Effective Field Theory Approaches to Particle Physics Beyond the Standard Model by Zhengkang Zhang A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in the University of Michigan 2018 Doctoral Committee: Professor James D. Wells, Chair Professor Fred C. Adams Professor Aaron T. Pierce Professor Jianming Qian Zhengkang Zhang [email protected] ORCID iD: 0000-0001-8305-5581 c Zhengkang Zhang 2018 Acknowledgements First of all, I would like to thank my advisor, James Wells. My development as a scientist has been greatly influenced by his invaluable guidance. He has always encouraged me to pursue independent research, to develop new ideas, and to form my own view of the field, while generously sharing his knowledge, experience and insights to guide my thinking | an approach I deeply appreciate. I would also like to thank Aaron Pierce for teaching me a great deal about the field, especially as my advisor at an early stage of my graduate studies. I am particularly grateful for his patient guidance through my first project, and his continued support and advice later on. Additionally, I would like to thank Christophe Grojean for his support and advice, especially during my stay at DESY Hamburg, where part of this dissertation was completed. I have greatly benefited from working with my other collaborators as well, including Se- bastian Ellis, Alexey Petrov, Stefan Pokorski, J´er´emieQuevillon, Bibhushan Shakya, Andrea Wulzer, Tevong You, and Yue Zhao. My thanks also go to Fred Adams and Jianming Qian for serving on my committee and providing valuable feedback. I am grateful to Ratindranath Akhoury, Henriette Elvang, Finn Larsen, Roberto Merlin, James Wells, and Kathryn Zurek for their inspiring classes from which I have learned a lot of interesting physics. I also would like to thank other (past and current) members of the Leinweber Center for Theoretical Physics (formerly Michigan Center for Theoretical Physics), especially Arash Arabi Ardehali, Raymond Co, Josh Foster, Gordy Kane, Jack Kearney, Nick Orlofsky, Sam Roland, Ben Safdi, and Bob Zheng, for many stimulating conversations. Special thanks go to Mengxing Ye, my brilliant partner in life, for accompanying me through this journey (and teaching me interesting condensed matter physics as well). The work in this dissertation was funded in part by the U.S. Department of Energy grant DE-SC0007859, the Rackham Summer Award, Rackham Research Grant, and Rackham Dissertation Fellowship. ii Table of Contents Acknowledgements ii List of Tablesv List of Figures viii List of Appendices xii Chapter 1: Introduction1 1.1 The Standard Model from an EFT perspective . .1 1.2 Precision analyses as indirect probes of new physics . .5 1.3 Bottom-up and top-down EFT approaches . .6 1.4 What's new? . .9 1.5 Outline of this dissertation . 10 Chapter 2: Precision Electroweak Analyses After the Higgs Boson Discovery 13 2.1 Introduction . 13 2.2 Standard Model parameters and observables . 14 2.3 The formalism . 16 2.4 New physics examples . 27 2.5 Conclusions . 34 Chapter 3: Resolving Charm and Bottom Quark Masses in Precision Higgs Analyses 35 3.1 Introduction . 35 3.2 Incorporating low-energy observables into a global precision analysis . 38 3.3 Recasting Higgs observables in terms of low-energy observables . 39 3.4 Theoretical uncertainties of Higgs partial widths . 44 3.5 Conclusions . 49 iii Chapter 4: EFT of Universal Theories and Its RG Evolution 50 4.1 Introduction . 50 4.2 Universal theories at LO and beyond . 53 4.3 RG effects in the electroweak sector . 63 4.4 RG effects in the Yukawa sector . 75 4.5 Conclusions . 78 Chapter 5: Time to Go Beyond TGC Interpretation of W Pair Production 81 5.1 Introduction . 81 5.2 Effective operators and anomalous couplings . 83 5.3 Triple gauge coupling measurements: from LEP2 to LHC . 85 5.4 Toward a high energy picture of Standard Model deviations . 