Relativistic resonances: Their masses, widths, lifetimes, superposition, and causal evolution

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 71, Issue 8, 2005, Pages 1-22

  Bohm, Arno R ^a   Sato, Yoshihiro ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ENERGY; MATHEMATICAL ANALYSIS; MATHEMATICAL PARAMETERS; NUCLEAR PHYSICS; QUANTUM THEORY; THEORETICAL STUDY;

EID: 18444375556     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.71.085018     Document Type: Article

References (100)

1. Particle Data Group, S. Eidelman et al., Phys. Lett. B 592, 1 (2004).
2. LEP Collaborations, LEP Electroweak Working Group, and SLD Heavy Flavour and Electroweak Groups, CERNEP-99-15; CERN-EP-2002-091.
3. T. Riemann, in Lecture Notes in Physics, edited by A. Bohm, H. D. Doebner, and P. Kielanowski (Springer-Verlag, Berlin, 1998), Vol. 504, p. 157; T. Riemann, Phys. Lett. B 293, 451 (1992); S. Kirsch and T. Riemann, Comput. Phys. Commun. 88, 89 (1995).
4. T. Riemann, in Lecture Notes in Physics, edited by A. Bohm, H. D. Doebner, and P. Kielanowski (Springer-Verlag, Berlin, 1998), Vol. 504, p. 157; T. Riemann, Phys. Lett. B 293, 451 (1992); S. Kirsch and T. Riemann, Comput. Phys. Commun. 88, 89 (1995).
5. T. Riemann, in Lecture Notes in Physics, edited by A. Bohm, H. D. Doebner, and P. Kielanowski (Springer-Verlag, Berlin, 1998), Vol. 504, p. 157; T. Riemann, Phys. Lett. B 293, 451 (1992); S. Kirsch and T. Riemann, Comput. Phys. Commun. 88, 89 (1995).
6. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 18; C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, New York, 1977), Vol. I, p. 340, Vol. II, pp. 1345, 1353-54; T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood Academic, New York, 1981), Chap. 13. The irreversible nature of quantum mechanical decay has been mentioned in these and other textbooks and lecture notes.
7. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 18; C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, New York, 1977), Vol. I, p. 340, Vol. II, pp. 1345, 1353-54; T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood Academic, New York, 1981), Chap. 13. The irreversible nature of quantum mechanical decay has been mentioned in these and other textbooks and lecture notes.
8. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 18; C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, New York, 1977), Vol. I, p. 340, Vol. II, pp. 1345, 1353-54; T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood Academic, New York, 1981), Chap. 13. The irreversible nature of quantum mechanical decay has been mentioned in these and other textbooks and lecture notes.
9. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 18; C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, New York, 1977), Vol. I, p. 340, Vol. II, pp. 1345, 1353-54; T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood Academic, New York, 1981), Chap. 13. The irreversible nature of quantum mechanical decay has been mentioned in these and other textbooks and lecture notes.
10. G. Gamow, Z. Phys. 51, 204 (1928); J. J. Thomson, Proc. London Math. Soc. 15, 197 (1884).
11. G. Gamow, Z. Phys. 51, 204 (1928); J. J. Thomson, Proc. London Math. Soc. 15, 197 (1884).
12. P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, Oxford, 1958), 4th ed.
13. B. A. Lippmann and J. Schwinger, Phys. Rev. 79, 469 (1950); M. Gell-Mann and H. L. Goldberger, Phys. Rev. 91, 398 (1953); W. Brenig and R. Hagg, Fortschr. Phys. 7, 183 (1959); R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982), 2nd ed., Chap. 7.
14. B. A. Lippmann and J. Schwinger, Phys. Rev. 79, 469 (1950); M. Gell-Mann and H. L. Goldberger, Phys. Rev. 91, 398 (1953); W. Brenig and R. Hagg, Fortschr. Phys. 7, 183 (1959); R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982), 2nd ed., Chap. 7.
15. B. A. Lippmann and J. Schwinger, Phys. Rev. 79, 469 (1950); M. Gell-Mann and H. L. Goldberger, Phys. Rev. 91, 398 (1953); W. Brenig and R. Hagg, Fortschr. Phys. 7, 183 (1959); R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982), 2nd ed., Chap. 7.
