Electroweak String Configurations with Baryon Number.pdf

arXiv:hep-ph/9401220v3 11 May 1994 Electroweak String Con?gurations with Baryon Number Tanmay Vachaspati Tufts Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155. e B. Field Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138. Abstract: In the context of electroweak strings, the baryon number anomaly equation may be reinterpreted as a conservation law for baryon number minus helicity. Since the helicity is a sum of the link and twist numbers, linked or twisted loops of electroweak string carry baryon number. We evaluate the change in the baryon number obtained by delinking loops of electroweakZ?string and show that twisted electroweak string segments may be regarded as extended sphalerons. We also suggest an alternative scenario for electroweak baryogenesis. 2 Over the past few years, there has been renewed interest in the study of classical solutions in the standard model of the electroweak interactions. Vortex solutions 1,2,3,4are of particular interest and there is indication 5,6,7that they may be the building blocks for other solutions, such as the sphaleron 2,8. The sphaleron, in turn, is of crucial interest to the study of baryon number violating processes and to the possibility of baryogenesis during the cosmological electroweak phase transition 9,10. The point of this paper is to show that electroweak string con?gurations can carry baryon number and play a (sphaleron-like) role in baryon number changing processes. The starting point for our analysis is the anomaly equation: ?μj μB = NF 32π 2 [?g 2W aμν?W aμν+g ′2Y μν?Y μν]. (1) in the usual notation (see Ref. 9 for example). The right-hand side of (1) is a total divergence and so the equation can be integrated. If we assume that the baryonic ?ux through the surface of the three volume of interest vanishes, the result relates the change in the baryon number within the volume,QB , to the Chern-Simons numbers of the ?elds: ?QB =N