Quantum leptogenesis I

Thermal leptogenesis explains the observed matter–antimatter asymmetry of the universe in terms of neutrino masses, consistent with neutrino oscillation experiments. We present a full quantum mechanical calculation of the generated lepton asymmetry based on Kadanoff–Baym equations. Origin of the asymmetry is the departure from equilibrium of the statistical propagator of the heavy Majorana neutrino, together with CP violating couplings. The lepton asymmetry is calculated directly in terms of Green’s functions without referring to “number densities”. Compared to Boltzmann and quantum Boltzmann equations, the crucial difference are memory effects, rapid oscillations much faster than the heavy neutrino equilibration time. These oscillations strongly suppress the generated lepton asymmetry, unless the standard model gauge interactions, which cause thermal damping, are properly taken into account. We find that these damping effects essentially compensate the enhancement due to quantum statistical factors, so that finally the conventional Boltzmann equations again provide rather accurate predictions for the lepton asymmetry.     

Nonequilibrium dynamics of scalar fields in a thermal bath

We study the approach to equilibrium for a scalar field which is coupled to a large thermal bath. Our analysis of the initial value problem is based on Kadanoff-Baym equations which are shown to be equivalent to a stochastic Langevin equation. The interaction with the thermal bath generates a temperature-dependent spectral density, either through decay and inverse decay processes or via Landau damping. In equilibrium, energy density and pressure are determined by the Bose-Einstein distribution function evaluated at a complex quasi-particle pole. The time evolution of the statistical propagator is compared with solutions of the Boltzmann equations for particles as well as quasi-particles. The dependence on initial conditions and the range of validity of the Boltzmann approximation are determined.     

Leptogenesis from first principles in the resonant regime

The lepton asymmetry generated by the out-of-equilibrium decays of heavy Majorana neutrinos with a quasi-degenerate mass spectrum is resonantly enhanced. In this work, we study this scenario within a first-principle approach. The quantum field theoretical treatment is applicable for mass splittings of the order of the width of the Majorana neutrinos, for which the enhancement is maximally large. The non-equilibrium evolution of the mixing Majorana neutrino fields is described by a formal analytical solution of the Kadanoff–Baym equations, that is obtained by neglecting the back-reaction. Based on this solution, we derive approximate analytical expressions for the generated asymmetry and compare them to the Boltzmann result. We find that the resonant enhancement obtained from the Kadanoff–Baym approach is smaller compared to the Boltzmann approach, due to additional contributions that describe coherent transitions between the Majorana neutrino species. We also discuss corrections to the masses and widths of the degenerate pair of Majorana neutrinos that are relevant for very small mass splitting, and compare the approximate analytical result for the lepton asymmetry with numerical results.     

Resonant leptogenesis

We study the scenario of thermal leptogenesis in which the leptonic asymmetries are resonantly enhanced through the mixing of nearly degenerate heavy Majorana neutrinos that have mass differences comparable to their decay widths. Field-theoretic issues arising from the proper subtraction of real intermediate states from the lepton-number-violating scattering processes are addressed in connection with an earlier developed resummation approach to unstable particle mixing in decay amplitudes. The pertinent Boltzmann equations are numerically solved after the enhanced heavy-neutrino self-energy effects on scatterings and the dominant gauge-mediated collision terms are included. We show that resonant leptogenesis can be realized with heavy Majorana neutrinos even as light as ∼1 TeV, in complete accordance with the current solar and atmospheric neutrino data.     

Self-consistent approach to off-shell transport

The properties of two forms of the gradient expanded Kadanoff-Baym equations, i.e., the Kadanoff-Baym and Botermans-Malfliet forms, suitable for describing the transport dynamics of particles and resonances with broad spectral widths, are discussed in context of conservation laws, the definition of a kinetic entropy, and the possibility of numerical realization. Recent results on exact conservations of charge and energy-momentum within Kadanoff-Baym form of quantum kinetics based on local coupling schemes are extended to two cases relevant in many applications. These concern the interaction via a finite-range potential and, relevant in nuclear and hadron physics, e.g., for the pion-nucleon interaction, the case of derivative coupling.     

