Symmetry breaking and the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math></span> amplitudes in the unphysical region

C. B. Lang; W. Porod

doi:10.1103/PhysRevD.21.1295

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Symmetry breaking and the $π K$ amplitudes in the unphysical region

C. B. Lang and W. Porod

Institut für Theoretische Physik der Universität Graz, Universitätsplatz 5, A-8010 Graz, Austria

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Phys. Rev. D 21, 1295 – Published 1 March, 1980

DOI: https://doi.org/10.1103/PhysRevD.21.1295

Abstract

We apply two different methods of analytic continuation (fixed- $t$ and hyperbolic dispersion relations with discrepancy) to determine the expansion parameters of the $π K$ amplitudes in the unphysical region near the symmetry point. Part of the available phase-shift data shows inconsistencies with crossing symmetry. The values we obtain for the parameters and for the so-called $σ$ term are then compared with predictions that we derive from different models of chiral-symmetry breaking.

References (26)

S. Ciulli, C. Pomponiu, and I. -S. Stefanescu, Phys. Rep. 17C, 133 (1975) E. Pietarinen, Nuovo Cimento 12A, 522 (1972) Nucl. Phys. B55, 541 (1973)
J. L. Petersen, CERN Report No. 77-04 (unpublished) Niels Bohr Institute Report No. NBI-HE-77-11 (unpublished)
G. Höhler, R. Koch, and E. Pietarinen, University of Karlsruhe Report No. TKP 77-11, 1977 (unpublished) G. Höhler, H. P. Jakob, and R. Strauss, Nucl. Phys. B39, 237 (1972)
H. Nielsen and G. C. Oades, Nucl. Phys. B55, 301 (1973) N. O. Johannesson and J. L. Petersen, ibid. B68, 397 (1974) N. Hedegaard-Jensen, ibid. B77, 173 (1974)
S. Blatnik, J. Stahov, and C. B. Lang, Nuovo Cimento 48A, 107 (1978)
C. B. Lang, Fortschr. Phys. 26, 509 (1978)
E. Reya, Rev. Mod. Phys. 46, 545 (1974) H. Pagels, Phys. Rep. 16C, 219 (1974)
S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) R. W. Griffith, Phys. Rev. 176, 1705 (1968)
S. L. Adler, Phys. Rev. 137, B1022 (1965)
M. Gell-Mann, Phys. Rev. 125, 1067 (1962) M. Gell-Mann, R. J. Oakes, and B. Renner, ibid. 175, 2195 (1968)
K. J. Barnes and C. J. Isham, Nucl. Phys. B17, 267 (1970) H. Genz and J. Katz, ibid. B21, 333 (1970) Phys. Rev. D 6, 908 (1972)
P. R. Auvil, Phys. Rev. D 6, 3209 (1972) P. Dittner, P. H. Dondi, and S. Eliezer, Nucl. Phys. B49, 242 (1972)
W. Marciano and H. Pagels, Phys. Rep. 36C, 137 (1978)
A. C. Hearn, reduce 2 User's Manual, University of Utah, 1973 (unpublished)
T. P. Cheng and R. Dashen, Phys. Rev. Lett. 26, 594 (1971)
C. B. Lang, Nucl. Phys. B93, 415 (1975) Nuovo Cimento 41A, 73 (1977)
M. J. Matison et al., Phys. Rev. D 9, 1872 (1974) A. Firestone et al., ibid. 5, 2188 (1972)
A. M. Bakker et al., Nucl. Phys. B24, 211 (1970) Y. Cho et al., Phys. Lett. 32B, 409 (1970) D. Linglin et al., Nucl. Phys. B57, 64 (1973) B. Jongejans et al., ibid. B67, 381 (1973)
R. Mercer et al., Nucl. Phys. B32, 381 (1972)
P. Estabrooks et al., Nucl. Phys. B133, 490 (1978)
H. Nielsen and G. C. Oades, Nucl. Phys. B49, 573 (1972) ibid.B49, 586 (1972)
G. E. Hite, R. J. Jacob, and F. Steiner, Phys. Rev. D 6, 3333 (1972)
T. W. B. Kibble, Phys. Rev. 117, 1159 (1960)
J. L. Basdevant, C. D. Froggatt, and J. L. Petersen, Nucl. Phys. B72, 413 (1974) private communication
G. C. Fox and M. L. Griss, Nucl. Phys. B80, 403 (1974)
[5], [20] C. B. Lang (unpublished)