16. B. A. Lippmann and J. Schwinger, Phys. Rev. 79, 469 (1950); M. Gell-Mann and H. L. Goldberger, Phys. Rev. 91, 398 (1953); W. Brenig and R. Hagg, Fortschr. Phys. 7, 183 (1959); R. G. Newton, Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982), 2nd ed., Chap. 7.
17. R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).
18. M. Gell-Mann and J. B. Hartle, in Physical Origins of Time Asymmetry, edited by J. J. Halliwell et al. (Cambridge University Press, Cambridge, England, 1994); UCSBTH-95-28, University of California at Santa Barbara, 1995; gr-qc/9509054.
19. R. Peierls, Proc. R. Soc. London A 166, 277 (1938); R. Peierls, in Proceedings of the 1954 Glasgow Conference on Nuclear and Meson Physics, edited by E. M. Bellamy et al. (Pergamon Press, New York, 1995).
20. R. Peierls, Proc. R. Soc. London A 166, 277 (1938); R. Peierls, in Proceedings of the 1954 Glasgow Conference on Nuclear and Meson Physics, edited by E. M. Bellamy et al. (Pergamon Press, New York, 1995).
21. J. von Neumann, Mathematica Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1955).
22. L. A. Khalfin, Sov. Phys. JETP 6, 1063 (1958); L. Fonda, G. C. Ghirardi, and A. Rimini, Rep. Prog. Phys. 41, 587 (1978).
23. L. A. Khalfin, Sov. Phys. JETP 6, 1063 (1958); L. Fonda, G. C. Ghirardi, and A. Rimini, Rep. Prog. Phys. 41, 587 (1978).
24. G. C. Hegerfeldt, Phys. Rev. Lett. 72, 596 (1994); A. Bohm, N. L. Harshman, and H. Walther, Phys. Rev. A 66, 012107 (2002).
25. G. C. Hegerfeldt, Phys. Rev. Lett. 72, 596 (1994); A. Bohm, N. L. Harshman, and H. Walther, Phys. Rev. A 66, 012107 (2002).
26. A. Bohm, S. Maxson, M. Loewe, and M. Gadella, Physica (Amsterdam) 236A, 485 (1997); A. Bohm, J. Math. Phys. (N.Y.) 22, 2813 (1981).
27. A. Bohm, S. Maxson, M. Loewe, and M. Gadella, Physica (Amsterdam) 236A, 485 (1997); A. Bohm, J. Math. Phys. (N.Y.) 22, 2813 (1981).
28. S. Weinberg, The Quantum Theory of Fields (Cambridge University Press, Cambridge, England, 1995), Vol. 1.
29. E. P.Wigner, Ann. Math. 40, 149 (1939); V. Bargmann and E. P. Wigner, Proc. Natl. Acad. Sci. USA 34, 211 (1984).
30. E. P.Wigner, Ann. Math. 40, 149 (1939); V. Bargmann and E. P. Wigner, Proc. Natl. Acad. Sci. USA 34, 211 (1984).
31. R. F. Streater and A. S. Wightman, PCT, Spin & Statistics, and All That (Benjamin, New York, 1986).
32. P. Kielanowski, quant-ph/0312178.
33. M. Veltman, Physica (Utrecht) 29, 186 (1963).
34. M. E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory (Perseus Books, Cambridge, 1995).
35. M. Consoli and A. Sirlin, CERN 86-02, Vol. 1, p. 63, 1986; D.Y. Bardin, A. Leike, T. Riemann, and M. Sachwitz, Phys. Lett. B 206, 546 (1988).
36. A. Sirlin, Phys. Rev. Lett. 67, 2127 (1991); Phys. Rev. Lett. B 267, 240 (1991).
37. A. Sirlin, Phys. Rev. Lett. 67, 2127 (1991); Phys. Rev. Lett. B 267, 240 (1991).
38. S. Willenbrock and G. Valencia, Phys. Lett. B 259, 373 (1991); R. G. Stuart, Phys. Lett. B 262, 113 (1991); 272, 353 (1991); A. Leike, T. Riemann, and J. Rose, Phys. Lett. B 273, 513 (1991); T. Bhattacharya and S. Willenbrock, Phys. Rev. D 47, 4022 (1993); H. G. J. Veltman, Z. Phys. C 62, 35 (1994); M. Passera and A. Sirlin, Phys. Rev. Lett. 77, 4146 (1996).
