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144 Pages·2014·2.34 MB·English

by  Julian Heeck

Dissertation
submitted to the
Combined Faculties of the Natural Sciences and Mathematics
of the Ruperto Carola University of Heidelberg, Germany,
for the degree of
Doctor of Natural Sciences
Put forward by
Julian Heeck
Born in Telgte, Germany
Oral examination: May 14th, 2014

Neutrinos
and
Abelian Gauge Symmetries
Referees:
Dr. Werner Rodejohann
Prof. Dr. Joerg Jaeckel

Abstract
We study the intimate connection between neutrinos and simple abelian gauge sym-
metries U(1), starting from the observation that the full global symmetry group of
′
the StandardModel, = U(1) U(1) U(1) , can bepromoted to a
G B−L× Le−Lµ× Lµ−Lτ
local symmetry group by introducing three right-handed neutrinos—automatically
making neutrinos massive. The unflavored part U(1) is linked to the Dirac
B L
−
vs.Majorananatureofneutrinos;wediscusstheB Llandscape—includinglepton-
−
number-violatingDiracneutrinos—andimplicationsforneutrinos,thebaryonasym-
metry, and experiments. Flavored subgroups U(1) can shed light on the pe-
′
⊂ G
culiar leptonic mixing pattern and mass ordering; we show how normal, inverted,
and quasi-degenerate mass hierarchy can arise from a U(1) in asimple andtestable
′
manner. We furthermorepresent all U(1) that can enforce viable texture zeros
′
⊂ G
in the neutrino mass matrices. Beyond , symmetries U(1) in the dark matter
DM
G
sector can give rise to naturally light sterile neutrinos, which provide a new portal
between visible and dark sector, and also resolve some longstanding anomalies in
neutrino experiments. Further topics under consideration are the mixing of vector
bosons with the Z boson, as well as the Stückelberg mechanism. The latter raises
the question why the photon should be massless—or stable for that matter!
Zusammenfassung
Wir befassen uns mit der innigen Verbindung zwischen Neutrinos und einfachen
abelschen Eichsymmetrien U(1), der Feststellung folgend, dass die volle globale
′
Symmetriegruppe des Standardmodells, = U(1) U(1) U(1) ,
G B−L × Le−Lµ × Lµ−Lτ
nach Einführungdreier rechtshändiger Neutrinos geeicht werden kann– was Neutri-
nosautomatischmassivmacht.DergenerationsunabhängigeTeilU(1) hängtda-
B L
−
bei mit der Dirac- oder Majorana-Natur der Neutrinos zusammen; wir untersuchen
die B L Landschaft – Leptonenzahl-verletzende Dirac-Neutrinos eingeschlossen –
−
und Implikationen für Neutrinos, die Baryonasymmetrie und Experimente. Genera-
tionsabhängige U(1) können die eigentümlichen leptonischen Mischungs- und
′
⊂ G
Massenparameter erklären; wir zeigen wie normale, invertierte und quasi-entartete
Massenhierarchien in einfacher und testbarer Weise durch solche U(1) erzeugt wer-
′
den können. Des Weiteren bestimmen wir alle Untergruppen U(1) die zu er-
′
⊂ G
laubten Textur-Nullen in Neutrino-Massenmatrizen führen. Jenseits von können
G
abelscheEichsymmetrienU(1) imSektorderdunklenMaterieaufnatürlicheWei-
DM
se zu leichten sterilen Neutrinos führen, welche nicht nur ein neues Portal zwischen
dem sichtbaren und dem dunklen Sektor öffnen, sondern auch seit langem beste-
hende Anomalien in einigen Neutrinoexperimenten auflösen. Als weitere Themen
behandeln wir die Mischung von Vektorbosonen mit dem Z, sowie den Stückelberg-
Mechanismus, welcher die Frage aufwirft, warum das Photon masselos sein sollte –
oder stabil!

