ULYSSES: Universal LeptogeneSiS Equation Solver

Abstract

ULYSSES is a python package that calculates the baryon asymmetry produced from leptogenesis in the context of a type-I seesaw mechanism. The code solves the semi-classical Boltzmann equations for points in the model parameter space as specified by the user. We provide a selection of predefined Boltzmann equations as well as a plugin mechanism for externally provided models of leptogenesis. Furthermore, the ULYSSES code provides tools for multi-dimensional parameter space exploration. The emphasis of the code is on user flexibility and rapid evaluation. It is publicly available at https://github.com/earlyuniverse/ulysses.

Program summary

Program Title: ULYSSES

CPC Library link to program files: https://doi.org/10.17632/rzd24f34h2.1

Developer’s repository link: github.com/earlyuniverse/ulysses

Licensing provisions: MIT

Programming language: python3

Nature of problem: Solving semi-classical momentum averaged Boltzmann equations for leptogenesis in the context of a type-I seesaw mechanism.

Solution method: Numerically solving coupled differential equations that can be complex.

Introduction

The two leading theories that explain the excess of matter over antimatter are leptogenesis [1] and electroweak baryogenesis [2], [3]. The latter theory has attracted much attention given its close relation with Higgs physics and much of the model parameter space has been explored. The former, in its various manifestations, appeals to many given its connection to neutrino masses and mixing. Although the mechanisms which generate the baryon asymmetry in both scenarios are vastly different, a common feature is the need to solve Boltzmann equations (BE) for points in the relevant model parameter space. ULYSSES is a python package that solves the semi-classical BE for leptogenesis in the context of a type-I seesaw mechanism and, to the authors knowledge, is the first publicly available code for this task.

The provided momentum-averaged BEs are based on the out-of-equilibrium decays of right-handed neutrinos and resonant leptogenesis. Effects such as lepton flavour, scatterings and spectator processes are also provided if the user wishes to apply them. For a given point in the model parameter space, ULYSSES calculates the final baryon asymmetry (provided in terms of the baryon-to-photon ratio, ${\eta }_B$, the baryonic yield, $Y_B$, and the baryonic density parameter, ${\Omega }_B{h}^2$) and plots the lepton asymmetry number density as a function of the time-evolution. For the user who wishes to undertake a multi-dimensional exploration of the parameter space, we provide instructions on how to use Multinest [4] in combination with ULYSSES. This allows visualisation of the multi-dimensional parameter space which is consistent with the measured baryon-to-photon ratio [5], [6]. We have designed the code in a modular fashion, separating the physics of the baryon asymmetry production from the parameter space exploration.

As this paper is a manual on how to use the ULYSSES code, we refrain from discussing the different regimes and subtleties of the leptogenesis mechanism and instead refer the reader to Refs. [7], [8], [9], [10] for broad reviews on various aspects of thermal and resonant leptogenesis.

The paper is organised as follows: in Section 2 we discuss the parametrisation and normalisation conventions ULYSSES applies. In Section 3, we describe the preprovided BEs and follow in Section 4 with installation instructions and a discussion of code dependencies. In Section 5, we explain the structure of the code and show the user how to calculate the baryon asymmetry for a point in the model parameter space. Scripts and examples of multi-dimensional parameter space exploration, as well as user options, are presented in Section 6 and finally we make concluding remarks in Section 7.