39. S. Willenbrock and G. Valencia, Phys. Lett. B 259, 373 (1991); R. G. Stuart, Phys. Lett. B 262, 113 (1991); 272, 353 (1991); A. Leike, T. Riemann, and J. Rose, Phys. Lett. B 273, 513 (1991); T. Bhattacharya and S. Willenbrock, Phys. Rev. D 47, 4022 (1993); H. G. J. Veltman, Z. Phys. C 62, 35 (1994); M. Passera and A. Sirlin, Phys. Rev. Lett. 77, 4146 (1996).
40. S. Willenbrock and G. Valencia, Phys. Lett. B 259, 373 (1991); R. G. Stuart, Phys. Lett. B 262, 113 (1991); 272, 353 (1991); A. Leike, T. Riemann, and J. Rose, Phys. Lett. B 273, 513 (1991); T. Bhattacharya and S. Willenbrock, Phys. Rev. D 47, 4022 (1993); H. G. J. Veltman, Z. Phys. C 62, 35 (1994); M. Passera and A. Sirlin, Phys. Rev. Lett. 77, 4146 (1996).
41. S. Willenbrock and G. Valencia, Phys. Lett. B 259, 373 (1991); R. G. Stuart, Phys. Lett. B 262, 113 (1991); 272, 353 (1991); A. Leike, T. Riemann, and J. Rose, Phys. Lett. B 273, 513 (1991); T. Bhattacharya and S. Willenbrock, Phys. Rev. D 47, 4022 (1993); H. G. J. Veltman, Z. Phys. C 62, 35 (1994); M. Passera and A. Sirlin, Phys. Rev. Lett. 77, 4146 (1996).
42. S. Willenbrock and G. Valencia, Phys. Lett. B 259, 373 (1991); R. G. Stuart, Phys. Lett. B 262, 113 (1991); 272, 353 (1991); A. Leike, T. Riemann, and J. Rose, Phys. Lett. B 273, 513 (1991); T. Bhattacharya and S. Willenbrock, Phys. Rev. D 47, 4022 (1993); H. G. J. Veltman, Z. Phys. C 62, 35 (1994); M. Passera and A. Sirlin, Phys. Rev. Lett. 77, 4146 (1996).
43. S. Willenbrock and G. Valencia, Phys. Lett. B 259, 373 (1991); R. G. Stuart, Phys. Lett. B 262, 113 (1991); 272, 353 (1991); A. Leike, T. Riemann, and J. Rose, Phys. Lett. B 273, 513 (1991); T. Bhattacharya and S. Willenbrock, Phys. Rev. D 47, 4022 (1993); H. G. J. Veltman, Z. Phys. C 62, 35 (1994); M. Passera and A. Sirlin, Phys. Rev. Lett. 77, 4146 (1996).
44. S. Willenbrock and G. Valencia, Phys. Lett. B 259, 373 (1991); R. G. Stuart, Phys. Lett. B 262, 113 (1991); 272, 353 (1991); A. Leike, T. Riemann, and J. Rose, Phys. Lett. B 273, 513 (1991); T. Bhattacharya and S. Willenbrock, Phys. Rev. D 47, 4022 (1993); H. G. J. Veltman, Z. Phys. C 62, 35 (1994); M. Passera and A. Sirlin, Phys. Rev. Lett. 77, 4146 (1996).
45. C.W. Oates, K. R. Vogel, and J. L. Hall, Phys. Rev. Lett. 76, 2866 (1996).
46. U. Volz, M. Majerus, H. Liebel, A. Schmitt, and H. Schmoranzer, Phys. Rev. Lett. 76, 2862 (1996).
47. H. Frauenfelder, The Mossbauer Effect (Benjamin, New York, 1962), Sec. 4.2. Agreement of τ and ℏ/Γ within 10% had been established earlier. This accuracy, however, is not better than expected from the Wesskopf-Wigner approximation [27,28].
