Finite-Energy Sum Rules and Their Application to πN Charge Exchange

R. Dolen, D. Horn, and C. Schmid
Phys. Rev. 166, 1768 – Published 25 February 1968
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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 πN 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 ρ poles. On the basis of the finiteenergy sum rules and the analysis of the πN 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.

  • Received 29 September 1967

DOI:https://doi.org/10.1103/PhysRev.166.1768

©1968 American Physical Society

Authors & Affiliations

R. Dolen*, D. Horn, and C. Schmid

  • California Institute of Technology, Pasadena, California

  • *Present address: Physics Department, University of California, Los Angeles, Calif. 90024.
  • Present address: Physics Department, Tel Aviv University, Tel Aviv, Israel.
  • Present address: Lawrence Radiation Laboratory, University of California, Berkeley, Calif.

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Issue

Vol. 166, Iss. 5 — February 1968

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