Leptogenesis from Oscillations of Heavy Neutrinos with Large Mixing Angles

Leptogenesis from Oscillations of Heavy Neutrinos with Large Mixing Angles

Abstract

The extension of the Standard Model by heavy right-handed neutrinos can simultaneously explain the observed neutrino masses via the seesaw mechanism and the baryon asymmetry of the Universe via leptogenesis. If the mass of the heavy neutrinos is below the electroweak scale, they may be found at the LHC, BELLE Two, NA62, the proposed SHIP experiment or a future high-energy collider. In this mass range, the baryon asymmetry is generated via CP-violating oscillations of the heavy neutrinos during their production. We study the generation of the baryon asymmetry of the Universe in this scenario from first principles of non-equilibrium quantum field theory, including spectator processes and feedback effects. We eliminate several uncertainties from previous calculations and find that the baryon asymmetry of the Universe can be explained with larger heavy neutrino mixing angles, increasing the chance for an experimental discovery. For the limiting cases of fast and strongly overdamped oscillations of right-handed neutrinos, the generation of the baryon asymmetry can be calculated analytically up to corrections of order one.

One Introduction

One point one Motivation

Over the past decades the Standard Model of particle physics has been established as a powerful theory explaining almost all phenomena that are observed in particle physics. Its full particle content has been discovered eventually, and its predictions to this end pass all precision tests. Nevertheless, it is clear that the Standard Model cannot be a complete theory of Nature. Any attempt to explain the observed neutrino flavour oscillations with the Standard Model field content relies on non-renormalizable interactions mediated by operators of mass dimension larger than four, which are generally associated with the existence of new heavy degrees of freedom that have been integrated out. Moreover, the Standard Model fails to explain several problems in cosmology. These include the origin of the matter-antimatter asymmetry in the Universe that can be quantified by the baryon-to-photon ratio.

eta naught B equals six point one times ten to the negative ten.

The addition of n naught s greater than or equal to two right-handed sterile neutrinos N naught i left parenthesis i equals one to n naught s right parenthesis can simultaneously explain the observed light neutrino masses via the seesaw mechanism and the baryon asymmetry of the Universe via leptogenesis. The sterile neutrinos are connected with the Standard Model solely through their Yukawa interactions Y with the Standard Model lepton doublets ell naught a left parenthesis a equals e comma mu comma tau right parenthesis and the Higgs field phi. The Lagrangian of this model is given by script L equals script L subscript S M plus one half bar N naught i left parenthesis i overrightarrow p minus M right parenthesis naught i j N naught j minus Y naught i a superscript star bar ell naught a varepsilon phi P subscript R N naught i minus Y naught i a bar N naught i P subscript L phi dagger varepsilon dagger ell naught a,

where script L subscript S M is the Standard Model Lagrangian. The spinors N naught i observe the Majorana condition N naught i superscript c equals N naught i, where the superscript c denotes charge conjugation. Besides, varepsilon is the antisymmetric S U two tensor with varepsilon to the power of one two equals one. The eigenvalues M naught i of M, which in good approximation equal the physical masses of the N naught i particles, introduce new mass scales in nature. The requirement to explain neutrino oscillation data does not fix the magnitudes of the masses M naught i, as oscillation experiments only constrain the combination m subscript nu equals v squared Y dagger M to the power of negative one Y star.

An overview of the implications of different choices of M naught i for particle physics and cosmology is provided by Ref. The relation between the parameters in the Lagrangian and neutrino oscillation data is given in Appendix A.

The magnitude of the M naught i is often assumed to be much larger than the electroweak scale. However, values below the electroweak scale are phenomenologically very interesting because they may allow for an experimental discovery of the N naught i particles and to potentially unveil the mechanism of neutrino mass generation. Various experimental constraints on this low-scale seesaw scenario are summarised in Ref. and references therein. In the present work, we focus on masses M naught i in the GeV range. Apart from some theoretical arguments, the study of this mass range is motivated by the possibility to test it experimentally. Heavy neutrinos with M naught i less than five GeV can be searched for in meson decays at B and K factories or fixed target experiments, including NA62, the SHIP experiment proposed at CERN or a similar setup at the DUNE beam at FNAL. Larger masses are accessible at the LHC, either via vector boson fusion left parenthesis M naught i greater than five hundred GeV right parenthesis, s-channel exchange of W bosons left parenthesis five hundred GeV greater than M naught i greater than eighty GeV right parenthesis or in real gauge boson decays left parenthesis M naught i less than eighty GeV right parenthesis, but the perspectives would be best at a high energy lepton collider ILC, FCC-ee, or the CEPC.

Since the N sub i are gauge singlets, they can interact with ordinary matter only via their quantum mechanical mixing with left-handed neutrinos that arises as a result of the Higgs mechanism and is the reason why the S M neutrinos become massive. This mixing can be quantified by the elements of the matrix

Event rates in experiments are proportional to combinations of the parameters

U sub a i squared equals the absolute value of theta U sub N sub a i squared,

which determine the interaction strength of the heavy neutrino N sub i with leptons of flavour a. Here U sub N is a unitary matrix that diagonalises the heavy neutrino mass matrix. For convenience, we also introduce the parameter

U sub i squared equals the sum over a of U sub a i squared that quantifies the total mixing of a given heavy neutrino of flavour i as well as the quantity

U two equals S U R equals the trace of theta plus theta.

It is of interest to determine for which range of values of U a i heavy neutrinos can simultaneously explain neutrino oscillation data and the BAU. In the present work, we improve on the network of equations that describes the generation of the BAU from GeV-scale sterile neutrinos and develop analytic approximations to the solutions for phenomenologically relevant limiting cases.