Creating the Baryon Asymmetry at the Electroweak Phase Transition*

Al temperatures above the weak phase transition, baryon and lepton number are badly vioiakd. We explore the suggestion that the baryon asymmetry might be produced at lhe transition, if the transition is first order. We find that the asymmetry is proportional to a CP violating parameter, a large power of the gauge coupling and to factors which depend on the details of the transition. In extensions of the standard model, such as multi-Higgs or supersymmetric models, the result may be consistent with observations. Submitted to Phys. Lett. D t Work #upported in part by the U.S. Department ol Energy under contract numbers DEAMO&76SF60010 and DEAC0376SFOO515, and by the National Science Foundation under grant I’llY8+04035. It has long been known that baryon and kpton number are not conserved in the standard model, as a consequence of anomalies.’ States of dillerent baryon number are smoothly connected toone another through dillerent conliguralions of the gauge and Higgs fields, sebrated by a potential barrier. At extremely low temperatures, baryon number violation, being a tunneling phenomenon in a weakly coupled theory, is highly suppressed. On the other hand, in the last few years, it has become clear that baryon number is badly violated al temperalures much above Mw (D L is conserved).)-s Indeed, once the temperalure is large compared to Mw, the syslem is well described by classical statislical mechanics. At temperatures below the weak phase transition, the lowest energy barrier is associated with the “sphakron”, a Eniteenergy aolulion of the classical equations d motion with a single negative mode.) The rate for barrier penetralion is essentially the Boltzmann factor for this configuration, which, using the computed values of the sphakron energy, yields a rate