Summary
Various problems are discussed that relate to osciilations in high-energy scattering. It is shown 1) that oscillations ass→∞ of a scattering amplitudeF(s, t) are not restricted by a polynomial bound and analyticity ins, 2) that for sufficiently larges, the numberN(s, r) of zeros ofF(s, t) within ‖t‖<r<t 0 (wheret 0 is the nearest singularity) satisfiesN(s, r)<C logs, whereC is a constant.
Riassunto
Si studiano vari problemi relativi alle oscillazioni nello scattering di alta energia. Si dimostra 1) che le oscillazioni, pers → ∞, di un'ampiezza di scatteringF(s, t) non sono limitate da un legame polimoniale e dall'analiticità ins, 2) che pers sufficientemente grande, il numeroN(s, r) degli zeri diF(s, t) entro ‖t‖<r<t 0 (dovet 0 è la più vicina singolarità) soddisfaN(s, r) <C logs, doveC è una costante.
Резюме
Обсуждаются различные проблемы, которые связаны с осцилляциями в рассеянии при высоких знергиях. Показывается: 1) что приs→∞ осцилляции амплитуды рассеянияF(s, t) не ограничены многочленной границей и аналитичностью поs, 2) что для достаточно большихs, N(s, r)-число нулейF(s, t) внутри ‖t‖<r<t 0 (гдеt 0 ближайшая сингулярность) удовлетворяет неравенствуN(s, r)<C logs, гдеC констанса.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Literatur
A. Martin: CERN preprint No. 66/488/5-TH.652 (1966).
N. N. Khuri andT. Kinoshita:Phys. Rev.,140, B 706 (1965).
Y. S. Jin andA. Martin:Phys. Rev.,135, B 1369 (1964).
A. Hille:Analytic Function Theory, vol.2 (Theorem 19.2.4).
N. N. Meimann:Sov. Phys. JETP,16, 1609 (1963).
R. J. Eden, P. V. Landshoff, D. I. Olive andJ. C. Polkinghorne:The Analytic S-Matrix (Cambridge, 1966).
R. J. Eden:Journ. Math. Phys., (in press) (1966).
J. D. Bessis: CERN preprint No. TH. 653 (1966).
E. Vogt andG. H. Wannier:Phys. Rev.,95, 1190 (1954).
J. Challifour andR. J. Eden:Journ. Math. Phys.,4, 359 (1963).
Author information
Authors and Affiliations
Additional information
Supported in part by the Air Force Office of Scientific Research, OAR, under grant No. AF EOAR 65–36, with the European Office of Aerospace Research, United States Air Force.
Traduzione a cura della Redazione.
Перевебено ребакиией.
Rights and permissions
About this article
Cite this article
Eden, R.J., Ŀukaszuk, L. Oscillations of scattering amplitudes at high energy. Nuovo Cimento A (1965-1970) 47, 817–821 (1967). https://doi.org/10.1007/BF02771397
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02771397