48. V. Weisskopf and E. P. Wigner, Z. Phys. 63, 54 (1930); 65, 18 (1930).
49. V. Weisskopf and E. P. Wigner, Z. Phys. 63, 54 (1930); 65, 18 (1930).
50. M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1964), Chap. 8.
51. R. G. Stuart, Phys. Rev. D 56, 1515 (1997).
52. G. Hoehler, Eur. Phys. J. C 3, 624 (1998).
53. A. Bernicha, G. Lopez Castro, and J. Pestieau, Nucl. Phys. A597, 623 (1996).
54. A. Bernicha, G. Lopez Castro, and J. Pestieau, Phys. Rev. D 50, 4454 (1994).
55. A. Bohm and N. L. Harshman, Nucl. Phys. B581, 91 (2000).
56. L. S. Schulman, Ann. Phys. (N.Y.) 59, 201 (1970).
57. A. Bohm and H. Kaldass, Phys. Rev. A 60, 4606 (1999).
58. A. Bohm, H. Kaldass, and S. Wickramasekara, Fortschr. Phys. 51, 569 (2003); 51, 604 (2003), where the detailed derivations are given.
59. A. Bohm, H. Kaldass, and S. Wickramasekara, Fortschr. Phys. 51, 569 (2003); 51, 604 (2003), where the detailed derivations are given.
60. A. Bohm, Quantum Mechanics: Foundations and Applications (Springer, New York, 2001), Chap. XVIII, 3rd ed.
61. H. Kaldass, in the Proceedings of the XXV International Colloquium on Group Theoretical Physics, Cocoyoc, Mexico, 2004, edited by G. S. Pogosyan, L. E. Vicent, and D. B. Wolf (World Scientific, Singapore, 2005), p. 333.
62. H. Kaldass et al., hep-th/0504182.
63. A. H. Rosenfeld, Rev. Mod. Phys. 39, 1 (1967).
64. R. H. Dalitz and R. G. Moorhouse, Proc. R. Soc. London A 318, 279 (1970).
65. B. H. Bransden and R. G. Moorhouse, The Pion-Nucleaon System (Princeton University Press, Princeton, NJ, 1973).
66. G. Höhler, πN Newsletter 9, 1 (1993).
67. R. J. Eden, P.V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S-matrix (Cambridge University Press, Cambridge, England, 1966); G. F. Chew, The Analytic S-Matrix (Benjamin, New York, 1966).
68. R. J. Eden, P.V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S-matrix (Cambridge University Press, Cambridge, England, 1966); G. F. Chew, The Analytic S-Matrix (Benjamin, New York, 1966).
69. A. Sirlin, in Proceedings of the Fourth International Symposium on Radiative Corrections (RADCOR98), Barcelona, Spain, 1998, edited by J. Sola (World Scientific, Singapore, 1999).
70. M. Passera and A. Sirlin, Phys. Rev. D 58, 113010 (1998).
71. A. Freitas, W. Hollik, W. Walter, and G. Weiglein, Phys. Lett. B 495, 338 (2000); Nucl. Phys. B632, 189 (2002).
72. A. Freitas, W. Hollik, W. Walter, and G. Weiglein, Phys. Lett. B 495, 338 (2000); Nucl. Phys. B632, 189 (2002).
73. P. Gambino and P. A. Grassi, Phys. Rev. D 62, 076002 (2000).
74. R. G. Stuart, Nucl. Phys. B498, 28 (1997).
75. P. A. Grassi, B. A. Kniehl, and A. Sirlin, Phys. Rev. D 65, 085001 (2002).
76. G. Colangelo, J. Gasser, and H. Leutwyler, Nucl. Phys. B603, 125 (2001).
77. T. D. Lee, R. Oehme, and C. N. Yang, Phys. Rev. 106, 340 (1957).
78. E. B. Norman, S. B. Gazes, S. G. Crane, and D. A. Bennett, Phys. Rev. Lett. 60, 2246 (1988).
79. S. R. Wilkinson et al., Nature (London) 387, 466 (1997); C. F. Barucha et al., Phys. Rev. A 55, R857 (1997).
80. S. R. Wilkinson et al., Nature (London) 387, 466 (1997); C. F. Barucha et al., Phys. Rev. A 55, R857 (1997).
81. A. Bohm and S. Wickramasekara, in Lecture Notes in Physics, edited by F. Benatti et al. (Springer, Berlin, 2003), Vol. 622, p. 315.
