Rigorous phase-modulus correlations for forward scattering amplitude at high energies

Jan Fischer; Pavel Kolář; Ivo Vrkoč

doi:10.1103/PhysRevD.13.133

Access by Xinjiang University

Rigorous phase-modulus correlations for forward scattering amplitude at high energies

Jan Fischer and Pavel Kolář^*

Ivo Vrkoč^†

Institute of Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia

Mathematical Institute, Czechoslovak Academy of Sciences, Prague, Czechoslovakia

^*Present address: Fyzikální ústav ČSAV, Na Slovance 2, 18040 Praha 8, Czechoslovakia.
^†Present address: Matematický ústav ČSAV, Žitná 25, 11567 Praha 1, Czechoslovakia.

PDF

Phys. Rev. D 13, 133 – Published 1 January, 1976

DOI: https://doi.org/10.1103/PhysRevD.13.133

Abstract

Starting from the basic results of axiomatic field theory a series of new asymptotic theorems for the symmetric $F_{S} (E)$ and the antisymmetric $F_{A} (E)$ forward scattering amplitudes are derived, $E$ being the laboratory energy. The spins are neglected in the present paper. Assuming that the phase of $F_{S}$ or $F_{A}$ is asymptotically bounded within a certain range of values the corresponding bounds on $| F_{S} | or | F_{A} |$ , respectively, are obtained. Further, we show that certain conditions on the ratio $\frac{Re F_{S} (E)}{Im F_{S} (E)}$ and on the signs of $Re F_{S} (E)$ and $Im F_{S} (E)$ for large enough energies can be formulated as criteria for the asymptotic behavior of the symmetric total cross section $σ_{S} (E)$ . Analogous results are obtained for the antisymmetric forward scattering amplitude. Finally, useful necessary and sufficient conditions for the asymptotic rise or boundedness of $σ_{S} (E)$ and $σ_{A} (E)$ are derived. The results obtained are discussed in light of existing high-energy models and high-energy experiments.

References (29)

U. Amaldi et al., Phys. Phys. Lett. 43B, 231 (1973) ibid.44B, 112 (1973) S. R. Amendolia et al., ibid. 44B, 119 (1973)
V. Bartenev et al., Phys. Rev. Lett. 31, 1367 (1973) W. F. Baker et al., in Proceedings of the XVII International Conference on High Energy Physics, London, 1974, edited by J. R. Smith (Rutherford Laboratory, Chilton, Didcot, Berkshire, England, 1974)
V. K. Birulev et al., JINR Dubna Report No. E 1-6851, 1972 (unpublished)
N. N. Khuri and T. Kinoshita, Phys. Rev. 137, B720 (1965)
N. N. Khuri, T. Kinoshita, Phys. Rev. 140, B706 (1965)
R. Wit, Acta Phys. Pol. 29, 771 (1966)
J. S. Jin and S. W. McDowell, Phys. Rev. 138, B1279 (1965)
H. Cornille, Nuovo Cimento 66A, 217 (1970)
G. Grunberg and Tran N. Truong, Phys. Rev. D 9, 2874 (1974)
Yu. S. Vernov, Zh. Eksp. Teor. Fiz. 50, 672 (1966) ibid.53, 191 (1967)
Yu. S. Vernov, Yad. Fiz. 10, 176 (1969)
M. Meiman, Zh. Eksp. Teor. Fiz. 43, 2277 (1962)
J. Bros, H. Epstein, and V. Glaser, Nuovo Cimento 31, 1265 (1964) Commun. Math. Phys. 1, 240 (1965)
Hung Cheng, J. K. Walker, and Tai Tsun Wu, Phys. Lett. 44B, 97 (1973) ibid.44B, 283 (1973)
P. Kroll, Lett. Nuovo Cimento 7, 745 (1973)
C. Bourrely and J. Fischer, Nucl. Phys. B61, 513 (1973)
C. Bourrely, J. Fischer, and Z. Sekera, Nucl. Phys. B67, 452 (1973)
W. Bartel and A. N. Diddens, CERN Internal Report No. NP 73-4, 1973 (unpublished)
L. Lukaszuk and B. Nicolescu, Lett. Nuovo Cimento 8, 405 (1973)
H. Epstein, V. Glaser, A. Martin, Commun. Math. Phys. 13, 257 (1969)
M. Froissart, Phys. Rev. 123, 1053 (1961) A. Martin, ibid. 129, 1432 (1963) Nuovo Cimento 42, 930 (1966)
Y. S. Jin and A. Martin, Phys. Rev. 135, 1369 (1964)
S. Weinberg, Phys. Rev. 124, 2049 (1961)
Tran N. Truong and W. S. Lam, Phys. Rev. D 6, 2875 (1972)
R. Boas, Entire Functions (Academic, New York, 1954), p. 3
K. Hoffman, Banach Spaces of Analytic Functions (Prentice-Hall, Englewood Cliffs, N. J., 1962)
I. I. Privalov, Granichnye svoystva analiticheskih funktsii, (Gostehizdat, Moskva-Leningrad, 1950) (German translation: VEB Deutscher Verlag der Wissenschaften, Berlin, 1956)
I. Vrkoč, Czech. Math. J. 98, 455 (1973)
G. M. Goluzin, Geometricheskaya teoria funktsii kompleksnogo peremennogo (Nauka, Moskva, 1966)

