Medium corrections to the CP-violating parameter in leptogenesis

In two recent papers, arXiv:0909.1559 and arXiv:0911.4122, it has been demonstrated that one can obtain quantum corrected Boltzmann kinetic equations for leptogenesis using a top-down approach based on the Schwinger-Keldysh/Kadanoff-Baym formalism. These "Boltzmann-like" equations are similar to the ones obtained in the conventional bottom-up approach but differ in important details. In particular there is a discrepancy between the CP-violating parameter obtained in the first-principle derivation and in the framework of thermal field theory. Here we demonstrate that the two approaches can be reconciled if causal n-point functions are used in the thermal field theory approach. The new result for the medium correction to the CP-violating parameter is qualitatively different from the conventional one. The analogy to a toy model considered earlier enables us to write down consistent quantum corrected Boltzmann equations for thermal leptogenesis in the Standard Model (supplemented by three right-handed neutrinos) which include quantum statistical terms and medium corrected expressions for the CP-violating parameter.Comment: 13 pages, 9 figure

Systematic approach to leptogenesis in nonequilibrium QFT: self-energy contribution to the CP-violating parameter

In the baryogenesis via leptogenesis scenario the self-energy contribution to the CP-violating parameter plays a very important role. Here, we calculate it in a simple toy model of leptogenesis using the Schwinger-Keldysh/Kadanoff-Baym formalism as starting point. We show that the formalism is free of the double-counting problem typical for the canonical Boltzmann approach. Within the toy model, medium effects increase the CP-violating parameter. In contrast to results obtained earlier in the framework of thermal field theory, the medium corrections are linear in the particle number densities. In the resonant regime quantum corrections lead to modified expressions for the CP-violating parameter and for the decay width. Most notably, in the maximal resonant regime the Boltzmann picture breaks down and an analysis in the full Kadanoff-Baym formalism is required.Comment: 28 pages, 14 figure

On the Soft Limit of the Large Scale Structure Power Spectrum: UV Dependence

We derive a non-perturbative equation for the large scale structure power spectrum of long-wavelength modes. Thereby, we use an operator product expansion together with relations between the three-point function and power spectrum in the soft limit. The resulting equation encodes the coupling to ultraviolet (UV) modes in two time-dependent coefficients, which may be obtained from response functions to (anisotropic) parameters, such as spatial curvature, in a modified cosmology. We argue that both depend weakly on fluctuations deep in the UV. As a byproduct, this implies that the renormalized leading order coefficient(s) in the effective field theory (EFT) of large scale structures receive most of their contribution from modes close to the non-linear scale. Consequently, the UV dependence found in explicit computations within standard perturbation theory stems mostly from counter-term(s). We confront a simplified version of our non-perturbative equation against existent numerical simulations, and find good agreement within the expected uncertainties. Our approach can in principle be used to precisely infer the relevance of the leading order EFT coefficient(s) using small volume simulations in an `anisotropic separate universe' framework. Our results suggest that the importance of these coefficient(s) is a $\sim 10 \%$ effect, and plausibly smaller.Comment: 25+5 pages, 10 figures, comments added, matches published versio

Effective description of dark matter as a viscous fluid

Treating dark matter at large scales as an effectively viscous fluid provides an improved framework for the calculation of the density and velocity power spectra compared to the standard assumption of an ideal pressureless fluid. We discuss how this framework can be made concrete through an appropriate coarse-graining procedure. We also review results that demonstrate that it improves the convergence of cosmological perturbation theory.Comment: 8 pages, 3 figures, talk by N. Tetradis at Quarks-2016, includes unpublished materia

Systematic approach to leptogenesis in nonequilibrium QFT: vertex contribution to the CP-violating parameter