82. A. Bohm, M. Gadella, and G. B. Mainland, Am. J. Phys. 57, 1103 (1989).
83. R. de la Madrid and M. Gadella, Am. J. Phys. 70, 626 (2002).
84. A. Bohm, Phys. Rev. A 60, 861 (1999).
85. I. Antoniou, M. Gadella, and G. P. Pronko, J. Math. Phys. (N.Y.) 39, 2459 (1998); A. Bohm et al., J. Math. Phys. (N.Y.) 38, 6072 (1997).
86. I. Antoniou, M. Gadella, and G. P. Pronko, J. Math. Phys. (N.Y.) 39, 2459 (1998); A. Bohm et al., J. Math. Phys. (N.Y.) 38, 6072 (1997).
87. M. Gadella, Lett. Math. Phys. 41, 279 (1997).
88. A. S. Wightman, in Relations de Dispersion et Particules Élémentaires, edited by C. De Witt and R. Omnès (Hermann, Paris, 1960), p. 159-226; H. Joos, Fortschr. Phys. 10, 65 (1962); A. J. Macfarlane, Rev. Mod. Phys. 34, 41 (1962).
89. A. S. Wightman, in Relations de Dispersion et Particules Élémentaires, edited by C. De Witt and R. Omnès (Hermann, Paris, 1960), p. 159-226; H. Joos, Fortschr. Phys. 10, 65 (1962); A. J. Macfarlane, Rev. Mod. Phys. 34, 41 (1962).
90. A. S. Wightman, in Relations de Dispersion et Particules Élémentaires, edited by C. De Witt and R. Omnès (Hermann, Paris, 1960), p. 159-226; H. Joos, Fortschr. Phys. 10, 65 (1962); A. J. Macfarlane, Rev. Mod. Phys. 34, 41 (1962).
91. P. von Brentano, Phys. Rep. 264, 57 (1996), and references therein. This paper uses a finite complex effective Hamiltonian omitting the background φbg and/or bj(s). A. M. Nathan, G. T. Garvey, P. Paul, and E. K. Warburton, Phys. Rev. Lett. 35, 1137 (1975).
92. P. von Brentano, Phys. Rep. 264, 57 (1996), and references therein. This paper uses a finite complex effective Hamiltonian omitting the background φbg and/or bj(s). A. M. Nathan, G. T. Garvey, P. Paul, and E. K. Warburton, Phys. Rev. Lett. 35, 1137 (1975).
93. J. Schwinger, Ann. Phys. (N.Y.) 9, 169 (1960).
94. Warren Nagourney, Jon Sandberg, and Hans Dehmelt, Phys. Rev. Lett. 56, 2797 (1986); J. C. Bergquist, Randall G. Hulet, Wayne M. Itano, and D. J. Wineland, Phys. Rev. Lett. 57, 1699 (1986).
95. Warren Nagourney, Jon Sandberg, and Hans Dehmelt, Phys. Rev. Lett. 56, 2797 (1986); J. C. Bergquist, Randall G. Hulet, Wayne M. Itano, and D. J. Wineland, Phys. Rev. Lett. 57, 1699 (1986).
96. L. K. Gibbons et al., Phys. Rev. D 55, 6625 (1997); Ph.D. thesis, University of Chicago, 1993), RX-1487, see Eq. (2.2).
97. M. Gadella, Int. J. Theor. Phys. 36, 2271 (1997).
98. L. S. Ferreira and E. Maglione, Int. J. Theor. Phys. 42, 2117 (2003); L. S. Ferreira, in Resonances, edited by E. Brandas et al. (Springer, Berlin, 1989), Vol. 352.
99. L. S. Ferreira and E. Maglione, Int. J. Theor. Phys. 42, 2117 (2003); L. S. Ferreira, in Resonances, edited by E. Brandas et al. (Springer, Berlin, 1989), Vol. 352.
100. A. Martin, in Unstable Particles in Z0 Physics, edited by Maurice Lévy et al. (Plenum, New York, 1991).