[c1] U. Amaldi et al., Phys. Phys. Lett. 43B, 231 (1973) ibid.44B, 112 (1973) S. R. Amendolia et al., ibid. 44B, 119 (1973)

[c2] V. Bartenev et al., Phys. Rev. Lett. 31, 1367 (1973) W. F. Baker et al., in Proceedings of the XVII International Conference on High Energy Physics, London, 1974, edited by J. R. Smith (Rutherford Laboratory, Chilton, Didcot, Berkshire, England, 1974)

[c3] V. K. Birulev et al., JINR Dubna Report No. E 1-6851, 1972 (unpublished)

[c4] N. N. Khuri and T. Kinoshita, Phys. Rev. 137, B720 (1965)

[c5] N. N. Khuri, T. Kinoshita, Phys. Rev. 140, B706 (1965)

[c6] R. Wit, Acta Phys. Pol. 29, 771 (1966)

[c7] J. S. Jin and S. W. McDowell, Phys. Rev. 138, B1279 (1965)

[c8] H. Cornille, Nuovo Cimento 66A, 217 (1970)

[c9] G. Grunberg and Tran N. Truong, Phys. Rev. D 9, 2874 (1974)

[c10] Yu. S. Vernov, Zh. Eksp. Teor. Fiz. 50, 672 (1966) ibid.53, 191 (1967)

[c11] Yu. S. Vernov, Yad. Fiz. 10, 176 (1969)

[c12] M. Meiman, Zh. Eksp. Teor. Fiz. 43, 2277 (1962)

[c13] J. Bros, H. Epstein, and V. Glaser, Nuovo Cimento 31, 1265 (1964) Commun. Math. Phys. 1, 240 (1965)

[c14] Hung Cheng, J. K. Walker, and Tai Tsun Wu, Phys. Lett. 44B, 97 (1973) ibid.44B, 283 (1973)

[c15] P. Kroll, Lett. Nuovo Cimento 7, 745 (1973)

[c16] C. Bourrely and J. Fischer, Nucl. Phys. B61, 513 (1973)

[c17] C. Bourrely, J. Fischer, and Z. Sekera, Nucl. Phys. B67, 452 (1973)

[c18] W. Bartel and A. N. Diddens, CERN Internal Report No. NP 73-4, 1973 (unpublished)

[c19] L. Lukaszuk and B. Nicolescu, Lett. Nuovo Cimento 8, 405 (1973)

[c20] H. Epstein, V. Glaser, A. Martin, Commun. Math. Phys. 13, 257 (1969)

[c21] M. Froissart, Phys. Rev. 123, 1053 (1961) A. Martin, ibid. 129, 1432 (1963) Nuovo Cimento 42, 930 (1966)

[c22] Y. S. Jin and A. Martin, Phys. Rev. 135, 1369 (1964)

[c23] S. Weinberg, Phys. Rev. 124, 2049 (1961)

[c24] Tran N. Truong and W. S. Lam, Phys. Rev. D 6, 2875 (1972)

[c25] R. Boas, Entire Functions (Academic, New York, 1954), p. 3

[c26] K. Hoffman, Banach Spaces of Analytic Functions (Prentice-Hall, Englewood Cliffs, N. J., 1962)

[c27] I. I. Privalov, Granichnye svoystva analiticheskih funktsii, (Gostehizdat, Moskva-Leningrad, 1950) (German translation: VEB Deutscher Verlag der Wissenschaften, Berlin, 1956)

[c28] I. Vrkoč, Czech. Math. J. 98, 455 (1973)

[c29] G. M. Goluzin, Geometricheskaya teoria funktsii kompleksnogo peremennogo (Nauka, Moskva, 1966)

Physical Review D

Export citation

Export citation

Rigorous phase-modulus correlations for forward scattering amplitude at high energies

Abstract

References (29)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation