Ambiguities in the partial-wave analysis of pseudoscalar-meson photoproduction

Physical Review C - Nuclear Physics

Volumn 54, Issue 3, 1996, Pages 1437-1440

  Keaton, Greg ^a   Workman, Ron ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030492254     PISSN: 05562813     EISSN: 1089490X     Source Type: Journal    
DOI: 10.1103/PhysRevC.54.1437     Document Type: Article

References (27)

1. It is often said that 2N-1 carefully chosen observables are required in order to reconstruct N independent amplitudes, up to an overall phase. That this is not generally true (due to quadrant ambiguities) is certainly "long known" if not "well known." See, for example, Ref. [11].
2. While a great deal has been written on the identification and resolution of ambiguities, little of this has been applied in typical partial-wave analyses. The interested reader should see I. Sabba Stefanescu, Z. Phys. C 41, 453 (1988), and references therein, as well as the book by K. Chadan and P.C. Sabitier, Inverse Problems in Quantum Scattering Theory (Springer- Verlag, New York, 1989).
3. While a great deal has been written on the identification and resolution of ambiguities, little of this has been applied in typical partial-wave analyses. The interested reader should see I. Sabba Stefanescu, Z. Phys. C 41, 453 (1988), and references therein, as well as the book by K. Chadan and P.C. Sabitier, Inverse Problems in Quantum Scattering Theory (Springer-Verlag, New York, 1989).
4. R.E. Cutkosky et al., Phys. Rev. D 20, 2839 (1979); R.E. Cutkosky, in Proceedings of the 4th Conference on Baryon Resonances, Toronto, 1980, edited by N. Isgur (unpublished), p. 19.
5. R.E. Cutkosky et al., Phys. Rev. D 20, 2839 (1979); R.E. Cutkosky, in Proceedings of the 4th Conference on Baryon Resonances, Toronto, 1980, edited by N. Isgur (unpublished), p. 19.
6. G. Höhler, in Pion-Nucleon Scattering, edited by H. Schopper, Landolt-Börnstein, New Series, Vol. I/9b2 (Springer-Verlag, Berlin, 1983).
7. A very readable survey of dispersion relation techniques is given by N.M. Queen and G. Violini, Dispersion Theory in High-Energy Physics (Wiley, New York, 1974).
8. I.G. Alekseev et al., Phys. Lett. B 351, 585 (1995).
9. N.W. Dean and P. Lee, Phys. Rev. D 5, 2741 (1972).
10. G. Keaton and R. Workman, Phys. Rev. C 53, 1434 (1996).
11. A.S. Omelaenko, Yad. Fiz. 34, 730 (1981) [Sov. J. Nucl. Phys. 34, 406 (1981)]; V.F. Grushin, E.M. Leikin, and A. Ya. Rotvain, Kratk. Soobshch. Fiz. 11, 20 (1978). See also A.A. Belyaev et al., Nucl. Phys. B213, 210 (1983). Here the method of Gersten [18] has been applied to the photoproduction of neutral pions. Neutral-pion photoproduction was chosen as it does not have a t-channel pion exchange. This helps to justify the restriction to a finite angular momentum cutoff. The possible problems associated with this method are similar to those found in the application of Barrelet's method to πN scattering. See the discussion in Sec. II of Ref. [4].
12. A.S. Omelaenko, Yad. Fiz. 34, 730 (1981) [Sov. J. Nucl. Phys. 34, 406 (1981)]; V.F. Grushin, E.M. Leikin, and A. Ya. Rotvain, Kratk. Soobshch. Fiz. 11, 20 (1978). See also A.A. Belyaev et al., Nucl. Phys. B213, 210 (1983). Here the method of Gersten [18] has been applied to the photoproduction of neutral pions. Neutral-pion photoproduction was chosen as it does not have a t-channel pion exchange. This helps to justify the restriction to a finite angular momentum cutoff. The possible problems associated with this method are similar to those found in the application of Barrelet's method to πN scattering. See the discussion in Sec. II of Ref. [4].
