Fermion Number Violation and Level Crossing on the Lattice

[摘要] The electroweak theory is believed to play an important role in the creation of the baryon asymmetry of the universe. This is due to anomalous fermion number violating processes which are believed to occur rapidly at the high temperatures prevailing in the early universe. However the perturbative methods used to estimate the rate of such processes break down at the very high temperatures occuring above the electroweak phase transition. Lattice gauge theories provide a useful non-perturbative tool for studying electroweak fermion number violation at high temperature. The most common technique involves measuring the Chern-Simons number Ncs of the gauge held with fermion number violation occuring whenever DeltaNcs =+/- However the measurement of Ncs on the lattice is known to be problematic. The level crossing picture provides a way of checking that fermion number really is violated in these simulations. We use two methods to investigate the level crossing phenomenon. In the first level crossing is signalled by the lowest eigenvalue diving to zero and a simultaneous flip in sign of the ''generalised chirality" which is a natural label for the eigenstates. This signal is interpreted as showing the lowest eigenvalue crossing zero. To provide further evidence that this is the case we introduce a new method which involves numerically solving the Dirac equation to follow the time development of the fermion states. Firstly the methods are applied to the U(l) model in 1 + I dimensions. Both methods give a clear signal for level crossing, the exact point at which the zero eigenvalue occurs depending on the Yukawa coupling. Similar results are obtained for the SU(2) model in 3+1 dimensions though the signal is affected by fluctuations in the background fields particularly for large Yukawa coupling. A clear signal is only obtained after cooling the backgrounds. These results provide further evidence that the high temperature configurations with DeltaNCS = +/-1 observed in lattice simulations are accompanied by fermion number violation.

[发布机构] University:University of Glasgow

[关键词] Theoretical physics