The generation of a baryon asymmetry via leptogenesis is usually studied by means of classical kinetic equations whose applicability to processes in the hot and expanding early universe is questionable. The approximations implied by the state-of-the-art description can be tested in a first-principle approach based on nonequilibrium field theory techniques. Here, we apply the Schwinger-Keldysh/Kadanoff-Baym formalism to a simple toy model of leptogenesis. We find that, within the toy model, medium effects increase the vertex contribution to the CP-violating parameter. At high temperatures it is a few times larger than in vacuum and asymptotically reaches the vacuum value as the temperature decreases. Contrary to the results obtained earlier in the framework of thermal field theory, the corrections are only linear in the particle number densities. An important feature of the Kadanoff-Baym formalism is that it is free of the double-counting problem, i.e. no need for real intermediate state subtraction arises. In particular, this means that the structure of the equations automatically ensures that the asymmetry vanishes in equilibrium. These results give a first glimpse into a number of new and interesting effects that can be studied in the framework of nonequilibrium field theory.Comment: 27 pages, 21 figure

Attribution of ozone changes to dynamical and chemical processes in CCMs and CTMs

Chemistry-climate models (CCMs) are commonly used to simulate the past and future development of Earth's ozone layer. The fully coupled chemistry schemes calculate the chemical production and destruction of ozone interactively and ozone is transported by the simulated atmospheric flow. Due to the complexity of the processes acting on ozone it is not straightforward to disentangle the influence of individual processes on the temporal development of ozone concentrations. A method is introduced here that quantifies the influence of chemistry and transport on ozone concentration changes and that is easily implemented in CCMs and chemistry-transport models (CTMs). In this method, ozone tendencies (i.e. the time rate of change of ozone) are partitioned into a contribution from ozone production and destruction (chemistry) and a contribution from transport of ozone (dynamics). The influence of transport on ozone in a specific region is further divided into export of ozone out of that region and import of ozone from elsewhere into that region. For this purpose, a diagnostic is used that disaggregates the ozone mixing ratio field into 9 separate fields according to in which of 9 predefined regions of the atmosphere the ozone originated. With this diagnostic the ozone mass fluxes between these regions are obtained. Furthermore, this method is used here to attribute long-term changes in ozone to chemistry and transport. The relative change in ozone from one period to another that is due to changes in production or destruction rates, or due to changes in import or export of ozone, are quantified. As such, the diagnostics introduced here can be used to attribute changes in ozone on monthly, interannual and long-term time-scales to the responsible mechanisms. Results from a CCM simulation are shown here as examples, with the main focus of the paper being on introducing the method

Sensitivity of age of air trends to the derivation method for non-linear increasing inert SF6

Mean age of air (AoA) is a diagnostic of transport along the stratospheric Brewer–Dobson circulation. While models consistently show negative trends, long-term time series (1975–2016) of AoA derived from observations show non-significant positive trends in mean AoA in the Northern Hemisphere. This discrepancy between observed and modelled mean AoA trends is still not resolved. There are uncertainties and assumptions required when deriving AoA from trace gas observations. At the same time, AoA from climate models is subject to uncertainties, too. In this paper, we focus on the uncertainties due to the parameter selection in the method that is used to derive mean AoA from SF$_{6}$ measurements in Engel et al. (2009, 2017). To correct for the non-linear increase in SF$_{6}$ concentrations, a quadratic fit to the time series at the reference location, i.e. the tropical surface, is used. For this derivation, the width of the AoA distribution (age spectrum) has to be assumed. In addition, to choose the number of years the quadratic fit is performed for, the fraction of the age spectrum to be considered has to be assumed. Even though the uncertainty range due to all different aspects has already been taken into account for the total errors in the AoA values, the systematic influence of the parameter selection on AoA trends is described for the first time in the present study. For this, we use the EMAC (ECHAM MESSy Atmospheric Chemistry) climate model as a test bed, where AoA derived from a linear tracer is available as a reference and modelled age spectra exist to diagnose the actual spatial age spectra widths. The comparison of mean AoA from the linear tracer with mean AoA from a SF$_{6}$ tracer shows systematic deviations specifically in the trends due to the selection of the parameters. However, for an appropriate parameter selection, good agreement for both mean AoA and its trend can be found, with deviations of about 1 % in mean AoA and 12 % in AoA trend. In addition, a method to derive mean AoA is evaluated that applies a convolution to the reference time series. The resulting mean AoA and its trend only depend on an assumption about the ratio of moments. Also in that case, it is found that the larger the ratio of moments, the more the AoA trend gravitates towards the negative. The linear tracer and SF$_{6}$ AoA are found to agree within 0.3 % in the mean and 6 % in the trend. The different methods and parameter selections were then applied to the balloon-borne SF$_{6}$ and CO$_{2}$ observations. We found the same systematic changes in mean AoA trend dependent on the specific selection. When applying a parameter choice that is suggested by the model results, the AoA trend is reduced from 0.15 to 0.07 years per decade. It illustrates that correctly constraining those parameters is crucial for correct mean AoA and trend estimates and still remains a challenge in the real atmosphere

