Tests of current algebra and partially conserved axial-vector current in the subthreshold region of the pion-nucleon system

Physical Review C - Nuclear Physics

Volumn 60, Issue 5, 1999, Pages 552041-552047

  Kaufmann, William B ^a   Hite, Gerald E ^b  

^a ARIZONA STATE UNIVERSITY   (United States)

^b TEXAS A AND M UNIVERSITY AT GALVESTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13044254782     PISSN: 05562813     EISSN: 1089490X     Source Type: Journal    
DOI: 10.1103/PhysRevC.60.055204     Document Type: Article

References (31)

1. [1] For an extensive review of topics in current algebra and PCAC see V. de Alfaro, S. Fubini, G. Furlan, and S. Rossetti, Currents in Hadron Physics (North-Holland, Amsterdam, 1973). See also the reviews by D. Campbell, in Nuclear Physics with Heavy Ions and Mesons, Proceedings of the Les Houches Summer School of Theoretical Physics, Les Houches, 1977, edited by R. Balian et al. (North Holland, Amsterdam, 1978); M. D. Scadron, Rep. Prog. Phys. 44, 213 (1981).
2. [1] For an extensive review of topics in current algebra and PCAC see V. de Alfaro, S. Fubini, G. Furlan, and S. Rossetti, Currents in Hadron Physics (North-Holland, Amsterdam, 1973). See also the reviews by D. Campbell, in Nuclear Physics with Heavy Ions and Mesons, Proceedings of the Les Houches Summer School of Theoretical Physics, Les Houches, 1977, edited by R. Balian et al. (North Holland, Amsterdam, 1978); M. D. Scadron, Rep. Prog. Phys. 44, 213 (1981).
3. [1] For an extensive review of topics in current algebra and PCAC see V. de Alfaro, S. Fubini, G. Furlan, and S. Rossetti, Currents in Hadron Physics (North-Holland, Amsterdam, 1973). See also the reviews by D. Campbell, in Nuclear Physics with Heavy Ions and Mesons, Proceedings of the Les Houches Summer School of Theoretical Physics, Les Houches, 1977, edited by R. Balian et al. (North Holland, Amsterdam, 1978); M. D. Scadron, Rep. Prog. Phys. 44, 213 (1981).
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7. [4] S. L. Adler, Phys. Rev. 140, B736 (1965). See also W. I. Weisberger, ibid. 143, 1302 (1966).
8. 2, m is the proton's mass, and μ is the charged pion's mass. The hyperbola corresponds to a = 0, where a is the IDR path parameter defined below.
9. [6] VPI phase-shift analysis SP98, courtesy of Professor R. Arndt. Internet access is through http://said.phys.vt.edu
10. [7] G. E. Hite, R. J. Jacob, and F. Steiner, Phys. Rev. D 6, 3333 (1973).
11. [8] Some preliminary results using the earlier VPI phase-shift analysis SM95 were given in W. Kaufmann, G. Hite, and R. Jacob, πN Newslett. 13, 16 (1997).
12. [9] G. E. Hite, R. J. Jacob, and M. D. Scadron, Phys. Rev. D 14, 1306 (1976). Over the years this region has also been explored by use of other dispersion relations. See Ref. [12] for a detailed review up to the early 1980s. Later work on evaluations of the sigma term may be traced from M. E. Sainio, Chiral Dynamics: Theory and Experiment, edited by A. M. Berstein and B. R. Holstein (Springer, Berlin, 1994), p. 212.
13. [9] G. E. Hite, R. J. Jacob, and M. D. Scadron, Phys. Rev. D 14, 1306 (1976). Over the years this region has also been explored by use of other dispersion relations. See Ref. [12] for a detailed review up to the early 1980s. Later work on evaluations of the sigma term may be traced from M. E. Sainio, Chiral Dynamics: Theory and Experiment, edited by A. M. Berstein and B. R. Holstein (Springer, Berlin, 1994), p. 212.
14. [10] Pioneering work in mapping this region was performed long ago by G. Höhler, H. P. Jacob, and R. Strauss, Nucl. Phys. B39, 237 (1972) and by H. Nielsen and G. C. Oades, ibid. B72, 310 (1974).
15. [10] Pioneering work in mapping this region was performed long ago by G. Höhler, H. P. Jacob, and R. Strauss, Nucl. Phys. B39, 237 (1972) and by H. Nielsen and G. C. Oades, ibid. B72, 310 (1974).
16. 2]. The physical boundary is given by φ(s,t,u) = 0. See T. W. B. Kibble, Phys. Rev. 117, 1159 (1960).
17. [12] G. Höhler, in πN Scattering: Phenomenological Analyses, edited by H. Schopper, Landolt-Börnstein, New Series, Group 1, Vol. 9b, Pt. 2 (Springer, Berlin, 1983). This handbook is an extremely useful compendium of information about the πN system. This book defines v =(s-u)/4m, which differs by the factor of 4m from the value used in the present article.
18. [13] S. Mandelstam, Phys. Rev. Lett. 4, 84 (1960).
19. [14] W. R. Frazer and J. R. Fulco, Phys. Rev. 117, 1603 (1960). The idea of determining ππ scattering lengths from πN scattering data is very old; see the historical summary in Sec. 4.1 of B. R. Martin, D. Morgan, and G. Shaw, Pion-Pion Interactions in Particle Physics (Academic Press, London, 1976). This reference also traces the early development of the discrepancy function.
20. [14] W. R. Frazer and J. R. Fulco, Phys. Rev. 117, 1603 (1960). The idea of determining ππ scattering lengths from πN scattering data is very old; see the historical summary in Sec. 4.1 of B. R. Martin, D. Morgan, and G. Shaw, Pion-Pion Interactions in Particle Physics (Academic Press, London, 1976). This reference also traces the early development of the discrepancy function.
21. [15] R. Müller, G. E. Hite, and R. J. Jacob, Z. Phys. C 8, 199 (1981); G. E. Hite and R. J. Jacob, Nucl. Phys. B134, 291 (1978).
22. [15] R. Müller, G. E. Hite, and R. J. Jacob, Z. Phys. C 8, 199 (1981); G. E. Hite and R. J. Jacob, Nucl. Phys. B134, 291 (1978).
23. [16] See, for example, Richard J. Jacob and Gerald E. Hite, Phys. Rev. D 11, 2466 (1975); E. Borie and F. Kaiser, Nucl. Phys. B126, 173 (1977).
24. [16] See, for example, Richard J. Jacob and Gerald E. Hite, Phys. Rev. D 11, 2466 (1975); E. Borie and F. Kaiser, Nucl. Phys. B126, 173 (1977).
25. [17] We thank Prof. R. Arndt for a discussion on this point.
26. (±) because every fixed-a path passes through the s-channel physical threshold. Each value of the path parameter gives a different extrapolation of the amplitudes to threshold. The variation in values of the threshold amplitude using these different paths is a measure of the uncertainty in the predicted scattering length.
27. -1, given by M. Kermani et al., πN Newslett. 13, 27 (1997).
28. [20] D. C. Moir, R. J. Jacob, and G. E. Hite, Nucl. Phys. B103, 477 (1976).
29. [21] See T. P. Cheng and R. Dashen, Phys. Rev. Lett. 26, 574 (1971) and the reviews in Ref. [1].
30. [22] The larger value is in accordance with our preliminary result [8] and also the work of M. Pavan and R. Arndt, πN Newslett. 13, 165 (1997), which is also based on the VPI phase-shift analysis.
31. [23] D. Sigg et al., Phys. Rev. Lett. 75, 3245 (1995).