Finite-Energy Sum Rules, Regge Cuts, and Forward <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>N</mi></math></span> Charge-Exchange Scattering

R. C. Johnson

doi:10.1103/PhysRevD.5.2768

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Finite-Energy Sum Rules, Regge Cuts, and Forward $π N$ Charge-Exchange Scattering

R. C. Johnson

Mathematics Department, Durham University, Durham, England

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Phys. Rev. D 5, 2768 – Published 1 June, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.2768

Abstract

Finite-energy sum rules (FESR) with logarithmic terms are formulated in a way amenable to simple and accurate approximation, thus allowing their convenient use in data fitting with Regge cuts. It is observed that a typical cut FESR contribution is similar to that of a pole lying perhaps half a unit lower in the $J$ plane. Therefore $ρ + ρ^{'}$ fits to $π^{-} p \to π^{0} n$ seem to imply decoupling of the $ρ \otimes P$ Regge cut from the nonflip amplitude at $t = 0$ . This is investigated in more detail, and its implications are pointed out.

References (15)

R. Dolen, D. Horn, and C. Schmid, Phys. Rev. 166, 1768 (1968)
R. J. N. Phillips, Rapporteur's talk at the Amsterdam International Conference on Elementary Particles, 1971 (unpublished)
C. Michael, Nucl. Phys. B8, 431 (1968)
J. Botke and J. R. Fulco, Phys. Rev. 182, 1837 (1969) R. Worden, Caltech. Report No. CALT 68-313, 1971 (unpublished)
J. D. Jackson and C. Quigg, Phys. Letters 29B, 236 (1969)
F. Schrempp, Phys. Letters 29B, 598 (1969), and (unpublished)
R. C. Arnold, Phys. Rev. 153, 1523 (1967) R. C. Arnold and M. L. Blackmon, ibid. 176, 2082 (1968) G. Cohen-Tannoudji, A. Morel, and H. Navelet, Nuovo Cimento 48A, 1075 (1967)
F. S. Henyey, G. L. Kane, J. Pumplin, and M. H. Ross, Phys. Rev. 182, 1579 (1969)
V. Barger and R. J. N. Phillips, Phys. Rev. 187, 2210 (1969)
L. Sertorio and M. Toller, Phys. Rev. Letters 19, 1146 (1967) S.-Y. Chu, B. R. Desai, and D. P. Roy, Phys. Rev. 187, 1896 (1969)
M. G. Olsson, Phys. Rev. 171, 1681 (1968)
J. W. Coleman, private communication
S. Almehed and C. Lovelace, CERN Report No. CERN-TH-1408, 1971 (unpublished)
C. Lovelace, in Proceedings of the Conference on ππ and Kπ Interactions at Argonne National Laboratory, 1969, edited by F. Loeffler and E. Malamud (Argonne National Laboratory, Argonne, Ill., 1969), p. 562
S. P. Denisov et al., in the Amsterdam International Conference on Elementary Particles, 1971 (unpublished)

[c1] R. Dolen, D. Horn, and C. Schmid, Phys. Rev. 166, 1768 (1968)

[c2] R. J. N. Phillips, Rapporteur's talk at the Amsterdam International Conference on Elementary Particles, 1971 (unpublished)

[c3] C. Michael, Nucl. Phys. B8, 431 (1968)

[c4] J. Botke and J. R. Fulco, Phys. Rev. 182, 1837 (1969) R. Worden, Caltech. Report No. CALT 68-313, 1971 (unpublished)

[c5] J. D. Jackson and C. Quigg, Phys. Letters 29B, 236 (1969)

[c6] F. Schrempp, Phys. Letters 29B, 598 (1969), and (unpublished)

[c7] R. C. Arnold, Phys. Rev. 153, 1523 (1967) R. C. Arnold and M. L. Blackmon, ibid. 176, 2082 (1968) G. Cohen-Tannoudji, A. Morel, and H. Navelet, Nuovo Cimento 48A, 1075 (1967)

[c8] F. S. Henyey, G. L. Kane, J. Pumplin, and M. H. Ross, Phys. Rev. 182, 1579 (1969)

[c9] V. Barger and R. J. N. Phillips, Phys. Rev. 187, 2210 (1969)

[c10] L. Sertorio and M. Toller, Phys. Rev. Letters 19, 1146 (1967) S.-Y. Chu, B. R. Desai, and D. P. Roy, Phys. Rev. 187, 1896 (1969)

[c11] M. G. Olsson, Phys. Rev. 171, 1681 (1968)

[c12] J. W. Coleman, private communication

[c13] S. Almehed and C. Lovelace, CERN Report No. CERN-TH-1408, 1971 (unpublished)

[c14] C. Lovelace, in Proceedings of the Conference on ππ and Kπ Interactions at Argonne National Laboratory, 1969, edited by F. Loeffler and E. Malamud (Argonne National Laboratory, Argonne, Ill., 1969), p. 562

[c15] S. P. Denisov et al., in the Amsterdam International Conference on Elementary Particles, 1971 (unpublished)

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Finite-Energy Sum Rules, Regge Cuts, and Forward $π N$ Charge-Exchange Scattering

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Finite-Energy Sum Rules, Regge Cuts, and Forward πN Charge-Exchange Scattering

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References (15)

Finite-Energy Sum Rules, Regge Cuts, and Forward $π N$ Charge-Exchange Scattering