Abstract
The dispersion relation is an indispensable tool for analyzing various problems in high energy physics. In this paper, we shall consider applications of a new type of dispersion relation to various problems.
Work supported in part by the U.S. Atomic Energy Commission.
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References
e.g. M. L. Goldberger and K. M. Watson, “Collision Theory” John-Wiley and Sons, N. Y. (1964).
e.g. G. Frye and R. L. Warnock, Phys. Rev. 130, 478 (1963); M. Sugawara and A. Tubis, ibid 130, 2127 (1963).
B. V. Geshkenbein, Yad. Fiz. 9, 1232 (1969) [English Translation, Soviet Journ. of Nucl. Phys. 9, 720 (1969)].
I. Raszillier, Lett. Nuovo Cimento 2, 349 (1971) and preprint, Institute of Physics, Bucharest (1971).
D. N. Levin, V. S. Mathur and S. Okubo, Phys. Rev. to be published. In this paper, we rediscovered the same results of reference (3) without being aware of its prior existence.
T. N. Truong and R. Vinh-Mau; Phys. Rev. 117, 2494 1969).
D. R. Palmer, Nuovo Cimento, to be published.
N. N. Meiman, Zh. Eksperim. i. Theor. Fiz. 44, 1228 (1963) [English Translation: Soviet Phys. J.E.T.P. 17, 830 (1963)].
S. Okubo, Phys. Rev. D4, 725 (1971) and D3, 2807 (1971).
L. F. Li and H. Pagels, Phys. Rev. D3, 2191 (1971) and D4, 255 (1971).
M. Gell-Mann, R. J. Oakes and B. Renner, P ys. Rev. 175, 2195 (1968); S. L. Glashow and S. Weinberg, Phys. Rev. Lett. 20, 224 (1968).
See reference (9). Actually, another possible solution \(\left ( \textup{A}_{44} \right) \frac{1}{2}+\left ( \textup{A}_{33} \right) \frac{1}{2}\leqslant \left ( \textup{V}_{44} \right) \frac{1}{2}\) has been rejected in view of the fact that it contradicts the exact SU (3) limit.
S. Okubo and I. F. Shih, Phys. Rev. D4, 2020 (1971); I. F. Shih and S. Okubo, Phys. Rev. D4, to appear in Dec. 1 (1971) issue.
C. Callan and S. B. Treiman, Phys. Rev. Lett. 16, 153 (1966); M. Suzuki, ibid 16, 212 (1966); V. S. Mathur, S. Okubo and L. K. Pandit, ibid, 16, 311 (1961). In view of a SU (3) consideration, we choose the the soft pion point at \(\textup{t}=\textup{m}_{\textup{K}} {2}-\textup{m}_{\textup{K}} {\pi}\). See R. Dashen and M. Weinstein, Phys. Rev. Lett. 22, 1337 (1969).
M. Ademollo and R. Gatto, Phys. Rev. Lett. 13, 264 (1965); H. R. Quinn and J. D. Bjorken, Phys. Rev. 171, 1660 (1968).
L. M. Chounet, J. M. Gaillard and M. K. Gaillard, CERN preprint (1971).
S. D. Drell, A. C. Finn, and A. C. Hearn, Phys. Rev. 136, 1439 (1964).
D. R. Palmer, Phys. Rev. D4, 1558 (1971).
Here, we use a version of the Phragmén and Lindelöf theorm due to Nevalinna, Eindeutige Analytische Funktionen, (Anfl. Springer Verlag. Berlin 1953, p. 44); E. Hille, Analytic Function Theory, Vol. II, (Ginn and Co. Boston, p. 412, 1962).
S. Ciulli, quoted in reference (4). Unfortunately, the present author did not have an opportunity to see this paper.
K. Hoffmann, Banach Spaces of Analytic Functions, (Prentice Hall, Englewood Cliffs, N. J. 1962); H. Helson, Lectures on Invariant Sub-spaces, (Academic Press, New York 1964).
H. Harari, Phys. Rev. Lett. 17, 1303 (1966). However, the normalization of t2 (υ,q2) is different by a factor π from the one used in this paper.
S. D. Drell and T. M. Yan, Phys. Rev. Lett. 24, 181 (1970).
M. Damashek and F. J. Gilman, Phys. Rev. D1, 1319 (1970).
Y. S. ** and A. Martin, Phys. Rev. 135, B1395 (1964).
A. Martin, “High-Energy Physics and Elementary Particles,” International Atomic Energy Agency, Vienna, 1965, p. 155; L. Lukaszuk and A. Martin, Nuovo Cimento, 52A, 122 (1967).
A. K. Common and R. Wit, Nuovo Cimento 3A, 179 (1971).
A. Martin, Nuovo Cimento 47, 265 (1969); A. K. Common, ibid 63, 863 (1969); F. J. Yndurain, ibid 64, 225 (1969).
B. Bonnier and R. Vinh Mau, Phys. Rev. 165, 1923 (1967).
D. N. Levin, S. Okubo and D. R. Palmer, Phys. Rev. D4, 1847 (1971); D. N. Levin and D. R. Palmer, Phys. Rev. D, to appear in the Dec. 15, 1971 issue.
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Okubo, S. (1973). Dispersion Inequalities and Their Application to the Pion’s Electromagnetic Radius and the Kℓ3 Parameters. In: Iverson, G., Perlmutter, A., Mintz, S. (eds) Fundamental Interactions in Physics and Astrophysics. Studies in the Natural Sciences, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-4586-2_9
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DOI: https://doi.org/10.1007/978-1-4613-4586-2_9
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