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On Effective Field Theory of Dark Matter

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On Effective Field Theory of Dark Matter On effective field theory of dark matter Ben Geytenbeek Supervisor: Dr. Ben Gripaios Cavendish Laboratory University of Cambridge This dissertation is submitted for the degree of Doctor of Philosophy Darwin College July 2021 Declaration I hereby declare that this thesis is the result of my own work and includes nothing which is the outcome of work done in collaboration except as declared in the preface and specified in the text and acknowledgements. It is not substantially the same work that has already been submitted before for any degree or other qualification except as declared in the preface and specified in the text. This dissertation doesnotexceed the prescribed word limit of 60,000 words for the Physics and Chemistry Degree Committee, including abstract, tables, footnotes and appendices but excluding table of contents, figure captions, list of figures, references and acknowledgements. Ben Geytenbeek July 2021 On effective field theory of dark matter Ben Geytenbeek 1 We investigate the feasibility of dark matter particles existing in the Universe as a spin- 2 fermion using effective field theories to parameterise the higher order physics. Our goal is to determine therequirements for exclusion of such particles by direct and indirect detection. In partI, based on ref. [1], we introduce a complete basis of operators up to dimension 5 for fermions that are part of singlet, doublet and triplet representation of the Standard Model SU(2) electroweak symmetry group. Such particles correspond to the bino, higgsino and wino of supersymmetry models respectively. We determine the thermal relic density of particles interacting with each of our operators and show that viable thermal relics that evade experimental constraints can exist with masses as low as as 100 GeV and up to 10 TeV due to the mass splittings that arise at dimension 5. In part II, based on ref. [2] we further investigate the effect of fermionic dark matter that may interact through an electromagnetic dipole interaction at dimension 5 on energy transport in the Sun. In particular, we test whether the models can provide a solution to the solar abundance problem, a theoretical discrepancy between the observations of helioseismology and the theoretical Standard Solar Model. We introduce all of the necessary theoretical implementation and show that, although introducing dark matter may alleviate the tension of the solar abundance problem, the required interaction strengths are strongly ruled out by direct detection experiments. Preface The following portions of this thesis were completed in collaboration with others: • The tabulation of α and κ coefficients in section 4.4.5 was completed by Pat Scott and Aaron Vincent using the derivation provided by the candidate. • The calculation of the frequency separation ratios in section 5.3 was completed by Aldo Serenelli using data provided by the candidate. Derivations of results from the literature are indicated in the text of this thesis. Ben Geytenbeek July 2021 Acknowledgements The journey of a PhD is long and arduous one, and mine has been no different. This work would not have been able to be completed without the help and support of the High Energy Physics group at the Cavendish Laboratory, in particular my supervisor Dr Ben Gripaios and the SUSY working group; especially during the weekly group meetings and subsequent lunches. The occupants of the HEP Library, in particular Mr Herschel Chawdhry have been instrumental in supporting my progress and providing light hearted relief over the years. I would also like to pay tribute to my former supervisors, collaborators and peers from the University of Adelaide who provided me with the inspiration to pursue a PhD in Cambridge, notably Prof Anthony Williams and A/Prof Martin White. The Physics Honours Class of 2015 in Adelaide has always encouraged and supported me both before and during my time in Cambridge when I have returned to visit, and have always made me feel welcome like I had never left, including Ryan Bignell, Tuong Cao, Joshua Charvetto, Raquel Hogben, Dona Kireta, Zach Matthews, Urwah Nawaz, Jason Oliver, Robert Perry, Andre Scaffidi, Kim Somfleth and the rest of the CoEPP and CSSM students andstaff. My attendance at Cambridge would not have been possible without the financial support of the Gates Cambridge Trust and the excellent work of the staff there to make everything as smooth as possible, in particular Jim Smith, Luisa Clarke, Celine Ophelders and Dr Jade Tran. The role of the Trust and Scholar’s Council in helping to navigate