Dark Matter Searches in the Crescendo of the 21st Century Experiments Leung, (John) Shing Chau A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy in Physics The Brown University May 2020 c Copyright 2020 by John Shing Chau Leung This dissertation by John Shing Chau Leung is accepted in its present form by the Department of Physics as satisfying the dissertation requirement for the degree of Doctor of Philosophy. Date Prof. JiJi Fan, Advisor Recommended to the Graduate Council Date Prof. Ian Dell'Antonio, Reader Date Prof. Savvas Koushiappas, Reader Approved by the Graduate Council Date Prof. Andrew Campbell, Dean of the Graduate School iii Vitae John Shing Chau Leung obtained his Bachelor of Science in Physics from the Chinese Uni- versity of Hong Kong in May, 2012. During his undergraduate years, John worked on cold atom physics with Chi Kwong Law and on particle physics experiment with Ming Chung Chu. He also participated in high energy experiment in the CMS experiment of CERN as a summer student, advised by Armando Lanaro. John obtained his Master of Philosophy in Physics from the Chinese University of Hong Kong in May, 2014. His thesis was on detector physics advised by Ming Chung Chu, and with collaboration with the ATLAS experiment of CERN advised by Maurice Sciveres. John joined the Brown University in August, 2014 and carried out research with JiJi Fan. iv Acknowledgments I would like to thank my advisor JiJi Fan, who gave me the dream opportunity to pursue physics research. I also thank Savvas Koushiappas and Ian Dell'Antonio for being my thesis committee members and, in general, being good friends and mentors. I thank Antal Jevicki for his care about me during my graduate study. And I thank Stephon Alexander for providing me research opportunity on cosmology. I also thank Evan McDonough for the collaborative research and helping me out with my postdoctoral position search. I am very grateful for Robert Sims for working together to develop several insightful projects. His company across the years of my doctoral study was also invaluable. I also give my thanks to Adrian Lam for his support and useful discussion about machine learning. I thank my officemates Jatan Buch and Kyriakos Vattis for the numerous delightful and informative physics and statistics discussions. Lastly, I would like to thank my undergraduate and master mentor Ming Chung Chu for his care and effort to help me develop my academic career. His dedication to students and their careers is something that I will not forget. v Contents 1 Introduction 1 2 Jet Observables and Stops at 100 TeV Collider 6 2.1 Introduction . .6 2.2 Basic of SUSY in a 100 TeV collider . .7 2.3 Simplified Models . .8 2.3.1 t~ H~ Simplified Model . .8 − 2.3.2 t~ g~ χ~0 Simplified Model . 10 − − 1 2.4 Event Generation and Jet Observables . 12 2.4.1 Event Generation . 12 2.4.2 Jet Clustering . 14 2.4.3 Jet Mass . 14 2.4.4 N-subjettiness . 16 2.4.5 Mass-drop . 17 2.5 Analysis: t~ H~ Simplified Model . 19 − 2.5.1 Boosted Top and Bottom Tagging . 19 2.5.2 Event Selection . 20 2.5.3 Exclusion and Discovery . 21 2.6 Analysis: t~ g~ χ~0 Simplified Model . 23 − − 1 2.6.1 Top-tagging . 23 2.6.2 Event Selection and Results . 25 vi 2.6.3 Improvement in Gluino Search . 29 2.7 Conclusions and Outlook . 30 3 Using Gaia DR2 to Constrain Local Dark Matter Density and Thin Dark Disk 32 3.1 Introduction . 32 3.2 Gaia Telescope and Measurement of Local Dark Matter Density . 36 3.3 Data Selection . 37 3.3.1 Preliminaries: selection function, color and volume cuts . 38 3.3.2 Vertical number density distribution . 40 3.3.3 Midplane velocity distribution . 43 3.4 Fiducial Analysis . 45 3.4.1 Equilibrium density modeling . 45 3.4.2 Local matter content: baryons, halo DM, and a thin DD . 46 3.4.3 Likelihood, model uncertainties, and priors . 49 3.4.4 Sampling the posterior . 51 3.5 Results . 53 3.5.1 Local DM density . 53 3.5.2 Constraints on a thin DD . 54 3.6 Discussion . 55 3.6.1 Effect of volume cuts . 55 3.6.2 Disequilibria in the solar neighborhood? . 56 3.6.3 Degeneracy between ρDM and ρb ..................... 56 3.6.4 Comparison of constraints between DR2 and TGAS . 57 3.7 Conclusions and Outlook . 60 4 The Gaia Sausage for Dark Matter Nuclear Interactions 63 4.1 Introduction . 63 4.2 Phenomenology of dark matter-nuclear Interaction . 66 4.2.1 DM velocity distributions . 66 vii 4.2.2 DM-nucleus scattering theory . 