Trouble in the valley? Instantons and multi-instantons in anomalous scattering

Abstract

The valley method is a nonperturbative tool for summing final-state corrections in high-energy baryon number ( B) violation. We use it to analyze recent claims that multi-instanton chains dominate the B-violating cross section σ b ̷ at energies for which the one-instanton contribution is still exponentially suppressed. We present a toy model in which this claim is incorrect, and is an artifact of retaining only nearest-neighbor instanton-anti-instanton forces. As a separate issue, we also examine the valley method itself, in the one-instanton sector. We show that for some choices of metric on configuration space, the valley bifurcates at a critical enegy, at which point the smooth exponential rise of σ b ̷ towards an observably large value apparently comes to a halt, and σ b ̷ remains unobservably small.