Summary
Schwinger’s new sum rule for the spin-dependent structure functions is derived from the superconvergence principle. The Regge behaviour of the virtual photon-nucleon scattering amplitude is deduced from the Van Hove model from which a superconvergence relation is shown to follow leading to the sum rule. The saturation of the sum rule is discussed.
Riassunto
Si deduce la nuova regola di somma di Schwinger per le funzioni di struttura dipendenti dallo spin in base al principio di superconvergenza. Si deduce il comportamento di Regge dell’ampiezza di scattering fotone-nucleone virtuale dal modello di Van Hove dal quale si vede che una relazione di superconvergenza segue conducendo alla regola di somma. Si discute la saturazione della regola di somma.
Реэюме
Иэ принципа сверхсходимости выводится новое правило сумм Щвин-гера для структурных функций, эависяших от спина. Устанавливается поведение Редже для амплитуды виртуального рассеяния фотона на нуклоне, исходя иэ модели Ван Хова. Покаэывается, что в зтой модели соотнощение сверхсходимости при-водит к правилу сумм. Обсуждается насышение правила сумм.
Similar content being viewed by others
Literatur
J. Schwinger:Proc. Nat. Acad. Sci.,72, 1, 1559 (1975).
W. Y. Tsai, L. De Raad andK. Milton:Phys. Rev. D,11, 3537 (1975).
See, for instance,V. de Alfaro, S. Fubini, G. Furlan andC. Rossetti:Currents in Hadron Physics (Amsterdam, 1973).
R. L. Heimann:Nucl. Phys.,64 B, 429 (1973).
R. Tarrach: CERN preprint TH. 1989 (1975).
W. A. Bardeen andW.-K. Tung:Phys. Rev.,173, 1423 (1968).
A. M. Harun ar-Rashid:Ann. of Phys.,80, 397, 425 (1975), and preprint ORO 245 (1975), Centre for Particle Theory, Department of Physics, University of Texas, Austin, Tex.
F. D. Gault andM. D. Scadron:Nucl. Phys.,15 B, 442 (1970).
L. Van Hove:Phys. Lett.,24 B, 183 (1967).
B. H. Kellett:Phys. Rev. D,7, 115 (1973).
M. Damashek andF. J. Gilman:Phys. Rev. D,1, 1319 (1970).
B. J. Bjorken andJ. D. Walecka:Ann. of Phys.,38, 35 (1966).
M. Gourdin andPh. Salin:Nuovo Cimento,27, 193, 309 (1963).
R. Delbourgo, Abdus Salam andJ. Strathdee:Proc. Roy. Soc., A284, 146 (1965).
R. G. Moorhouse: invited talk at theTriangle Conference, Slovakia, 1975, CERN preprint Th. 2103.
A. J. G. Hey: Daresbury Lecture Notes DL/R33.
Author information
Authors and Affiliations
Additional information
To speed up publication, the author of this paper has agreed to not receive the proofs for correction.
Rights and permissions
About this article
Cite this article
Harun ar-Rashid, A.M. A simple derivation of schwinger’s sum rule for spin-dependent structure functions. Nuov Cim A 33, 447–459 (1976). https://doi.org/10.1007/BF02729862
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02729862