13. A.S. Omelaenko, Yad. Fiz. 34, 730 (1981) [Sov. J. Nucl. Phys. 34, 406 (1981)]; V.F. Grushin, E.M. Leikin, and A. Ya. Rotvain, Kratk. Soobshch. Fiz. 11, 20 (1978). See also A.A. Belyaev et al., Nucl. Phys. B213, 210 (1983). Here the method of Gersten [18] has been applied to the photoproduction of neutral pions. Neutral-pion photoproduction was chosen as it does not have a t-channel pion exchange. This helps to justify the restriction to a finite angular momentum cutoff. The possible problems associated with this method are similar to those found in the application of Barrelet's method to πN scattering. See the discussion in Sec. II of Ref. [4].
14. A.S. Omelaenko, Yad. Fiz. 34, 730 (1981) [Sov. J. Nucl. Phys. 34, 406 (1981)]; V.F. Grushin, E.M. Leikin, and A. Ya. Rotvain, Kratk. Soobshch. Fiz. 11, 20 (1978). See also A.A. Belyaev et al., Nucl. Phys. B213, 210 (1983). Here the method of Gersten [18] has been applied to the photoproduction of neutral pions. Neutral-pion photoproduction was chosen as it does not have a t-channel pion exchange. This helps to justify the restriction to a finite angular momentum cutoff. The possible problems associated with this method are similar to those found in the application of Barrelet's method to πN scattering. See the discussion in Sec. II of Ref. [4].
15. B. Saghai and F. Tabakin, Phys. Rev. C 53, 66 (1996).
16. I.S. Barker, A. Donnachie, and J.K. Storrow, Nucl. Phys. B95, 347 (1975).
17. R.L. Walker, Phys. Rev. 182, 1729 (1969).
18. K.M. Watson, Phys. Rev. 95, 228 (1954).
19. S. Minami, Prog. Theor. Phys. 11, 213 (1954); S. Hayakawa, M. Kawaguchi, and S. Minami, ibid. 11, 332 (1954). The effect of Minami's ambiguity is given, in terms of multipole amplitudes, by H. Pilkuhn, The Interactions of Hadrons (Wiley, New York, 1967), Chap. 10-7.
20. S. Minami, Prog. Theor. Phys. 11, 213 (1954); S. Hayakawa, M. Kawaguchi, and S. Minami, ibid. 11, 332 (1954). The effect of Minami's ambiguity is given, in terms of multipole amplitudes, by H. Pilkuhn, The Interactions of Hadrons (Wiley, New York, 1967), Chap. 10-7.
21. S. Minami, Prog. Theor. Phys. 11, 213 (1954); S. Hayakawa, M. Kawaguchi, and S. Minami, ibid. 11, 332 (1954). The effect of Minami's ambiguity is given, in terms of multipole amplitudes, by H. Pilkuhn, The Interactions of Hadrons (Wiley, New York, 1967), Chap. 10-7.
22. z will change sign at all angles, and yet it is constrained to equal -1 at θ=0° and +1 at 180°. Choices such as φ=θ or φ=∈sinθ leave all observables invariant at 0° and 180°. Some choices, such as φ=θ, can be eliminated if we require that the amplitudes smoothly connect to energy regions where this ambiguity is resolved.
23. λ′μ′ [see, for example, A.R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton, New Jersey, 1957), Sec. 4.3]. However, since this choice is motivated by simplicity (and not physics), we have omitted the details.
24. E. Barrelet, Nuovo Cimento A 8, 331 (1972).
25. A. Gersten, Nucl. Phys. B12, 537 (1969).
26. R.A. Arndt, I.I. Strakovsky, and R.L. Workman, Phys. Rev. C 53, 430 (1996).
27. In a typical energy-dependent analysis, these ambiguities are implicitly removed through a restriction of the analytic forms used in fitting the data.