Leptogenesis in flavor models with type I and II seesaws

In type I seesaw models with flavor symmetries accounting for the lepton mixing angles the CP asymmetry in right-handed neutrino decays vanishes in the limit in which the mixing pattern is exact. We study the implications that additional degrees of freedom from type II seesaw may have for leptogenesis in such a limit. We classify in a model independent way the possible realizations of type I and II seesaw schemes, differentiating between classes in which leptogenesis is viable or not. We point out that even with the interplay of type I and II seesaws there are generic classes of minimal models in which the CP asymmetry vanishes. Finally we analyze the generation of the lepton asymmetry by solving the corresponding kinetic equations in the general case of a mild hierarchy between the light right-handed neutrino and the scalar triplet masses. We identify the possible scenarios in which leptogenesis can take place.     

Generalized gradient expansions in quantum transport equations

Gradient expansions in quantum transport equations of a Kadanoff-Baym form have been reexamined. In a consistent approach the expansion should be performed also inside the self-energy in the scattering integrals of these equations. In the first perturbation order this internal expansion gives new correction terms to the generalized Boltzmann equation. These correction terms are found here for several typical systems. Possible corrections to the theory of a linear response to weak electric fields are also discussed.     

Quantum Decoherence of Gaussian Steering and Entanglement in Hawking Radiation and Thermal Bath

We study the effects of Hawking radiation and bath temperature on quantum steering and entanglement for a two-mode Gaussian state exposed in the background of a black hole and immersed in the two independent thermal baths. We find that both the effects can destroy the quantum steering and entanglement. Quantum steering always exists sudden death for any Hawking temperature and any bath temperature, but entanglement does not in zero-temperature thermal bath. Both the Hawking radiation and the asymmetry of thermal baths can induce the asymmetry of quantum steering, but the latter effect is much weaker than the former. An unintuitive result is that the observer who stays in the Hawking radiation or in the thermal bath with higher temperature has more stronger steerability than the other one. We also find that Hawking radiation and thermal noise can change the asymptotic behavior of steering and entanglement versus the squeezing parameter.

     

Penetration depth anisotropy in d-density wave scenario

We discuss thermalization of a test particle schematized as a harmonic oscillator and coupled to a Boltzmann heat bath of finite size and with a finite bandwidth for the frequencies of its particles. We find that complete thermalization only occurs when the test particle frequency is within a certain range of the bath particle frequencies, and for a certain range of mass ratios between the test particle and the bath particles. These results have implications for the study of classical and quantum behaviour of high-frequency nanomechanical resonators.     

Quantum kinetics and thermalization in a particle bath model

We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.     

Leptogenesis via a varying Weinberg operator:a semi-classical approach

In this paper, we introduce leptogenesis via a varying Weinberg operator from a semi-classical perspective.This mechanism is motivated by the breaking of an underlying symmetry which triggers a phase transition that causes the coupling of the Weinberg operator to become dynamical. Consequently, a lepton anti-lepton asymmetry arises from the interference of the Weinberg operator at two different spacetime points. Using the semi-classical approach,we treat the Higgs as a background field and show that a reflection asymmetry between leptons and anti-leptons is generated in the vicinity of the bubble wall. We solve the equations of motion of the lepton and anti-lepton quasiparticles to obtain the final lepton asymmetry.     

Nonconservation of lepton current and asymmetry of relic neutrinos

The neutrino asymmetry, \({n_v} - {n_{\bar v}}\), in the plasma of the early Universe generated both before and after the electroweak phase transition (EWPT) is calculated. It is well known that in the Standard Model the leptogenesis before the EWPT, in particular, for neutrinos, owes to the Abelian anomaly in a massless hypercharge field. At the same time, the generation of neutrino asymmetry in the Higgs phase after the EWPT has not been considered previously due to the absence of any quantum anomaly in an external electromagnetic field for such electroneutral particles as neutrinos, in contrast to the Adler anomaly for charged left- and right-handed massless electrons in the same electromagnetic field. Using the Boltzmann equation for neutrinos modified to include the Berry curvature term in momentum space, we establish a violation of the macroscopic neutrino current in the plasma after the EWPT and exactly reproduce the non-conservation of the lepton current in the symmetric phase before the EWPT that owes to the contribution of the triangle anomaly in an external hypercharge field but already without computing the corresponding Feynman diagrams. We apply the new kinetic equation to calculate the neutrino asymmetry by taking into account the Berry curvature and the electroweak interaction with plasma particles in the Higgs phase, including that after the neutrino decoupling in the absence of their collisions in the plasma. We find that this asymmetry is too small for observations. Thus, a difference between the relic neutrino and antineutrino densities, if it exists, must appear already in the symmetric phase of the early Universe before the EWPT.     

