Tomislav Prokopec

Transport equations for chiral fermions to order ℏ and electroweak baryogenesis: Part I

Abstract This is the second in a series of two papers. While in Paper I [Ann. Phys. 314 (2004) 208] we derive semiclassical Boltzmann transport equations and study their flow terms, here we make use of the results from that paper and address the collision terms. We use a model Lagrangean, in which fermions couple to scalars through Yukawa interactions and approximate the self-energies by the one-loop expressions. This approximation already contains important aspects of thermalization and scatterings required for quantitative studies of transport in plasmas. We compute the CP-violating contributions to both the scalar and the fermionic collision term. CP-violating sources appear at order ℏ in gradient and in a weak coupling expansion, as a consequence of a CP-violating split in the fermionic dispersion relation. This represents the first controlled calculation of CP-violating collisional sources, thus establishing the existence of `spontaneous baryogenesis sources in the collision term. The calculation is performed by the use of the spin quasiparticle states established in Paper I. Next, we present the relevant leading order calculation of the relaxation rates for the spin states and relate them to the more standard relaxation rates for the helicity states. We also analyze the associated fluid equations, make a comparison between the source arising from the semiclassical force in the flow term and the collisional source, and observe that the semiclassical source tends to be more important in the limit of inefficient diffusion/transport.

Photon mass from inflation

We consider vacuum polarization from massless scalar electrodynamics in de Sitter inflation. The theory exhibits a 3+1 dimensional analog of the Schwinger mechanism in which a photon mass is dynamically generated. The mechanism is generic for light scalar fields that couple minimally to gravity. The nonvanishing of the photon mass during inflation may result in magnetic fields on cosmological scales.

First principle derivation of semiclassical force for electroweak baryogenesis

We perform a systematic gradient expansion on kinetic equations and derive the CP-violating semiclassical force for fermions propagating in presence of a CP-violating wall at a first order electroweak phase transition. The force appears at order in the flow term of the kinetic equation and agrees with the semiclassical force used for baryogenesis computations. In particular we consider the force for charginos in both the MSSM and NMSSM. We then study the continuity equations for the vector and axial vector currents and stress the role of the latter as the one containing baryogenesis sources. We also show that there is no CP-violating force for bosons to order in gradient expansion.

One loop vacuum polarization in a locally de Sitter background

Abstract We compute the one loop vacuum polarization from massless, minimally coupled scalar QED in a locally de Sitter background. Gauge invariance is maintained through the use of dimensional regularization, whereas conformal invariance is explicitly broken by the scalar kinetic term as well as through the conformal anomaly. A fully renormalized result is obtained. The one loop corrections to the linearized, effective field equations do not vanish when evaluated on-shell. In fact the on-shell one loop correction depends quadratically on the inflationary scale factor, similar to a photon mass. The contribution from the conformal anomaly is insignificant by comparison.

Primordial spectrum of gauge fields from inflation

Abstract We show that conformal invariance of gauge fields is naturally broken in inflation, having as a consequence amplification of gauge fields. The resulting spectrum of the field strength is approximately B l ∝l −1 , where l is the relevant coherence scale. One realisation of our scenario is scalar electrodynamics with a scalar whose mass is large enough to evade observational constraints — the obvious candidates being supersymmetric partners of the standard-model fermions. Our mechanism also leads naturally to amplification of the standard-model Z -boson field due to its coupling to the electroweak Higgs field. At preheating, the spectrum of the Z field is transferred to the hypercharge field, which remains frozen in the plasma and is converted into a magnetic field at the electroweak phase transition. With a reasonable model of field evolution one obtains a magnetic field strength of the order of 10 −29 Gauss on a scale of 100 pc, the size of the largest turbulent eddy in a virialised galaxy. Resonant amplification in preheating can lead to primordial fields as large as 10 −24 Gauss, consistent with the seed field required for the galactic dynamo mechanism.

Kinetic description of fermion flavor mixing and CP-violating sources for baryogenesis

Abstract We derive transport equations for fermionic systems with a space–time dependent mass matrix in flavor space allowing for complex elements leading to CP violation required for electroweak baryogenesis. By constructing appropriate projectors in flavor space of the relevant tree level Kadanoff–Baym equations, we split the constraint equations into “diagonal” and “transversal” parts in flavor space, and show that they decouple. While the diagonal densities exhibit standard dispersion relations at leading order in gradients, the transverse densities exhibit a novel on-shell structure. Next, the kinetic equations are considered to second order in gradients and the CP-violating source terms are isolated. This requires a thorough discussion of a flavor independent definition of charge-parity symmetry operation. To make a link with baryogenesis in the supersymmetric extension of the Standard Model, we construct the Green functions for the leading order kinetic operator and solve the kinetic equations for two mixing fermions (charginos). We take account of flavor blind damping, and consider the cases of inefficient and moderate diffusion. The resulting densities are the CP-violating chargino currents that source baryogenesis.

Production of Massless Fermions during Inflation

We compute the one loop self energy, in a locally de Sitter background, for a massless fermion which is Yukawa-coupled to a massless, minimally coupled scalar. We then solve the modified Dirac equation resulting from inclusion of the self energy. We find faster-than-exponential growth in the fermion wave function, consistent with the production of fermions through a process in which a scalar and a fermion-anti-fermion pair are ripped out of the vacuum by inflation.

Natural magnetogenesis from inflation

We consider the gravitational generation of the massive Z-boson field of the standard model, due to the natural breaking of its conformal invariance during inflation. The electroweak symmetry restoration at the end of inflation turns the almost scale-invariant superhorizon Z-spectrum into a hypermagnetic field, which transforms into a regular magnetic field at the electroweak phase transition. The mechanism is generic and is shown to generate a superhorizon spectrum of the form B~1/L on a length-scale L regardless of the choice of inflationary model. Scaled to the epoch of galaxy formation such a field suffices to trigger the galactic dynamo and explain the observed galactic magnetic fields in the case of a spatially flat, dark energy dominated Universe with GUT-scale inflation. The possibility of further amplification of the generated field by preheating is also investigated. To this end we study a model of Supersymmetric Hybrid Inflation with a Flipped SU(5) grand unified symmetry group.

Axial currents from CKM matrix CP violation and electroweak baryogenesis

Abstract The first principle derivation of kinetic transport equations suggests that a CP-violating mass term during the electroweak phase transition can induce axial vector currents. Since the important terms are of first order in gradients there is a possibility to construct new rephasing invariants that are proportional to the CP phase in the Cabibbo–Kobayashi–Maskawa matrix and to circumvent the upper bound of CP-violating contributions in the Standard Model, the Jarlskog invariant. Qualitative arguments are given that these new contributions still fail to explain electroweak baryogenesis in extensions of the Standard Model with a strong first order phase transition.

Photon mass generation during inflation: de Sitter invariant case

We calculate the one-loop vacuum polarization tensor of scalar electrodynamics in a locally de Sitter space-time, endowed with a nearly minimally coupled, light scalar field. We show that the photon dynamics is well approximated by a (local) Proca Lagrangean. Since the photon mass can be much larger than the Hubble parameter, the photons may propagate slowly during inflation. Finally, we briefly discuss magnetic field generation on cosmological scales, and point out that while the spectrum of the magnetic field is identical to that obtained from the massless scalar, BlB0/l, the amplitude B0 may be significantly enhanced, implying that the seed field bound for the galactic dynamo can be easily met.