authors:
;  [1];  [1]
  1. Institute of Nuclear and Particle Physics and Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701 (United States)
Publication Date:
OSTI Identifier:
21293911
Resource Type:
Journal Article
Journal Name:
Physical Review. C, Nuclear Physics
Additional Journal Information:
Journal Volume: 80; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevC.80.044002; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2813
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CHIRALITY; COUPLED CHANNEL THEORY; ENERGY DEPENDENCE; GEV RANGE; LIPPMANN-SCHWINGER EQUATION; NUCLEON-NUCLEON INTERACTIONS; NUCLEON-NUCLEON POTENTIAL; PHASE SHIFT; PIONS; RENORMALIZATION; S WAVES; SCATTERING; SCATTERING AMPLITUDES; SCATTERING LENGTHS; SPECTRAL FUNCTIONS

Citation Formats

Yang, C -J, Elster, Ch, Phillips, D R, and Helmholtz-Institut fuer Strahlen- und Kernphysik. Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves. United States: N. p., 2009. Web. doi:10.1103/PHYSREVC.80.044002.
Yang, C -J, Elster, Ch, Phillips, D R, & Helmholtz-Institut fuer Strahlen- und Kernphysik. Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves. United States. https://doi.org/10.1103/PHYSREVC.80.044002
Yang, C -J, Elster, Ch, Phillips, D R, and Helmholtz-Institut fuer Strahlen- und Kernphysik. 2009. "Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves". United States. https://doi.org/10.1103/PHYSREVC.80.044002.
@article{osti_21293911,
title = {Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves},
author = {Yang, C -J and Elster, Ch and Phillips, D R and Helmholtz-Institut fuer Strahlen- und Kernphysik},
abstractNote = {We extend our subtractive-renormalization method to evaluate the {sup 1}S{sub 0} and {sup 3}S{sub 1}-{sup 3}D{sub 1} NN-scattering phase shifts up to next-to-next-to-leading order (NNLO) in chiral effective theory. We show that, if energy-dependent contact terms are employed in the NN potential, the {sup 1}S{sub 0} phase shift can be obtained by carrying out two subtractions on the Lippmann-Schwinger equation. These subtractions use knowledge of the the scattering length and the {sup 1}S{sub 0} phase shift at a specific energy to eliminate the low-energy constants in the contact interaction from the scattering equation. For the J=1 coupled channel, a similar renormalization can be achieved by three subtractions that employ knowledge of the {sup 3}S{sub 1}scattering length, the {sup 3}S{sub 1} phase shift at a specific energy, and the {sup 3}S{sub 1}-{sup 3}D{sub 1} generalized scattering length. In both channels a similar method can be applied to a potential with momentum-dependent contact terms, except that in that case one of the subtractions must be replaced by a fit to one piece of experimental data. This method allows the use of arbitrarily high cutoffs in the Lippmann-Schwinger equation. We examine the NNLO S-wave phase shifts for cutoffs as large as 19 GeV and show that the presence of linear energy dependence in the NN potential creates spurious poles in the scattering amplitude. In consequence the results are in conflict with empirical data over appreciable portions of the considered cutoff range. We also identify problems with the use of cutoffs greater than 1 GeV when momentum-dependent contact interactions are employed. These problems are ameliorated, but not eliminated, by the use of spectral-function regularization for the two-pion exchange part of the NN potential.},
doi = {10.1103/PHYSREVC.80.044002},
url = {https://www.osti.gov/biblio/21293911}, journal = {Physical Review. C, Nuclear Physics},
issn = {0556-2813},
number = 4,
volume = 80,
place = {United States},
year = {Thu Oct 15 00:00:00 EDT 2009},
month = {Thu Oct 15 00:00:00 EDT 2009}
}