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Relativistic many-body Hamiltonian approach to mesons

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Publication Date
2002-01-14
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Cotanch, Stephen R.
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Elsevier Science Bv
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We represent QCD at the hadronic scale by means of an effective Hamiltonian, H, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicitly broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon applications for the u, d, s and c quark flavors and compute the mass spectrum for the pseudoscalar, scalar and vector mesons. We also perform a comparative study of alternative many-body techniques for approximately diagonalizing, H: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. The Dirac structure of the field theoretical Hamiltonian naturally generates spin dependent interactions, including tensor, spin-orbit and hyperfine, and we clarify the degree of level splitting due to both spin and chiral symmetry effects. Significantly, we find that roughly two thirds of the pi-rho mass difference is due to chiral symmetry and that only the RPA preserves chiral symmetry. We also document how hadronic mass scales are generated by chiral symmetry breaking in the model vacuum. In addition to the vacuum condensates, we compute meson decay constants and detail the Nambu-Goldstone realization of chiral symmetry by numerically verifying the Gell-Mann-Oakes-Renner relation.
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©2002 Elsevier Science B.V. All rights reserved. The authors are grateful for comments and discussions with P. Bicudo, J.E. Ribeiro and A. Szczepaniak. This work is supported in part by grants DOE DE-FG02-97ER41048 and NSF INT-9807009. F.J. Llanes-Estrada was a SURA-Jefferson Laboratory graduate fellowship recipient. Supercomputer time from NERSC is also acknowledged.
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[1] A.P. Szczepaniak, E.S. Swanson, C.-R. Ji, S.R. Cotanch, Phys. Rev. Lett. 76 (1996) 2011. [2] D.G. Robertson, E.S. Swanson, A.P. Szczepaniak, C.-R. Ji, S.R. Cotanch, Phys. Rev. D 59 (1999) 074019. [3] F.J. Llanes-Estrada, S.R. Cotanch, Phys. Rev. Lett. 84 (2000) 1102. [4] E. Gubankova, C.-R. Ji, S.R. Cotanch, Phys. Rev. D 62 (2000) 125012. [5] F.J. Llanes-Estrada, S.R. Cotanch, Phys. Lett. B 504 (2001) 15. [6] A. Le Yaouanc, L. Oliver, O. Pene, J.-C. Raynal, Phys. Rev. D 29 (1984) 1233; A. Le Yaouanc, L. Oliver, S. Ono, O. Pene, J.-C. Raynal, Phys. Rev. D 31 (1985) 137. [7] S.L. Adler, A.C. Davis, Nucl. Phys. B 244 (1984) 469. [8] P. Bicudo, J.E. Ribeiro, Phys. Rev. D 42 (1990) 5; P. Bicudo, J.E. Ribeiro, J. Rodrigues, Phys. Rev. C 52 (1995) 4; P. Bicudo, dissertation presented to Instituto Superior Tecnico de Lisboa, 1987; P. Bicudo, J.E. Ribeiro, private communication. [9] R. Brockmann, W. Weise, E. Werner, Phys. Lett. B 122 (1983) 201; V. Bernard, R. Brockmann, M. Schaden, W. Weise, E. Werner, Nucl. Phys. A 412 (1984) 349; W. Weise, Int. Rev. Nucl. Phys., Vol. 1, World Scientific, 1984, p. 57. [10] D. Zwanziger, Nucl. Phys. B 485 (1997) 185. [11] N. Brambilla, A. Pineda, J. Soto, A. Vairo, Phys. Rev. D 60 (1999) 091502. [12] A.P. Szczepaniak, E.S. Swanson, Phys. Rev. D 55 (1997) 3987 and preprint. [13] F.J. Llanes-Estrada, A.P. Szczepaniak, S.R. Cotanch, to be published and private communication. [14] C.D. Roberts, A.G. Williams, Prog. Part. Nucl. Phys. 33 (1994) 477. [15] C.D. Roberts, R.T. Cahill, J. Praschifka, Ann. Phys. 188 (1988) 20; C.D. Roberts, R.T. Cahill, M.E. Sevior, N. Iannella, Phys. Rev. D 49 (1994) 125. [16] V.A. Miransky, Dynamical Symmetry Breaking in Quantum Field Theory, World Scientific, 1993. [17] P.C. Tandy, Prog. Part. Nucl. Phys. 39 (1997) 117. [18] A. Dobado, A. Gomez-Nicola, A.L.Maroto, J.R. Pelaez, Effective Lagrangians for the Standard Model, Springer Verlag, New York, 1997. [19] J. Gasser, H. Leutwyler, Ann. Phys. 158 (1984) 142. [20] P. Maris, C.D. Roberts, Phys. Rev. C 56 (1997) 3369. [21] J.M. Eisenberg, W. Greiner, Nuclear Theory, North Holland, 1976, Vol. 2, Appendix A, and Vol. 3. [22] P. Ring, P. Schuck, The Nuclear Many Body Problem, Springer-Verlag, New York, 1980. [23] R. Mattueck, A Guide to Feynman Diagrams in the Many Body Problem, Dover, 1992. [24] R. Dashen, Phys. Rev. D 3 (1971) 1879. [25] D.J. Thouless, Nucl. Phys. 22 (1961) 78. [26] Eur. Phys. J. C 15 (2000) 1–878. [27] A. De Rujula, H. Georgi, S.L. Glashow, Phys. Rev. D 12 (1975) 147. [28] P. Bicudo, Phys. Rev. C 60 (1999) 035209. [29] F.J. Gilman, R. Kauffman, Phys. Rev. D 36 (1987) 2761. [30] D. Kekez, D. Klabucar, M.D. Scadron, J. Phys. G 26 (2000) 1335. [31] Th. Feldmann, Int. J. Mod. Phys. A 15 (2000) 159. [32] N. Isgur, Phys. Rev. D 62 (2000) 014025. [33] N.A. Tornqvist, S. Ono, Phys. Rev. D 29 (1984) 110; Y. P. Kuang, T.-M. Yan, Phys. Rev. D 41 (1990) 155; A. Bradley, D. Robson, Z. Phys. C 6 (1980) 57; A. Arneodo, J.L. Femenias, Z. Phys. C 3 (1970) 37; Y.-B. Ding, K.-T. Chao, D.-H. Qin, Phys. Rev. D 51 (1995) 5064; Y.-B. Ding, K.-T. Chao, D.-H. Qin, Phys. Rev. D 44 (1991) 3562; R.-M. Richard, Z. Phys. C 4 (1980) 211; A. Bradley, D. Robson, Phys. Lett. B 93 (1980) 69. [34] M.E. Rose, Elementary Theory of Angular Momentum, Dover, 1995.
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