Protecting the Baryon Asymmetry in Theories with R-parity Violation

We propose a mechanism for hiding the primordial baryon asymmetry from interactions that could wash it out. It requires the introduction of a baryon number carrying singlet which is in equilibrium in the early universe and shares any existing baryon asymmetry. It decouples from the Standard Model particles before all the interactions required to wash out the asymmetry are in equilibrium (T ≃ 10 TeV), and decays after the electroweak phase transition, but before nucleosynthesis. This mechanism can conserve a baryon asymmetry in models (a) with B − L = 0, such as many SU(5) GUTs, or (b) with B − L violating interactions in thermal equilibrium, such as SUSY with broken Rparity. As a result, cosmological constraints on R-parity violating operators are relaxed considerably. Making the observed baryon asymmetry of the universe (BAU) [1, 2, 3] in supersymmetric theories [4] with R-parity violation [5, 6] can be a challenging task. The difficulty is that such theories contain B − L violating interactions which are naturally in thermal equilibrium above the electroweak phase transition, in conjunction with the anomalous [7] B + L violating Standard Model processes. Together, these interactions can wash out any BAU present in the early universe [8, 9]. The Hubble expansion rate at T ≃ 100 GeV is then so much smaller than particle interaction rates, that it is difficult (but not impossible [10]) to find enough perturbative out-of-equilibrium dynamics to (re)generate an asymmetry. Since Supersymmetric theories with R-parity violation have recently attracted attention [5, 6], it is of interest to consider how this problem can be avoided. One way around it is to create the asymmetry at [3] or after the electroweak phase transition [3, 10]. In this letter, we follow a second approach, which is to assume the asymmetry is generated earlier, but protected by an approximate symmetry. We hide the primordial BAU in a pair of SU(3)×SU(2)×U(1) singlets, S and S̄, with unit baryon number (B = 1) during the critical period (ie. the time when all interactions required to washed out any BAU are in thermal equilibrium). As S and S̄ decay the BAU will be transferred back to the Standard Model quarks. Three ingredients are required to generate a baryon asymmetry [11]: baryon number violation, C and CP violation, and some out-of-equilibrium process. These are all present in the Standard Model (SM) at the electroweak phase transition; however, there is insufficient perturbative CP violation [12] in the SM, and the non-perturbative B + L violation would be in thermal equilibrium after the transition for most allowed values of the Higgs mass [13] (in which case any asymmetry produced would be destroyed). This suggests that the observed baryon asymmetry cannot be made in the Standard Model, and is evidence for some kind of new physics. There are numerous extensions of the Standard Model that include viable baryogenesis mechanisms [1, 2, 3]. It is particularly interesting that it may be possible to create the BAU at the electroweak phase transition for certain regions of parameter space in the Minimal Supersymmetric Standard model (MSSM) [14]. However, we may not live in these regions of parameter space, so an alternative mechanism is certainly desirable. In this letter, we assume that the asymmetry was created before the phase transition. Two generic and popular mechanisms for this are the out-of-equilibrium decay of heavy GUT (Grand Unified Theory) particles produced in the decay of the inflaton [15], or the Affleck-Dine mechanism in Supersymmetry and Supergravity [16]. In any case, the asymmetry produced is in thermal equilibrium in the early Universe at temperatures above the electroweak phase transition. If interactions capable of washing out the asymmetry are simultaneously present, the asymmetry will be lost. This can happen for an asymmetry with B−L = 0 within the Standard Model, and for any asymmetry in Supersymmetric models with sufficient Rp violation [9]. Recently, there has been considerable interest in supersymmetric models with broken Rparity[5], so we will briefly review their baryogenesis difficulties. Rp is a multiplicative symmetry [17] which assigns to each scalar or fermionic field in the model the charge (−1)3B+L+2S , where S is the particle spin. Rp conservation in supersymmetric theories was introduced to eliminate renormalizable B and L number violating interactions, which, if present simultaneously, would induce proton decay. Requiring R-parity conservation to ensure proton stability may be too strong a constraint, since it is sufficient to build models that eliminate either L or B violating interactions. However, such models may still have problems preserving the cosmological baryon asymmetry; if interactions that take B or L to zero are in thermal equilibrium in the presence of the anomalous B+L violation, then any previously existing asymmetry would be washed out [8, 9]. A primordial asymmetry with B − L 6= 0 can be protected if there is no perturbative B violation, and at least one lepton flavor is effectively conserved. This constrains the L violating couplings in one generation to be small enough that they are not in chemical equilibrium at the relevant temperatures. This scenario is incompatible with our theoretical prejudice of relating lepton flavor violation to quark flavor violation. Furthermore, it may be in contradiction with the experimental evidence for neutrino oscillations. The main purpose of this letter is to demonstrate that these cosmological constraints on Rp violating couplings can be circumvented by introducing new particles that can temporarily store the baryon asymmetry. Let us consider an extension of the MSSM with the additional fields and their quantum numbers given in table 1. The most general superpotential involving these new particles can be written as Wnew = λ ′T̄U D + λTDS + λ̄TQQ+mT T̄T +mSS̄S , (1) where U c and D (Q) are the right (left) handed quark fields and we assume the hierarchy The property of gauge coupling unification can be maintained by including a additional pair of Higgs doublets with mass mT . For simplicity we neglect all interactions involving these Higgs doublets.