[c1] S. Ciulli, C. Pomponiu, and I. -S. Stefanescu, Phys. Rep. 17C, 133 (1975) E. Pietarinen, Nuovo Cimento 12A, 522 (1972) Nucl. Phys. B55, 541 (1973)

[c2] J. L. Petersen, CERN Report No. 77-04 (unpublished) Niels Bohr Institute Report No. NBI-HE-77-11 (unpublished)

[c3] G. Höhler, R. Koch, and E. Pietarinen, University of Karlsruhe Report No. TKP 77-11, 1977 (unpublished) G. Höhler, H. P. Jakob, and R. Strauss, Nucl. Phys. B39, 237 (1972)

[c4] H. Nielsen and G. C. Oades, Nucl. Phys. B55, 301 (1973) N. O. Johannesson and J. L. Petersen, ibid. B68, 397 (1974) N. Hedegaard-Jensen, ibid. B77, 173 (1974)

[c5] S. Blatnik, J. Stahov, and C. B. Lang, Nuovo Cimento 48A, 107 (1978)

[c6] C. B. Lang, Fortschr. Phys. 26, 509 (1978)

[c7] E. Reya, Rev. Mod. Phys. 46, 545 (1974) H. Pagels, Phys. Rep. 16C, 219 (1974)

[c8] S. Weinberg, Phys. Rev. Lett. 17, 616 (1966) R. W. Griffith, Phys. Rev. 176, 1705 (1968)

[c9] S. L. Adler, Phys. Rev. 137, B1022 (1965)

[c10] M. Gell-Mann, Phys. Rev. 125, 1067 (1962) M. Gell-Mann, R. J. Oakes, and B. Renner, ibid. 175, 2195 (1968)

[c11] K. J. Barnes and C. J. Isham, Nucl. Phys. B17, 267 (1970) H. Genz and J. Katz, ibid. B21, 333 (1970) Phys. Rev. D 6, 908 (1972)

[c12] P. R. Auvil, Phys. Rev. D 6, 3209 (1972) P. Dittner, P. H. Dondi, and S. Eliezer, Nucl. Phys. B49, 242 (1972)

[c13] W. Marciano and H. Pagels, Phys. Rep. 36C, 137 (1978)

[c14] A. C. Hearn, reduce 2 User's Manual, University of Utah, 1973 (unpublished)

[c15] T. P. Cheng and R. Dashen, Phys. Rev. Lett. 26, 594 (1971)

[c16] C. B. Lang, Nucl. Phys. B93, 415 (1975) Nuovo Cimento 41A, 73 (1977)

[c17] M. J. Matison et al., Phys. Rev. D 9, 1872 (1974) A. Firestone et al., ibid. 5, 2188 (1972)

[c18] A. M. Bakker et al., Nucl. Phys. B24, 211 (1970) Y. Cho et al., Phys. Lett. 32B, 409 (1970) D. Linglin et al., Nucl. Phys. B57, 64 (1973) B. Jongejans et al., ibid. B67, 381 (1973)

[c19] R. Mercer et al., Nucl. Phys. B32, 381 (1972)

[c20] P. Estabrooks et al., Nucl. Phys. B133, 490 (1978)

[c21] H. Nielsen and G. C. Oades, Nucl. Phys. B49, 573 (1972) ibid.B49, 586 (1972)

[c22] G. E. Hite, R. J. Jacob, and F. Steiner, Phys. Rev. D 6, 3333 (1972)

[c23] T. W. B. Kibble, Phys. Rev. 117, 1159 (1960)

[c24] J. L. Basdevant, C. D. Froggatt, and J. L. Petersen, Nucl. Phys. B72, 413 (1974) private communication

[c25] G. C. Fox and M. L. Griss, Nucl. Phys. B80, 403 (1974)

[c26] [5], [20] C. B. Lang (unpublished)

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Symmetry breaking and the $π K$ amplitudes in the unphysical region

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Symmetry breaking and the πK amplitudes in the unphysical region

Abstract

References (26)

Symmetry breaking and the $π K$ amplitudes in the unphysical region