Derivation of the effective pion-nucleon Lagrangian within heavy baryon chiral perturbation theory |
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| Institution: | 1. Indian Institute of Technology, Kanpur 208 016, UP, India;2. University of Rochester, Rochester, NY 14627, USA;1. Instituto de Física Corpuscular (IFIC), Centro Mixto CSIC-Universidad de Valencia, E-46071 Valencia, Spain;2. Department of Physics, Aligarh Muslim University, Aligarh 202 002, India;3. Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino, 10125 Torino, Italy;4. Department of Physics, Colorado State University, Fort Collins, CO 80523, USA;5. Department of Physics, Hampton University, Hampton, VA, 23668, USA;6. Fermi National Accelerator Laboratory, Batavia, IL 60510, USA;7. Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;8. Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA;9. Northwestern University, Evanston, IL 60208, USA;10. Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506, USA;11. Center of Neutrino Physics, Virginia Tech, Blacksburg, VA 24061, USA;12. Department of Physics and Astronomy, Ghent University, B-9000 Gent, Belgium;13. Queen Mary University of London, London, UK;14. Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA;15. ESNT, CEA, IRFU, Service de Physique Nucléaire, Université de Paris-Saclay, F-91191 Gif-sur-Yvette, France;p. Department of Physics and Astronomy, University of South Carolina, Columbia, SC 29208, USA;q. Jefferson Laboratory, Newport News, VA 23606, USA;r. IFAE, Barcelona Institute Science and Technology, Barcelona, Spain;s. Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan;t. J-PARC Branch, KEK Theory Center, KEK, Tokai, 319-1106, Japan;u. Institute of Theoretical Physics, University of Wrocław, Wrocław, Poland;1. The Racah Institute of Physics, The Hebrew University, Jerusalem, Israel;2. Department of Physics, NRCN, P.O.B. 9001, Beer-Sheva 84190, Israel;3. School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel;4. Massachusetts Institute of Technology, Cambridge, MA 02139, USA |
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| Abstract: | We develop a method for constructing the heavy baryon chiral perturbation theory (HBChPT) Lagrangian, to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the non-relativistic formalism. We obtain complete lists of independent terms in LHBChPT through O(q3) for off-shell nucleons. Then, eliminating equation-of-motion (e.o.m.) terms at the relativistic and non-relativistic level (both within HBChPT), we obtain LHBChPT for on-shell nucleons, through O(q3). The extension of the method (to obtain on-shell LHBChPT within HBChPT) to higher orders is also discussed. |
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