Bloch Wave Function for the Periodic Sphaleron Potential and Unsuppressed Baryon and Lepton Number Violating Processes

TL;DR

This paper models baryon and lepton number violating processes in electroweak theory using Bloch wave functions, revealing they can occur without suppression at energies around 9.0 TeV, potentially detectable at the LHC.

Contribution

It introduces a quantum mechanical model with Bloch wave functions for sphaleron potential, showing unsuppressed baryon-lepton violation at high energies.

Findings

Processes occur without exponential suppression at energies above 9.0 TeV.

Potential detection of these processes at the LHC is feasible.

The band structure indicates possible high-energy baryon-lepton violation.

Abstract

For the periodic sphaleron potential in the electroweak theory, we find the one-dimensional time-independent Schr\"{o}dinger equation with the Chern-Simons number as the coordinate, construct the Bloch wave function and determine the corresponding conducting (pass) band structure. We show that the baryon-lepton number violating processes can take place without the exponential tunneling suppression (at zero temperature) at energies around and above the barrier height (sphaleron energy) at 9.0 TeV. Phenomenologically, probable detection of such processes at LHC is discussed.