Deriving stratospheric age of air spectra using an idealized set of chemically active trace gases

Analysis of stratospheric transport from an observational point of view is frequently realized by evaluation of the mean age of air values from long-lived trace gases. However, this provides more insight into general transport strength and less into its mechanism. Deriving complete transit time distributions (age spectra) is desirable, but their deduction from direct measurements is difficult. It is so far primarily based on model work. This paper introduces a modified version of an inverse method to infer age spectra from mixing ratios of short-lived trace gases and investigates its basic principle in an idealized model simulation. For a full description of transport seasonality the method includes an imposed seasonal cycle to gain multimodal spectra. An ECHAM/MESSy Atmospheric Chemistry (EMAC) model simulation is utilized for a general proof of concept of the method and features an idealized dataset of 40 radioactive trace gases with different chemical lifetimes as well as 40 chemically inert pulsed trace gases to calculate pulse age spectra. It is assessed whether the modified inverse method in combination with the seasonal cycle can provide matching age spectra when chemistry is well-known. Annual and seasonal mean inverse spectra are compared to pulse spectra including first and second moments as well as the ratio between them to assess the performance on these timescales. Results indicate that the modified inverse age spectra match the annual and seasonal pulse age spectra well on global scale beyond 1.5 years of mean age of air. The imposed seasonal cycle emerges as a reliable tool to include transport seasonality in the age spectra. Below 1.5 years of mean age of air, tropospheric influence intensifies and breaks the assumption of single entry through the tropical tropopause, leading to inaccurate spectra, in particular in the Northern Hemisphere. The imposed seasonal cycle wrongly prescribes seasonal entry in this lower region and does not lead to a better agreement between inverse and pulse age spectra without further improvement. Tests with a focus on future application to observational data imply that subsets of trace gases with 5 to 10 species are sufficient for deriving well-matching age spectra. These subsets can also compensate for an average uncertainty of up to ±20&thinsp;% in the knowledge of chemical lifetime if a deviation of circa ±10&thinsp;% in modal age and amplitude of the resulting spectra is tolerated.</p

Hard-Thermal-Loop Corrections in Leptogenesis I: CP-Asymmetries

We investigate hard-thermal-loop (HTL) corrections to the CP-asymmetries in neutrino and, at high temperature, Higgs boson decays in leptogenesis. We pay special attention to the two leptonic quasiparticles that arise at non-zero temperature and find that there are four contributions to the CP-asymmetries, which correspond to the four combinations of the two leptonic quasiparticles in the loop and in the final states. In two additional cases, we approximate the full HTL-lepton propagator with a zero-temperature propagator that employs the thermal lepton mass m_l(T), or the asymptotic thermal lepton mass sqrt{2} m_l(T). We find that the CP-asymmetries in the one-mode approaches differ by up to one order of magnitude from the full two-mode treatment in the interesting temperature regime T \sim M_1. The asymmetry in Higgs boson decays turns out to be two orders of magnitude larger than the asymmetry in neutrino decays in the zero-temperature treatment. The effect of HTL corrections on the final lepton asymmetry are investigated in paper II of this series.Comment: 38 pages, 14 figure