Optimal Bounds on Cross-Section Moments in <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mo>−</mo><mi>π</mi></math></span> and <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mo>−</mo><mi>N</mi></math></span> Scattering

Alasdair C. Steven

doi:10.1103/PhysRevD.7.2709

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Optimal Bounds on Cross-Section Moments in $π - π$ and $π - N$ Scattering

Alasdair C. Steven

Cavendish Laboratory, University of Cambridge, Cambridge, England

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Phys. Rev. D 7, 2709 – Published 1 May, 1973

DOI: https://doi.org/10.1103/PhysRevD.7.2709

Abstract

Froissart-like bounds are derived for a selection of moments of the total cross section in $π - π$ and $π - N$ scattering. These bounds stem from an economical set of constraints - unitarity and the Froissart-Gribov representation of the $D$ -wave scattering length in the crossed channel $α \frac{t}{2}$ -which are rigorous to within the value assigned to this scattering length. The results are optimally tight for the given constraints and represent a substantial improvement on the bounds of Yndurain and Common, from whose work this paper has been developed. In the case of $π - N$ scattering, it is possible to invert the argument by using experimental data on total cross sections to impose a lower bound on $α \frac{t}{2}$ .

References (14)

F. J. Yndurain, Phys. Letters 31B, 368 (1970)
A. K. Common, Nuovo Cimento 59A, 115 (1970)
F. J. Yndurain and A. K. Common, Nucl. Phys. B26, 167 (1971)
M. Einhorn and R. Blankenbecler, Ann. Phys. (N.Y.) 67, 480 (1971)
F. J. Yndurain and A. K. Common, Nucl. Phys. B34, 509 (1972)
G. Giacomelli, CERN Report No. CERN-HERA 69-3 (unpublished)
D. Morgan and G. Shaw, Nucl. Phys. B10, 261 (1969)
B. Bonnier and P. Gauron, Nucl. Phys. B36, 11 (1972)
J. C. Le Guillou, A. Morel, and H. Navelet, Nuovo Cimento 5A, 659 (1971)
R. Roskies, Phys. Rev. D 2, 247 (1971)
M. R. Pennington, Nuovo Cimento 5A, 644 (1971)
G. Wanders, in Springer Tracts in Modern Physics, Vol. 57, edited by G. Höhler (Springer, Berlin, 1972)
G. Wanders, in Lecture Notes from GIFT Seminar, 1971 (unpublished)
S. M. Roy, Phys. Letters 36B, 353 (1971)

[c1] F. J. Yndurain, Phys. Letters 31B, 368 (1970)

[c2] A. K. Common, Nuovo Cimento 59A, 115 (1970)

[c3] F. J. Yndurain and A. K. Common, Nucl. Phys. B26, 167 (1971)

[c4] M. Einhorn and R. Blankenbecler, Ann. Phys. (N.Y.) 67, 480 (1971)

[c5] F. J. Yndurain and A. K. Common, Nucl. Phys. B34, 509 (1972)

[c6] G. Giacomelli, CERN Report No. CERN-HERA 69-3 (unpublished)

[c7] D. Morgan and G. Shaw, Nucl. Phys. B10, 261 (1969)

[c8] B. Bonnier and P. Gauron, Nucl. Phys. B36, 11 (1972)

[c9] J. C. Le Guillou, A. Morel, and H. Navelet, Nuovo Cimento 5A, 659 (1971)

[c10] R. Roskies, Phys. Rev. D 2, 247 (1971)

[c11] M. R. Pennington, Nuovo Cimento 5A, 644 (1971)

[c12] G. Wanders, in Springer Tracts in Modern Physics, Vol. 57, edited by G. Höhler (Springer, Berlin, 1972)

[c13] G. Wanders, in Lecture Notes from GIFT Seminar, 1971 (unpublished)

[c14] S. M. Roy, Phys. Letters 36B, 353 (1971)

Physical Review D

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Optimal Bounds on Cross-Section Moments in $π - π$ and $π - N$ Scattering

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Optimal Bounds on Cross-Section Moments in π−π and π−N Scattering

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References (14)

Optimal Bounds on Cross-Section Moments in $π - π$ and $π - N$ Scattering