Variational field theoretic approach to relativistic meson-nucleon scattering |
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| Institution: | 1. Department of Natural Sciences, University of Cyprus, CY-1678 Nicosia, Cyprus;2. Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland;3. TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., Canada V6T 2A3;4. Department of Physics and Mathematical Physics and Research Centre for the Subatomic Structure of Matter, University of Adelaide, Adelaide, S.A. 5005, Australia;1. Département de Physique Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France;2. RIKEN Nishina Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan;3. Center for Nuclear Study, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan;4. Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain;5. Department of Physics, Technische Universitat Darmstadt, Germany;6. Institut de Physique Nucleaire Orsay, IN2P3-CNRS, F-91406 Orsay Cedex, France;7. LPC Caen, ENSICAEN, Universite de Caen, CNRS/IN2P3, F-14050 Caen, France;8. Department of Physics, Tohoku University, Aramaki Aza-Aoba 6-3, Aoba, Sendai, Miyagi 980-8578, Japan;9. Department of Applied Physics, University of Miyazaki, Gakuen-Kibanadai-Nishi 1-1, Miyazaki 889-2192, Japan;10. Department of Physics, Ehwa Womans University, Republic of Korea;11. Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan;12. Department of Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro, Tokyo 152-8551, Japan;13. MTA Atomki, P.O. Box 51, Debrecen H-4001, Hungary;14. Department of Physics, Kyoto University, Kitashirakawa, Sakyo, Kyoto 606-8502, Japan;15. Department of Physics, Kyushu University, Nishi, Fukuoka 819-0395, Japan;p. Department of Physics, Technische Universitat Munchen, Germany;q. Center for Exotic Nuclear Studies, Institute for Basic Science, Daejeon 34126, Republic of Korea;r. School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China;1. Physics Department, University of Trento, Via Sommarive 14, I-38123 Trento, Italy;2. INFN-TIFPA Trento Institute of Fundamental Physics and Applications, Via Sommarive, 14, 38123 Povo TN, Italy;3. Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA;4. Institute for Nuclear Theory, University of Washington, Seattle, WA 98195, USA;5. Department of Physics, The City College of New York, New York, NY 10031, USA;6. Institut de Physique Nucléaire, CNRS/IN2P3, Univ. Paris-Sud, Université Paris-Saclay, F-91406 Orsay, France;7. Department of Physics, University of Arizona, Tucson, AZ 85721, USA;1. Nuclear Physics Institute of the Czech Academy of Sciences, 25069 Řež, Czech Republic;2. Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Břehová 7, 11519 Prague 1, Czech Republic;3. Racah Institute of Physics, The Hebrew University, 91904 Jerusalem, Israel;4. ESNT, IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France;5. Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL, United Kingdom |
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| Abstract: | Non-perturbative polaron variational methods are applied, within the so-called particle or world-line representation of relativistic field theory, to study scattering in the context of the scalar Wick-Cutkosky model. Important features of the variational calculation are that it is a controlled approximation scheme valid for arbitrary coupling strengths, the Green functions have all the cuts and poles expected for the exact result at any order in perturbation theory and that the variational parameters are simultaneously sensitive to the infrared as well as the ultraviolet behaviour of the theory. We generalize the previously used quadratic trial action by allowing more freedom for off-shell propagation without a change in the on-shell variational equations and evaluate the scattering amplitude at first order in the variational scheme. Particular attention is paid to the s-channel scattering near threshold because here non-perturbative effects can be large. We check the unitarity of a our numerical calculation and find it greatly improved compared to perturbation theory and to the zeroth order variational results. |
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