# Suppression of baryon number violation in electroweak collisions: Numerical results

## TL;DR

This study investigates the suppression of baryon number violation in electroweak collisions, showing that such processes remain exponentially suppressed even at energies well above the sphaleron energy, with implications for high-energy physics.

## Contribution

It provides a semiclassical analysis of baryon number violation suppression across different energy regimes, including new insights into solutions above the sphaleron energy.

## Key findings

- Suppression exponent closely matches low energy estimates below sphaleron energy.
- Above sphaleron energy, solutions correspond to barrier jumps but remain suppressed.
- Baryon number violation stays exponentially suppressed up to at least 250 TeV.

## Abstract

We present a semiclassical study of the suppression of topology changing, baryon number violating transitions induced by particle collisions in the electroweak theory. We find that below the sphaleron energy the suppression exponent is remarkably close to the analytic estimates based on a low energy expansion about the instanton. Above the sphaleron energy, the relevant semiclassical solutions have qualitatively different properties from those below the sphaleron: they correspond to jumps on top of the barrier. Yet these processes remain exponentially suppressed, and, furthermore, the tunneling exponent flattens out in energy. We also derive lower bounds on the tunneling exponent which show that baryon number violation remains exponentially suppressed up to very high energies of at least 30 sphaleron masses (250 TeV).