Gravitational leptogenesis, C, CP and strong equivalence

Abstract

The origin of matter-antimatter asymmetry is one of the most important outstanding problems at the interface of particle physics and cosmology. Gravitational leptogenesis (baryogenesis) provides a possible mechanism through explicit couplings of spacetime curvature to appropriate lepton (or baryon) currents. In this paper, the idea that these strong equivalence principle violating interactions could be generated automatically through quantum loop effects in curved spacetime is explored, focusing on the realisation of the discrete symmetries C, CP and CPT which must be broken to induce matter-antimatter asymmetry. The related issue of quantum corrections to the dispersion relation for neutrino propagation in curved spacetime is considered within a fully covariant framework.

Leptogenesis from loop effects in curved spacetime

“…At one loop (see figure 4), we immediately see Σ(x , x) − Σ c (x , x) = 0, with 16) since the couplings occur only in the combination (λ † λ) ij for which the diagonal elements are manifestly real. However, at two loops, there are two diagrams (figure 5) which give non-zero contributions to Σ(x , x)−Σ c (x , x).…”

“…Consider a quasi-plane wave solution for the lepton field (x) = u(x)e −iΘ(x) , so that the momentum of the particle is given by p µ = ∂ µ Θ. As discussed in [16], when an operator of the form b ∂ µ Rj µ , coupling the derivative of the Ricci scalar to the lepton current, is added to the Dirac action, it gives different dispersion relations for particles and antiparticles. To see this, note that the modified equations of JHEP04(2016)030…”

“…One of the most direct ways to study the propagation of particles in gravitational backgrounds, and the effects of curvature on their dynamics, is to use effective field theory [16,18,19]. As discussed in the previous sections, the screening cloud surrounding an interacting particle gives it an effective size, causing it to experience tidal forces.…”

“…A careful discussion of the action of C, P and T on this, and remaining operators appearing in L eff was given in [16]. The presence of a C and CP violating operator ensures that the second Sakharov condition holds, namely that the complete theory contains C and CP violation, which is provided here by the complex couplings λ iα .…”

“…When one integrates out the heavy sterile neutrinos, this phenomenon generates operators in the effective action that couple particle fields to various curvature tensors, suppressed by a seesaw scale cutoff. The most general such action [16], constructed from a complete basis of hermitian operators, is given to linear order in curvature and leading order in derivatives by…”