Theory ofπ−NScattering in the Strip Approximation to the Mandelstam Representation

Abstract

The strip approximation to the Mandelstam representation is applied to the $\pi -N$ problem, and the basic equations given. The asymptotic behavior of the invariant amplitudes in the physical regions is discussed in terms of the unitarity condition on partial-wave amplitudes, the constancy of high-energy scattering cross sections, and the Pomeranchuk theorem, and it is shown to imply that no subtractions should be necessary except in the $J=\frac{1}{2}$ wave of the $\pi -N$ channel and the $J=0\mathrm{}$ wave of the $\pi +\pi \to N+\overline{N}$ channel. This obviates the difficulties encountered by earlier workers when they subtracted higher waves.