On Preserving a B + L Asymmetry Produced in the Early Universe

One of the most efficient mechanisms for producing the baryon asymmetry of the Universe is the decay of scalar condensates in a SUSY GUT as was first suggested by Affleck and Dine. We show that given a large enough asymmetry, the baryon number will be preserved down to low temperatures even if B − L = 0, because the baryon number carrying scalars form bose condensates that give the W a mass. We derive the conditions on the condensate needed to suppress electroweak sphaleron interactions which would otherwise drive the baryon asymmetry to zero when B − L = 0. This work was supported in part by DoE grants DE-FG02-94ER-40823 and DE-AC03-76SF00098, by NSF grant AST-91-20005 and by NSERC. On leave of absence from Department of Physics, Tohoku University, Sendai, 980 Japan Models for baryogenesis at the weak scale and above have been under considerable scrutiny since the realization that baryon number violation due to non-perturbative electroweak interactions is rapid at high temperatures [1]. Baryon number violating interactions mediated by sphalerons in fact violate B + L while conserving B − L. Thus any model of baryogenesis above the weak scale which also conserves B−L is likely to produce a negliglible baryon asymmetry once sphaleron interactions have been incorporated [2]. This conclusion is clearly important as the simplest models of baryogenesis typically conserve B −L. There are, however, several modifications to these simplest scenarios which can overcome this problem. One possibility is that the baryon asymmetry is generated during the electroweak phase transition [3], though it is unlikely that this can be done within the standard model. It is possible that a more complicated grand unified theory which violates B−L, (such as SO(10) rather than SU(5)) produces a baryon asymmetry which is only reshuffled by sphaleron interactions. Or, an extension of the standard model which violates lepton number and hence B−L (for instance the inclusion of right handed neutrinos used to generate neutrino masses via the see-saw mechanism [4]), can produce a lepton asymmetry which is transformed into a baryon asymmetry at the weak scale [5, 6, 7]. Alternatively, the conditions under which sphalerons are able to destroy a prior baryon asymmetry have come under consideration. For example, lepton mass effects in the presence of lepton flavour asymmetries and B + L violating electroweak interactions can generate a baryon asymmetry even though B + L = B − L = 0 [8, 9]. It has also been shown that because of the very small value of the electron Yukawa coupling constant, the equilibrium condition that leads to B = L = 0 is only valid at late times (temperatures T < ∼ 1 TeV) close to the electroweak phase transition [10, 11]. At higher temperatures the decoupling of the right-handed electron in some sense safe-guards the baryon asymmetry. Though in the standard model sphalerons win in the end, the destruction of the baryon asymmetry is exponentially sensitive to parameters of the model. In an extension of the standard model the baryon asymmetry may yet survive. There are also attempts to protect baryon asymmetry introducing new fields [12]. In this letter, we explore another possibility. We consider the effect of scalar Bose– Einstein (B-E) condensates on the sphaleron interaction rate in a B − L conserving supersymmetric grand unified theory. The presence of a B-E condensate gives rise to gauge boson masses, which, if they persist down to temperatures close to the electroweak phase transi-