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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

TMF, 1970 Volume 5, Number 2, Pages 235–243 (Mi tmf4203)

This article is cited in 5 papers

Sum rules for the ratio of the $\pi^{\pm} p$-scattering amplitudes

V. Z. Baluni, Yu. S. Vernov


Abstract: Analyticity, unitarity, and crossing symmetry are used to obtain an exact integral relationship between $|f_{+}(E)/f_{-}(E)|$ and the difference of the phases of $f_{+}(E)$ and $f_{-}(E)$ and the analogous relationship between $|f_{+}(E)f_{-}(E)|$ and the sum of the phases of these amplitudes [$(f_{\pm}(E)$ are the $\pi^{\pm}-p$-forward scattering amplitudes]. Restrictions on $\displaystyle\int_{1}^{E}\ln\biggl|\frac{f_{+}(E')}{f_{-}(E')}\biggr|\, \frac{dE'}{\sqrt{{E'}^2-1}}$ are found.

Received: 15.04.1970


 English version:
Theoretical and Mathematical Physics, 1970, 5:2, 1114–1120


© Steklov Math. Inst. of RAS, 2024