# Role of Bloch Waves in baryon-number violating processes

## TL;DR

This paper investigates how Bloch wave methods can be used to estimate baryon-number-violating processes in the electroweak theory, clarifying the relation between different sphaleron barrier scenarios and improving the approximation methods.

## Contribution

It provides a detailed analysis of the Bloch-wave approach, connecting single and multiple sphaleron barriers, and introduces corrections to the idealized models for more realistic predictions.

## Key findings

- Clarified the relation between single and multiple sphaleron barriers.
- Modified the Bloch wave approximation for realistic scenarios.
- Connected the approach to nucleosynthesis processes.

## Abstract

In the Bloch-wave approach to estimate the baryon-number-violating scattering cross section in the standard electroweak theory in the laboratory, we clarify the relation between the single sphaleron barrier and multiple (near periodic) sphaleron barrier cases. We explain how a realistic consideration modifies/corrects the idealized Bloch wave and the resonant tunneling approximation. The basic approach is in part analogous to the well-known triple-$\alpha$ process to form carbon in nucleosynthesis.