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

Understand

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.