Chern-Simmons number diffusion in the symmetric electroweak phase

Details Chern-Simmons number diffusion in the symmetric electroweak phase Chern-Simmons number diffusion in the symmetric electroweak phase

Nov 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt.......177m&link_type=abstract

Thesis (PhD). PRINCETON UNIVERSITY, Source DAI-B 58/05, p. 2487, Nov 1997, 165 pages.

Mathematics

Logic

6

Scientific paper

It has been known since the work of t'Hooft that baryon number is violated in the Minimal Standard Model, because of the topologically nontrivial vacuum structure of SU(2) in 3 + 1 dimensions and the chiral coupling of SU(2) to fermions. At low temperatures (kbT<100GeV, which has been the case since the universe was 10-9 seconds old) the rate of baryon number violation occurs by exponentially rare vacuum tunneling events; the halflife of the deuteron due to these decays should exceed 1080 years. However, the obstacle to baryon number violation at higher temperatures is a thermal barrier, which falls with temperature and dissolves altogether at the electroweak phase transition (at a temperature kbT~ mH~100GeV). The consequences for cosmology are profound; 'initial' baryon number is erased, but the matter abundance in the universe today may have been generated when the universe cooled through the phase transition. This thesis studies the baryon number violation rate above the phase transition temperature, which is immediately relevant to the study of matter generation at the phase transition. I argue that the rate, which is dominated by very infrared processes, can be understood in terms of the classical field dynamics of the infrared modes. Their dynamics are nonperturbative, but can be studied numerically by lattice techniques. I implement the classical lattice system numerically, and then work to eliminate lattice artifacts, first by studying the elimination of nonrenormalizeable operators in the infrared dynamics, then by improving the matching between the lattice and continuum length scales and couplings, and finally by finding a topological means to track Chern-Simons number. I conclude that the baryon number violation rate depends in a nontrivial way on the interactions between the (approximately classical) infrared degrees of freedom and the short wavelength 'hard' modes.

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