Study of neutrinoless double beta decay in the Standard Model extended with sterile neutrinos

Abstract

We study a model where the Standard Model is augmented with three sterile neutrinos. By adopting a particular parameterization of a (6×6)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(6\ imes 6)$$\\end{document} unitary matrix—in this context, light neutrino masses being generated via a type-I seesaw mechanism—we analytically derive the masses of the sterile states using an exact seesaw relation. The masses of the sterile states are derived in terms of the lightest mass of active neutrinos and active–active and active–sterile mixing angles and phases; they can be all light, all heavy, or a mixture of light and heavy compared to the active states. This can be attributed to the interplay of the CP-violating (CPV) phases of the mixing matrix. As both active and sterile states can mediate the neutrinoless double beta decay (0νββ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\ u \\beta \\beta $$\\end{document}) process, their contributions to the effective mass of the electron neutrino, |mee|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|m_{ee}|$$\\end{document}, become a function of the mass of the lightest active state and active–active and active–sterile mixing angles and phases. We explore the parameter space of |mee|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|m_{ee}|$$\\end{document}, keeping in mind the present and future sensitivity of 0νββ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\ u \\beta \\beta $$\\end{document} decay searches. By making use of constraints from charged lepton flavor-violating (cLFV) processes and non-unitarity, we explore the role of additional CPV phases and active–sterile mixing angle values. The numerical values thus obtained for |mee|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|m_{ee}|$$\\end{document} can vary from as low as O(10-4)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathscr {O}(10^{-4})$$\\end{document} to saturating the present experimental limit. We also check the reliability of our result by calculating the branching ratio of μ→eγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu \\rightarrow e \\gamma $$\\end{document}, a prominent cLFV process, and non-unitarity in this framework.