Leptogenesis from heavy right-handed neutrinos in CPT violating backgrounds

Abstract

We discuss leptogenesis in a model with heavy right-handed Majorana neutrinos propagating in a constant but otherwise generic CPT -violating axial time-like background (motivated by string theory). At temperatures much higher than the temperature of the electroweak phase transition, we solve approximately, but analytically (using Padé approximants), the corresponding Boltzmann equations, which describe the generation of lepton asymmetry from the tree-level decays of heavy neutrinos into Standard Model leptons. At such temperatures these leptons are effectively massless. The current work completes in a rigorous way a preliminary treatment of the same system, by some of the present authors. In this earlier work, lepton asymmetry was crudely estimated considering the decay of a righthanded neutrino at rest. Our present analysis includes thermal momentum modes for the heavy neutrino and this leads to a total lepton asymmetry which is bigger by a factor of two as compared to the previous estimate. Nevertheless, our current and preliminary results for the freezeout are found to be in agreement (within a ∼ 12.5% uncertainty). Our analysis depends on a novel use of Padé approximants to solve the Boltzmann equations and may be more widely useful in cosmology.

Gravitational and chiral anomalies in the running vacuum universe and matter-antimatter asymmetry

“…10 10 Nonetheless, we should remark at this point that, independently of our considerations here, it was pointed out in [54] that the predictions of [50] for leptogenesis due to primordial chiral fermions depend heavily on the ultraviolet completion of the theory, in our case the full string theory, given that mainly modes in the deep quantum-gravity/string-theory regime contribute to the lepton asymmetry; moreover, as argued in [54,55], by performing proper ultraviolet regularization, including higher-than-quadratic-order derivative terms, one may effectively obtain much smaller lepton number than the one claimed in [50], since the cutoff µ is effectively replaced by the Hubble constant during the de Sitter phase. Par contrast, in our approach, there are no primordial fermions, and leptogenesis during the radiation era occurs in a completely different way [37,38] to be discussed in section III B, due to the presence of a constant Lorentz Violating axial background of the KR field. The latter is induced by the gravitational anomaly (54), and, as we shall show below, remains undiluted at the end of inflation, provided transplanckian modes (66) are included.…”

“…At the end of inflation, the proper decay of the running vacuum to matter and radiation components will reheat the universe and lead to the appearance of fermions among other matter. If such fermions have anomalous axial currents, then matter-antimatter asymmetry in the observable universe could be due to such an anomaly in the post-inflationary era through the mechanism advocated in [36][37][38], as we now proceed to explain. 12 12 We remind the reader that in our approach we do not discuss the role of (primordial) fermionic excitations during inflation, since we assume that only bosonic gravitational degrees of freedom describe the stringinspired Universe.…”

“…The coupling of the KR axion to the gravitational anomaly leads to undiluted KR background fields at the end of inflation, which violate spontaneously Lorentz and CPT symmetry. This, in turn, plays an important rôle in generating lepton asymmetry in models involving (heavy) right-handed neutrinos [35][36][37][38], through the decays of the latter into standard model particles in the presence of the KR background. The lepton asymmetry can then be communicated to the baryon sector via standard Baryon (B) and Lepton (L) number violating, but B-L conserving, sphaleron processes in the Standard-Model (SM) sector of the model [39].…”

“…In our model this is provided by the generation of chiral femion matter with anomalous axial currents, such as chiral leptons in the SM sector or other chiral fermions that might exist in beyond the standard model (BSM) physics models, which cancel the gravitational anomalies during this epoch. The coupling of the (undiluted) KR axion to right-handed massive neutrino matter during the early radiation era succeeding inflation is essential for leptogenesis via the mechanism of [35][36][37][38].…”

“…There are models [43], however, in which the KR axion couples to chiral matter (such as Majorana right handed neutrinos) via shift-symmetry breaking interactions, possibly generated by nonperturbative effects (string instantons), and via shift-symmetry-preserving kinetic mixing to other axions that are abundant in string theory [44]. In fact, such a mixing allows for the generation of a Majorana mass for the right handed neutrinos, which is a crucial feature for the aforementioned leptogenesis scenario [36][37][38]. These string theory axions can then play the rôle of additional components of DM (in some of these scenarios, there is also a non-perturbative generated potential for the KR axion itself, at late eras, which thus implies its potential role as a massive DM candidate).…”