Abstract
The variational formalism of Einhorn and Blankenbecler is used to derive and evaluate numerically finite-energy bounds on the real and imaginary parts of an elastic scattering amplitude F(s, t). Previously, convergent bounds have been obtained by using the Jin-Martin theorem if Im F(s, t0) < (ss0)2 where t0 is the positron of the nearest t-channel singularity. However, this introduces logarithmic factors of unknown scale, so to get bounds at finite energies we replace (s/s0)2 by a phenomenological value of Im F(s, t0) found by extrapolation of the differential cross section. This procedure improves the bound of Singhand Roy at high energies and is also very successful at low energies.
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