Is baryon number violated when electroweak strings intercommute?

We reexamine the self-helicity and the intercommutation of electroweak strings. A plausible argument for baryon number conservation when electroweak strings intercommute is presented. The connection between a segment of electroweak string and a sphaleron is also discussed. ⋆ Address after Sep. 1: School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 One of the most basic observational facts in cosmology is the predominance of matter over antimatter. In 1967 Sakharov [1] considered the possibility that the Universe began in a baryon-symmetric state but that particle interactions produced a net asymmetry. In addition to baryon-number violation, this requires C and CP violation as well as a departure from thermal equilibrium. [2] In the standard electroweak theory all three conditions are satisfied. Baryogenesis during the weak phase transition [3] is particularly interesting as it may eventually be experimentally verifiable. Recently, there has been a revival of interest in the study of classical solutions in the standard model of the electroweak interactions. [4] It has been conjectured [5,6,7] that a segment of electroweak string, which connects a monopole to an antimonopole is a kind of “stretched“ sphaleron. Since the sphaleron [8,9] is of crucial interest to the study of baryon number violation processes, one may contemplate the role electroweak strings in baryogenesis shortly after the cosmological electroweak phase transition. [10] In a recent Letter, [6] it is pointed out that the baryon number anomaly equation may be interpreted as a conservation law for baryon number minus helicity. Since the helicity is a sum of link and twist numbers, linked and twisted loops of electroweak string necessarily carry baryon number. It is also claimed that helicity and hence baryon number is conserved when electroweak strings intercommute. [11] However, two things put the argument given by those authors for baryon number conservation during intercommutation in doubt. First, the configuration after intercommutation given in Ref. 6 is implausible. Second, self-helicity is not properly accounted for in that Letter. The main point of this Letter is to give a careful calculation of self-helicity and present a plausible electroweak string configuration after intercommutation. A proper calculation of helicity with our field configuration after intercommutation suggests that helicity is conserved when electroweak strings intercommute. We also clarify the connection between the sphaleron and a segment of Z string connecting a monopole and an antimonopole. We will briefly review the concept of helicity of electroweak strings. [6,7] Our start-