Vacuum exchanges

G. F. Chew andS. C. Frautschi:Phys. Rev. Lett.,7, 394 (1961).

K. Igi:Phys. Rev. Lett.,9, 76 (1962);Phys. Rev.,130, 820 (1963).

B. Udgaonkar:Phys. Rev. Lett.,8, 144 (1962). The interpretation of theP′ is unclear in this paper due to the neglect of the signature factor.

M. G. Olsson: University of Winsconsin preprint (July 1967);Phys. Lett.,26 B, 310 (1968);Phys. Rev. (to be published).

This technique of «extended analyticity» was first used byY. Liu andS. Okubo:Phys. Rev. Lett.,19, 190 (1967).

This method of derivation is similar to that employed byA. Della Selva, L. Masperi andR. Odorico:Nuovo Cimento,52 A, 1357 (1967). A more detailed discussion of the CMSR is contained inM. G. Olsson: to be published.

A. Logunov, L. Soloview andA. Tavkhelidze:Phys. Lett.,24 B, 181 (1967);D. Horn andC. Schmid: California Institute of Technology preprint CALT-68-127 (unpublished).

V. Meshcheriakov, K. Rerikh, A. Tavkhelidze andV. Zhuravlev:Phys. Lett.,25 B, 341 (1967);M. G. Olsson:Phys. Rev. Lett.,19, 550 (1967).

W. Gilbert:Phys. Rev.,108, 1078 (1957).

Low-energy data were taken from the compilation ofN. P. Klepikov, V. A. Meshcheryakov andS. N. Sokolov: Dubna report D-584. Other low-energy data usedO. T. Vik andH. Rugge:Phys. Rev.,129, 2311 (1963). Medium-energy data used were from the recent English experimentA. A. Carter, K. F. Riley, R. J. Tapper, D. V. Bugg, R. S. Gilmore, K. M. Knight, D. C. Salter, G. H. stafford, E. J. N. Wilson, J. D. Davies, J. D. Dowell, P. M. Hattersley, R. J. Homer andA. W. O'Dell:Phys. Rev.,168, 1457 (1968). At higher energies the experiments used wereA. Diddens, E. W. Jenkins, T. F. Kycia andK. F. Riley:Phys. Rev. Lett.,10, 262 (1963);A. Citron, W. Galbraith, T. F. Kycia, B. A. Leontic, R. H. Phillips, A. Rousset andP. H. Stapp:Phys. Rev.,144, 1101 (1966); andK. J. Foley, R. S. Jones, S. J. Lindenbaum, W. A. Love, S. Ozaki, E. D. Platner, C. A. Quarles andE. H. Willen:Phys. Rev. Lett.,19, 330 (1967).

An additional Regge pole can be artificially inserted into the problem at the beginning and a test made whether CMSR changes or not. The CMSR resultI(ε) is not sensitive to these variations for ε>−5.

A discussion of the calculational details in a similar analysis is contained inM. G. Olsson:Phys. Rev. (to be published). The sum rules are only weakly dependent on the pole coupling constant. The value of the threshold amplitude was taken to beT(μ)=(0±0.06) (GeV)−1.

K. J. Foley, R. S. Jones, S. J. Lindenbaum, W. A. Love, S. Ozaki, E. D. Platner, C. A. Quarles andE. H. Willen:Phys. Rev. Lett.,19, 193 (1967). ref. (4)S. Weinberg:Phys. Rev. Lett.,18, 507 (1967).

J. Scanio:Phys. Rev.,152, 1337 (1966);O. Miyamura andF. Takagi: Tohoku University preprint (December 1967);R. K. Logan andM. S. K. Razmi:Phys. Rev.,169, 1167 (1968);M. Restignoli, L. Sertorio andM. Toller:Phys. Rev.,150, 1389 (1966).

W. D. Walker, J. Carroll, A. Garfinkel andB. Y. Oh:Phys. Rev. Lett.,18, 630 (1967):E. Malamud andP. E. Schlein:Phys. Rev. Lett.,19, 1056 (1967).

G. Höhler andG. Eisenbeiss: Institut für Theoretische Kernphysik der Technischen Hochschule preprint.