72 4.3 Effect of the DM velocity distribution on DD recoil spectrum . 76 4.4 Statistical framework . 80 4.5 Results . 83 4.5.1 DM Mass - coupling . 84 4.5.2 Mediator - DM mass . 88 4.5.3 Model discrimination . 90 4.5.4 Combining forecasts for different targets . 93 4.6 Conclusions and Outlook . 94 5 Concluding Remarks 97 Bibliography 100 A The WIMP Miracle 131 B Statistical verification of Gaia's dark disk constraint 133 B.1 Constructing a Volume Complete Density . 133 B.1.1 Color-magnitude modeling . 133 B.1.2 Poisson process likelihood . 134 B.2 Uncertainty Analysis . 136 B.3 Variation of Midplane Cut . 137 B.4 Bootstrap Statistics . 138 C Extended Materials for Dark Matter Direct Detection Forecast 145 C.1 DD basics . 145 C.2 Nuclear form factors in NREFT . 147 C.3 Some benchmark models . 148 C.4 Next-generation experiments . 149 viii List of Figures 1.1 Methods of dark matter detection. .3 2.1 Stop simplified models. .9 2.2 Sample Feynman diagrams for signal in the t~ H~ simplified model. 10 − 2.3 Sample Feynman diagrams for signal in the t~ g~ χ~0 simplified model. 11 − − 1 2.4 Sample Feynman diagrams for SUSY background in the t~ g~ χ~0 simplified − − 1 model. 12 2.5 H (left) and E (right) distributions for SM processes. 13 T 6 T 2.6 H (left) and E (right) distributions for SUSY processes for m~ = 4 TeV, T 6 T t m = 2 TeV and m 0 = 200 GeV. 13 g~ χ~1 2.7 Jet mass distributions for t~t~∗ and QCD samples. 15 2.8 τ3;2 distribution of leading top candidate jet in t~t~∗ and QCD samples. 16 2.9 Mass-drop distributions for the leading jet with pT > 1 TeV in signals and backgrounds. Left: mass drop distributions of tt¯ background and t~ tB~ ! SUSY sample. Right: mass drop distributions of QCD background and t~ ! bH~ ± SUSY sample. We also require the muon to have pT > 200 GeV except for the dashed QCD distribution, which is obtained without any muon pT cut. 18 ix 2.10 Boosted top and b tagging efficiencies for the leading jet (fraction of total events with the leading jet tagged) in different event samples as a function of jet pT : SUSY events with stops decaying only to bH~ ± (blue) or tB~ (pink), SUSY events with stops decaying to either neutral or charged H~ in the full t~ H~ simplified model (blue dotted), SM tt¯ background (black), SM QCD − background (red) and SM tt¯ + W=Z background (light blue). We assumed mt~ = 4 TeV and mH~ , mB~ = 500 GeV. 21 2.11 The discovery and exclusion contours for the t~ H~ simplified model at a − 1 100 TeV collider with an integrated luminosity of 3 ab− . We assume a 10% systematic uncertainty for both the signal and the background. The solid lines are 5 σ discovery contour (left) and exclusion at 95% C.L.(right). The dashed lines are the 1 σ boundaries. 22 ± 2.12 Distributions of r for stop-bino and stop-higgsino simplified models given − mt~ = 4 TeV, mH~ ; mB~ = 500 GeV. 24 2.13 The 2σ exclusion contour of t~ B~ simplified model based on r assuming the − − signal events are from t~ H~ model. The dashed contours are 1 σ boundaries. 24 − ± 2.14 (a) QCD mistag rate vs signal efficiency for top-tagging the leading top candi- date jet. (b) Top-tagging efficiency for signal and SM processes as a function of jet pT ....................................... 26 3.1 Flowchart of our analysis. 35 3.2 Skymaps showing the number (left) and variance (right) of good AL obser- 2 5 vations in 3:36 deg (Nside = 2 ) HEALPix pixels. The white regions are the parts of the sky which do not pass our selection cuts defined in the main text. 38 3.3 Effective volume completeness for each stellar type. The completeness of DR2 (solid) is significantly improved as compared to TGAS (dashed) for A (blue), F (green), and early G (orange) stars. 41 x 3.4 Binned vertical number density profiles for A, F, and early G stars. Also shown is the median predicted density (dotted line) and the 68% confidence interval (shaded region) for each tracer population obtained from our dynam- ical analysis described in Sec. 3.4. 42 3.5 Midplane velocity distributions of A, F, and early G stars after subtracting w (left). The best-fit Gaussian distribution to f0( w ) with error bars that j j include contributions from the statistical uncertainty due to Poisson error and the asymmetry in w and + w bins (right). 44 −| j j j 3.6 The predicted number density of a tracer in a model containing a thin DD with 2 surface density ΣDD = 20 M =pc and scale height hDD = 10 pc (dashed).