Dark matter in a Z3-symmetry extension of the Standard Model

86 Pages·2015·0.79 MB·English

by  Luan Vinícius Koerich

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MASTER’S DISSERTATION IFT–D.007/15
Dark matter in a Z -symmetry
3
extension of the Standard Model
Luan Vin´ıcius Koerich
Supervisor
Rogerio Rosenfeld
Co-supervisor
Nicol´as Bernal
August 2015

Thisworkisdedicatedtomyparents,
toGeórgia,tomysisterandmynephew,
andtomyfamily,forhelpingmecope.

Contents
Abstract ix
Acknowledgements xi
Introduction 1
1 Universeinexpansion 3
1.1 Aspectsofcosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Theuniverseinequilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 TheBoltzmannequation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 Darkmatter 25
2.1 Evidencesandgeneralpropertiesofthedarkmatter . . . . . . . . . . . . . . . . 25
2.2 Thedeparturefromequilibriumandthefreeze-out . . . . . . . . . . . . . . . . . 28
3 Strongly-interactingmassiveparticles 39
3.1 Themodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Semi-analyticalandnumericalsolutionsfortheBoltzmannequations . . . . . . . 42
3.3 SolvingtheBoltzmannequationforanarbitrarycross-section . . . . . . . . . . . 49
Conclusions 61
A Numericalsolutions 63
A.1 Constantandup-to-a-powertemperature-dependentcross-sections . . . . . . . . 63
A.2 Arbitrarytemperature-dependentcross-section . . . . . . . . . . . . . . . . . . . 67
v
vi
Resumo
Amatériaescuraéresponsávelporcercade85%detodaamatériadouniverso. Sabe-sequeela
possuiumlongotempodevida,queéneutraeinteragecomamatériacomumapenasgravitacion-
almente. Muitosmodelosforamaventadosparadescreveraspossíveispartículasdematériaescura,
muitos deles baseados emextensõesdo modelo padrão para partículaselementares. Emparticular,
háosmodelosdepartículasmassivasinterativasporforçaforte,osSIMPs,queestendemomodelo
padrãocomumsetorescalarextracontendotodasaspartículasdematériaescura,cujaestabilidade
égarantidaporumasimetriadiscreta,aqual respeitam. Essasimetriatambémestendeaspossível
interaçõesentreaspartículasdematériaescuraparaalémdausualauto-aniquilaçãodeparesedo
contextodoproblemadeLee-Weinberg,descritopelaspartículasmassivasinteragentesporforça
fraca,osWIMPs. Nestetrabalhopostulamosaexistênciadeumsetorescalarcomumasimetria
discreta Z ,consequente de uma quebra de simetria U(1) global. Esta simetria permite que
3 DM
processos de semi-aniquilação e aniquilação 3 → 2 também ocorram, além do usual processo
de auto-aniquilação. Estudaremos esses três cenários, encontrando as soluções das equações
de Boltzmann e comparando suas respectivas abundâncias com o resultado observacional, para
podermosavaliarnossomodelo. Começaremosporrevisarimportantesconceitosdacosmologia
padrãoeporapresentaromodelo. Entãorevisaremosassoluçõesnuméricasparaasequações,e
apresentaremosnossosprópriosresultadosparasoluçõessemi-analíticasdosprocessosdesemi-
aniquilaçãoedeaniquilação3 → 2. Concluiremosporapresentarnossosprópriosresultadospara
a solução da equação de Boltzmann para o processo 3 → 2 usando uma seção de choque que é
dependentedatemperatura,calculadacomopacoteCalcHEP.
Palavras-chaves: Matériaescura,SIMPs,equaçãodeBoltzmann.
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viii
Abstract
Dark matter accounts for approximately 85% of all the matter in the universe. It is known to
havealonglifetime,tobeneutralandtointeractwithordinarymatteralmostonlygravitationally.
There have been several models to suggest possible particles for the dark matter, many of them
relyingonextensionstothestandardmodelofelementaryparticles. Inparticular,thereareSIMP
(strongly-interactingmassiveparticles)models,whichextendthestandardmodelbyanextrascalar
sector containing the dark-matter particles, whose stability is provided by a discrete symmetry.
This symmetry also extends the possible interactions between the dark-matter particles to beyond
theusualpairannihilationandLee-Weinbergscenariodescribed bytheWIMP(weakly-interacting
massiveparticles)models. Inourstudy,wepostulatetheexistenceofanextendeddarksectorwith
Z
a discretesymmetry,whichistheconsequenceofaglobalU(1) symmetrybreaking. This
3 DM
symmetryallowsthesemi-annihilationand3 → 2annihilationprocessestotakeplace,besidesthe
usual self-annihilation process. We will study each of these three scenarios, solving the respective
Boltzmann equations and comparing the correspondent relic abundance to the observed one, in
order to verify the liability of each of them. We will start by reviewing important aspects of
standardcosmology andpresentingour model. Thenwe willreviewthenumerical solutionsfor
the equations, and present our own results for semi-analytical solutions to the semi- and 3 → 2
annihilationprocesses. Wewillendbypresentingourownresultsonsolvingthe3 → 2Boltzmann
equationforatemperature-dependentcross-section,calculatedwiththeCalcHEPpackage.
Keywords: Darkmatter,SIMPs,Boltzmannequation.
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