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Prog. Theor. Phys. Vol. 44 No. 5 (1970) pp. 1317-1339
The Reggeization of the Bethe-Salpeter Scattering Amplitudes
Hideki Matsumoto
Institute of Physics, College of General Education, University of Tokyo, Meguro-ku, Tokyo
(Received June 11, 1970)
Abstract:
The Reggeization of the Bethe-Salpeter amplitude is investigated with general kernels. Assuming some integral representations for the interaction kernels and the modified propagator of the scattering particles with unequal masses, we obtain a sufficient condition for the kernels to be of the Hilbert-Schmidt type. Provided that this condition is satisfied, we prove the following, by studying the meromorphy domain of the partial-wave amplitudes:
1) the Sommerfeld-Watson transformation can be performed,
2) the asymptotic behavior of the leading trajectory as s →-∞ (s: total mass squared) is determined by the rightmost fixed singularity of the kernels, and
3) if the spectral functions of the integral representations are non-negative definite, the derivative of the largest eignvalue µMax(s, l) = {λMin(s, l)}-1 with respect to the angular momentum l is negative for s < 0 and l > -1, and the leading trajectory is real for s < 0 and is nondegenerate.
URL :
http://ptp.ipap.jp/link?PTP/44/1317/
DOI : 10.1143/PTP.44.1317
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