Contents
Disclaimer 1
Acknowledgments 3
1 Introduction 5
1.1 Neutrinos Oscillate and Have Mass . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.1 Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.2 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.1.3 Neutrinoless Double Beta Decay . . . . . . . . . . . . . . . . . . . . . 12
1.1.4 Summary of Open Questions in Neutrino Physics . . . . . . . . . . . . 16
1.2 Baryon Asymmetry of the Universe . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Baryon and Lepton Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5 Motivation of Symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Unflavored Symmetries 29
2.1 Unbroken B L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
−
2.1.1 B L Gauge Boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
−
2.1.2 Dirac Leptogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2 Majorana B L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
−
2.2.1 Seesaw Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.2 Thermal Leptogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.3 Scalar Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3 Dirac B L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
−
2.3.1 Effective ∆(B L)= 4 Operators . . . . . . . . . . . . . . . . . . . . 40
−
2.3.2 Lepton-Number-Violating Dirac Neutrinos . . . . . . . . . . . . . . . . 42
2.3.3 Neutrinoless Quadruple Beta Decay . . . . . . . . . . . . . . . . . . . 43
2.3.4 New Dirac Leptogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3 Flavored Symmetries 55
3.1 Neutrino Hierarchies: Normal Spectrum . . . . . . . . . . . . . . . . . . . . . 56
3.1.1 The Right Symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1.2 Gauge Boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.2 Neutrino Hierarchies: Inverted Spectrum . . . . . . . . . . . . . . . . . . . . . 61
3.2.1 Three Right-Handed Neutrinos and a Z Symmetry . . . . . . . . . . 62
2
3.2.2 Five Right-Handed Neutrinos and a Z Symmetry . . . . . . . . . . . 63
2
3.2.3 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3 Neutrino Hierarchies: Quasi-Degenerate Spectrum . . . . . . . . . . . . . . . 67
3.3.1 Neutrino Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.3.2 Gauge Boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.4 Texture Zeros and Vanishing Minors . . . . . . . . . . . . . . . . . . . . . . . 70
3.4.1 Classification and Current Status . . . . . . . . . . . . . . . . . . . . . 71
3.4.2 Realization via Flavor Symmetries . . . . . . . . . . . . . . . . . . . . 73
3.4.3 Summary of Texture Zeros . . . . . . . . . . . . . . . . . . . . . . . . 78
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4 Dark Symmetries 81
4.1 Light Sterile Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Exotic Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.3 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3.1 Relic Density and Thermal History . . . . . . . . . . . . . . . . . . . . 90
4.3.2 Direct and Indirect Detection . . . . . . . . . . . . . . . . . . . . . . . 94
4.4 Model Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5 Summary and Outlook 99
A Stückelberg Mechanism 103
A.1 Gauge Boson Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
A.2 Photon Mass and Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
B Gauge Boson Mixing 111
B.1 Kinetic Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
B.2 Kinetic and Mass Mixing with Three Abelian Groups . . . . . . . . . . . . . 113
B.2.1 Kinetic and Mass Mixing . . . . . . . . . . . . . . . . . . . . . . . . . 114
B.2.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
B.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
List of Abbreviations and Acronyms 121
Bibliography 123
Disclaimer
The research presented in this thesis contains original results already published in peer-
reviewed journals. This is indicated at the appropriate places—typically at the beginning of
the chapters—but in essence it comes down to this:
Chapter 2 contains work published in “Neutrinoless quadruple beta decay” [1] (in col-
•
laboration with W. Rodejohann) (Sec. 2.3.3) and “Leptogenesis with lepton-number-
violating Dirac neutrinos” [2] (Sec. 2.3.4).
Chapter3containsworkpublishedin“Neutrinohierarchiesfromagaugesymmetry”[3]
•
(in collaboration with W. Rodejohann)(Secs. 3.1 and 3.2), “Gauged L L symmetry
µ τ
−
at the electroweak scale” [4] (in collaboration with W. Rodejohann) (Sec. 3.3), and
“Vanishing minors in the neutrino mass matrix from abelian gauge symmetries” [5] (in
collaboration with T. Araki and J. Kubo (Sec. 3.4), as well as the proceedings found
in Refs. [6,7].
Chapter 4 is a slightly rewritten version of “Exotic charges, multicomponent dark mat-
•
ter and light sterile neutrinos” [8] (in collaboration with H. Zhang).
Appendix A.2 contains almost verbatim the paper “How stable is the photon?” [9].
•
In appendix B.2 we present the results from “Kinetic and mass mixing with three
•
abelian groups” [10] (in collaboration with W. Rodejohann).
In order to keep the thesis pithy and topically coherent, we will not cover all work that
has been published during the course of this Ph.D. (having already displaced potentially
distracting topics adjacent to the main part to the appendices). In particular, we omit a
discussion of the papers
“Hidden O(2) and SO(2) symmetry in lepton mixing” [11] (in collaboration with
•
W.Rodejohann)—connectingthesmallneutrino-mixingparameters∆m2 andθ with
12 13
an approximate global symmetry.
“Seesaw parametrization for n right-handed neutrinos” [12]—studying the effects of a
•
varying number n = 3 of right-handed neutrinos in the seesaw mechanism, especially
6
on neutrino mass anarchy.
“Sterile neutrino anarchy” [13] (in collaboration with W. Rodejohann)—extending the
•
neutrino mass anarchy framework to the 3+2 scenario of light sterile neutrinos.