ar X iv : h ep - p h / 98 07 30 7 v 1 9 J ul 1 99 8 DESY 98 - 082 UCRHEP - T 230 June 1998 Gauged B − 3 L τ and Baryogenesis

It has recently been shown that by extending the minimal standard model to include a right-handed partner to ντ , it is possible to gauge the B − 3Lτ quantum number consistently. If we add two scalar triplets, one trivial (ξ1) and one nontrivial (ξ2) under B − 3Lτ , it is possible also to have desirable neutrino masses and mixing for neutrino oscillations. At the same time, a lepton asymmetry can be generated in the early universe through the novel mechanism of the decay of the heavier ξ1 into the lighter ξ2 plus a neutral singlet (ζ). This lepton asymmetry then gets converted into a baryon asymmetry at the electroweak phase transition. It has recently been shown[1] that the minimal standard SU(3)C × SU(2)L × U(1)Y gauge model of quarks and leptons may be extended to include an anomaly-free gauge factor U(1)B−3Lτ if ντ has a right-handed singlet partner, but not νe or νμ. The scale of symmetry breaking of this B−3Lτ gauge group may even be lower[2] than that of electroweak symmetry breaking. In the minimal standard model, there are dimension-six baryon-number nonconserving operators[3] of the form QL which would induce the proton to decay. In the B − 3Lτ gauge model, the lowest dimensional baryon-number nonconserving operator is of the form Q9Lτ , hence such processes are suppressed by 22 powers of some higher energy scale and become totally negligible. To obtain a baryon asymmetry of the universe in this model, it is natural to propose instead that a primordial lepton asymmetry is generated[4, 5] which then gets converted into a baryon asymmetry during the electroweak phase transition[6]. In order to generate a lepton asymmetry in the early universe, we must have leptonnumber nonconserving interactions which also violate C and CP , as well as the existence of an epoch when such processes are out of thermal equilibrium[7]. The canonical way[4] of achieving this is to use heavy right-handed singlet neutrinos which also allow the known lefthanded neutrinos (νe, νμ, ντ ) to acquire small seesaw masses. An equally attractive scenario was recently proposed[5] where heavy Higgs triplets are used. In the B − 3Lτ gauge model, since νe and νμ have no right-handed singlet partners, the natural thing to do is to adopt a variation of the latter mechanism. In fact, as we see below, the requirement of a desirable neutrino mass matrix and the absence of an unwanted pseudo-Goldstone boson together imply a successful leptogenesis scenario in this model without any further extension. In the standard model, a general neutrino mass matrix may be obtained with the addition of one heavy Higgs triplet, but to generate a lepton asymmetry, two such triplets are required[5]. In the minimal B−3Lτ gauge model, only ντ gets a mass. Furthermore, because B − 3Lτ is a gauge symmetry, it is not obvious a priori how that will affect the conversion