Monogamy of Einstein‐Podolsky‐Rosen Steering in the Background of an Asymptotically Flat Black Hole

We study the behavior of monogamy deficit and monogamy asymmetry for Einstein‐Podolsky‐Rosen steering of Gaussian states under the influence of the Hawking effect. We demonstrate that the monogamy of quantum steering shows an extreme scenario in the curved spacetime: the first part of a tripartite system cannot individually steer two other parties, but it can steer the collectivity of the remaining two parties. We also find that the monogamy deficit of Gaussian steering, a quantifier of genuine tripartite steering, are generated due to the influence of the Hawking thermal bath. Our results elucidate the structure of quantum steering in tripartite quantum systems in curved spacetime.     

Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains

We simulate numerically the dynamics of strongly correlated bosons in a two-leg ladder subject to a time-dependent energy bias between the two chains. When all atoms are initially in the leg with higher energy, we find a drastic reduction of the interchain particle transfer for slow linear sweeps, in quantitative agreement with recent experiments. This effect is preceded by a rapid broadening of the quasimomentum distribution of atoms, signaling the presence of a bath of low-energy excitations in the chains. We further investigate the scenario of quantum quenches to fixed values of the energy bias. We find that for a large enough density the momentum distribution relaxes to that of an equilibrium thermal state with the same energy.     

CP violation in neutrino oscillation and leptogenesis

We study the correlation between CP violation in neutrino oscillations and leptogenesis in the framework with two heavy Majorana neutrinos and three light neutrinos. Among three unremovable CP phases, a heavy Majorana phase contributes to leptogenesis. We show how the heavy Majorana phase contributes to Jarlskog determinant J as well as neutrinoless double beta decay by identifying a low energy CP-violating phase which signals the CP-violating phase for leptogenesis. For some specific cases of the Dirac mass term of neutrinos, a direct relation between lepton number asymmetry and J is obtained. We also study the effect coming from the phases which are not related to leptogenesis.     

Reheating and leptogenesis in a SUGRA inspired brane inflation

We have studied extensively phenomenological implications in a specific model of brane inflation driven by background supergravity (Choudhury and Pal, 2011) [1], via thermal history of the universe and leptogenesis pertaining to the particle physics phenomenology of the early universe. Using the one loop corrected inflationary potential we have investigated for the analytical expression as well as the numerical estimation for brane reheating temperature for standard model particles. This results in some novel features of reheating from this type of inflation which have serious implications in the production of heavy Majorana neutrinos needed for leptogenesis through the reheating temperature. We have also derived the expressions for the gravitino abundance during reheating and radiation dominated era. We have further estimated different parameters at the epoch of phase transition and revealed their salient features. At the end we have explicitly given an estimate of the amount of CP violation through the effective CP phase which is related to baryon asymmetry as well as gravitino dark matter abundance.     

Insensitivity of leptogenesis with flavor effects to low energy leptonic CP violation

If the baryon asymmetry of the Universe is produced by leptogenesis, CP violation is required in the lepton sector. In the seesaw extension of the standard model with three hierarchical right-handed neutrinos, we show that the baryon asymmetry is insensitive to the Pontecorvo-Maki-Nagakawa-Sakata phases: thermal leptogenesis can work for any value of the observable phases. This result was well known when there were no flavor effects in leptogenesis; we show that it remains true when flavor effects are included.     

Soft leptogenesis in Higgs triplet model

We consider the minimal supersymmetric triplet seesaw model as the origin of neutrino masses and mixing as well as of the baryon asymmetry of the Universe, which is generated through soft leptogenesis employing a CP-violating phase and a resonant behavior in the supersymmetry breaking sector. We calculate the full gauge-annihilation cross section for the Higgs triplets, including all relevant supersymmetric intermediate and final states, as well as coannihilations with the fermionic superpartners of the triplets. We find that these gauge annihilation processes strongly suppress the resulting lepton asymmetry. As a consequence of this, successful leptogenesis can occur only for a triplet mass at the TeV scale, where the contribution of soft supersymmetry breaking terms enhances the CP and lepton asymmetry. This opens up an interesting opportunity for testing the model in future colliders.     

Perturbative and nonperturbative contributions to a simple model for baryogenesis

Single field baryogenesis, a scenario for Dirac leptogenesis sourced by a time-dependent scalar condensate, is studied on a toy model. We compare the creation of the charge asymmetry by the perturbative decay of the condensate with the nonperturbative decay, a process of particle production commonly known in the context of inflation as preheating. Neglecting backreaction effects, we find that over a wide parametric range perturbative decay and preheating contribute by the same order of magnitude to the baryon asymmetry.