# Semiclassical Study of Baryon and Lepton Number Violation in High-Energy Electroweak Collisions

## TL;DR

This paper uses a semiclassical approach to calculate the suppression of baryon and lepton number violation in high-energy electroweak collisions, finding it remains exponentially suppressed up to very high energies and that low-energy approximations are valid only up to the sphaleron energy.

## Contribution

It introduces a computational semiclassical method to evaluate suppression exponents for topology-changing processes in electroweak collisions, extending understanding to higher energies.

## Key findings

- Baryon and lepton number violation remains exponentially suppressed up to at least 250 TeV.
- Low energy expansion approximations are valid only up to 8 TeV.
- The method provides results for s-wave scattering across a wide initial data range.

## Abstract

We make use of a semiclassical method for calculating the suppression exponent for topology changing transitions in high-energy electroweak collisions. In the Standard Model these processes are accompanied by violation of baryon and lepton number. By using a suitable computational technique we obtain results for s-wave scattering in a large region of initial data. Our results show that baryon and lepton number violation remains exponentially suppressed up to very high energies of at least 30 sphaleron masses (250 TeV). We also conclude that the known analytic approaches inferred from low energy expansion provide reasonably good approximations up to the sphaleron energy (8 TeV) only.