the complexities of Cambridge cannot be understated, and I am thankful for everyone who I served with on Council or the Orientation Committee for their dedication and service, notably Margaret Comer, Emma Glennon, Marina Velickovic and Kevin Chew. My time in Cambridge would not be complete without the support and friendships from the various communities I have become involved with. In particular, the broader Gates Community has been outstandingly welcoming to me, the Darwin College Cricket Club and Cavendish Laboratory Cricket Club have been excellent avenues for entertainment and the Cambridge University Real Tennis Club has been a wonderful community. From the latter, I particularly want to thank Kees Ludekens, Peter Paterson, Dr Victoria Harvey and Dr Christie Marrian for their support with both coaching and developing interesting projects off court. Finally, I owe a great deal of appreciation for those friends and family not listed above who have aided, encouraged and supported me whilst providing excellent entertainment and friendship. In particular, I thank Annalise Higgins, Krittika D’Silva and Annika Pecchia-Bekkum for the various adventures and incidents over the course of my studies. Most notably, Jacqueline Siu, whose support for me has been unwavering and with whom I have shared many amazing adventures throughout my time in Cambridge. Lastly, the support of my family in Australia has been instrumental to my progress throughout my PhD. Table of contents List of figures xiii 1 Introduction 1 1.1 Early history of dark matter observations . .1 1.2 Galactic rotation curves . .2 1.3 Colliding galaxy clusters . .3 1.4 Dark matter cosmological density . .4 1.4.1 Cosmic microwave background . .5 1.4.2 Big bang nucleosynthesis . .6 1.5 Dark matter candidates . .7 1.5.1 Theoretical bounds on dark matter particles . .7 1.5.2 Weakly interacting massive particles . .7 1.5.3 SuperWIMPs . .8 1.5.4 Axions . .8 1.5.5 Sterile Neutrinos . 10 1.5.6 Hidden dark matter . 11 1.6 Direct detection searches . 11 1.6.1 Spin independent dark matter searches . 11 1.6.2 Spin dependent dark matter searches . 14 1.7 Indirect Detection Searches and Solar Neutrinos . 15 1.8 Supersymmetry and neutralinos . 17 1.8.1 Supersymmetry fundamentals . 17 1.8.2 Spontaneous symmetry breaking in supersymmetry . 18 1.8.3 Supersymmetric dark matter candidates . 23 1.9 Effective field theories . 24 xii Table of contents I Neutralino thermal relics with effective field theory operators 27 2 Effective field theory model building 29 2.1 Dimension 3 - Mass terms . 30 2.1.1 Singlet . 30 2.1.2 Doublet . 30 2.1.3 Triplet . 32 2.1.4 Mixed models . 32 2.2 Dimension 4 - Kinetic terms . 32 2.2.1 Singlet . 32 2.2.2 Doublet . 33 2.2.3 Triplet . 33 2.2.4 Mixed models - Yukawa terms . 34 2.3 Dimension 5 - Effective field theory operators . 35 2.3.1 Singlet . 35 2.3.2 Doublet . 36 2.3.3 Triplet . 38 2.3.4 Mixed models . 38 2.4 Mass splittings from spontaneous symmetry breaking . 39 2.5 Electromagnetic dipole terms . 43 2.5.1 Correspondence between operators and dipole moments . 43 2.5.2 Anapole moments . 46 3 Relic density 49 3.1 Relic density Boltzmann equations . 50 3.2 Experimental constraints on physical models . 55 3.3 Sommerfeld enhancement . 56 3.4 Relic density calculations . 63 3.4.1 Higgsino electromagnetic dipole interactions . 65 3.4.2 Higgs-higgsino interaction with neutralino mass splitting . 65 3.4.3 Higgs-higgsino interaction without neutralino mass splitting . 67 3.4.4 Wino inelastic magnetic dipole . 68 3.4.5 Wino-Higgs interaction . 69 3.5 Discussion . 70 Table of contents xiii II Electromagnetic dipole dark matter in solar energy transport 73 4 Theory of dark matter in the Sun 75 4.1 Solar abundance problem . 75 4.2 Electromagnetic scattering cross sections . 78 4.2.1 Scattering cross sections of electromagnetic dipole dark matter . 79 4.2.2 Nucleus electromagnetic current and form factors . 81 4.2.3 Scattering of electric dipole dark matter . 84 4.2.4 Scattering of magnetic dipole dark matter . 88 4.2.5 Scattering of anapole dark matter . 92 4.3 Population of dark matter particles in the Sun . 94 4.4 Energy transport . 99 4.4.1 Knusden vs. LTE transport . 101 4.4.2 Energy transport due to electric dipole dark matter . 102 4.4.3 Energy transport due to magnetic dipole dark matter . 103 4.4.4 Energy transport due to anapole dark matter . 105 4.4.5 Tabulation of diffusivity and conductivity coefficients . 107 4.4.6 Effectiveness of energy transport . 109 5 Simulating dark matter in the Sun 113 5.1 Solar neutrino fluxes . 114 5.2 Helioseismology . 116 5.3 Frequency separation ratios . 119 5.4 Depth of the convection zone . 120 5.5 Surface helium abundance . ..
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