Finite-Energy Sum Rules and Their Application toπNCharge Exchange

Abstract

We derive and discuss the finite-energy sum rules, which form consistency conditions imposed by analyticity on the Regge analysis of a scattering amplitude. Their finite form makes them particularly useful in practical applications. We discuss the various applications, emphasizing a new kind of bootstrap predicting the Regge parameters from low-energy data alone. We apply our methods to $\ensuremath{\pi}N$ charge exchange and are able to derive many interesting features of the high-energy amplitudes at various $t$. In particular, we establish the existence of zeros of the amplitudes and of additional $\ensuremath{\rho}$ poles. On the basis of the finiteenergy sum rules and the analysis of the $\ensuremath{\pi}N$ amplitudes, we present theoretical and experimental evidence that double counting is involved in the interference model, which adds direct-channel resonances to the exchanged Regge terms.