89 5.5 Conclusions . 91 Chapter 6: Covariant Diagrams for One-Loop Matching 92 6.1 Introduction . 92 6.2 Gauge-covariant functional matching . 95 6.3 Covariant diagrams . 104 6.4 Examples . 116 6.5 Conclusions . 143 Chapter 7: EFT Approach to Trans-TeV Supersymmetry 146 7.1 Introduction . 146 7.2 Matching the MSSM onto the SMEFT . 151 7.3 Bottom-tau Yukawa unification . 174 7.4 Higgs couplings in TeV-scale SUSY . 183 7.5 Conclusions . 190 Chapter 8: Summary and Outlook 192 Appendices 194 Bibliography 213 iv List of Tables 2.1 (From [131]) The list of observables, their experimental and reference values, and percent relative uncertainties. 17 2.2 (From [131]) Expansion coefficients, as defined in Eq. (2.20), calculated in the (5) basis of input observables containing ∆αhad. These encode the dependence of the output observables on each input observable. 21 2.3 (From [131]) Percent relative uncertainties for the expansion coefficients cii0 , with all input observables varied in their 1σ range. 24 2.4 (From [131]) The rii0 's defined in Eq. (2.25), characterizing the ratios of second-order vs. first-order terms in the expansion (in units of percentage). 25 2.5 (From [131]) Expansion coefficients calculated in the basis of input observables containing α(mZ ), which are derived from the numbers in Table 2.2 by a change of basis described in Section 2.3.4.................... 28 2.6 (From [131]) The b coefficients defined in Eq. (2.68), characterizing the shift in the output observables due to new physics that shifts vector boson self-energies. 32 4.1 (From [111]) Warsaw basis operator combinations that appear in Luniversal in (4.1), in the notation of [3]. In these expressions, repeated generation y a ! y a y a indices i; j; k; l are summed over, H σ D µH = H σ (DµH) − (DµH) σ H, y ! y y H D µH = H (DµH) − (DµH) H. The Yukawa matrices yu, yd, ye should not be confused with the hypercharges Yf . The SM vector and scalar currents A a α JGµ, JW µ, JBµ, Jy are defined in (4.2). ..................... 54 4.2 (From [111]) Expressions of the 16 universal parameters in terms of the War- saw basis Wilson coefficients in (4.1). These parameters completely charac- terize the indirect BSM effects in universal theories at the dimension-6 level. More details of the universal parameters, including their definition from the effective Lagrangian and their expressions in other bases, can be found in [109]. 56 v 4.3 (From [109, 111]) Higgs basis couplings in terms of the universal parameters. ^ ^ ∆1;2;3 are independent linear combinations of S; T ; W; Y defined in (4.4). c4f collectively denotes four-fermion effective couplings, and dV f stands for the dipole-type V ff couplings. Compared with [7], we have written the fractional W q W mass shift as δm instead of δm, and defined [δgL ]ij in the gauge-eigenstate rather than mass-eigenstate basis. 57 6.1 (From [60]) Building blocks of covariant diagrams for integrating out heavy bosonic fields (and fermionic fields as well if one follows the approach of Eq. (6.60) to square their quadratic operator), in the absence of mixed heavy- light contributions and open covariant derivatives in the X matrix, as derived in Section 6.3.1. All previous universal results in the literature [55,56] can be easily reproduced by computing one-loop covariant diagrams built from these elements; see Section 6.4.1............................ 112 6.2 (From [60]) Additional building blocks of covariant diagrams in the presence of mixed heavy-light contributions to matching, as derived in Section 6.3.2. Example applications can be found in Sections 6.4.2, 6.4.3 and 6.4.5..... 112 6.3 (From [60]) Additional building blocks of covariant diagrams in the presence of open covariant derivatives in the X matrix, as derived in Section 6.3.3, up µ yµ to one-open-covariant-derivative terms PµZ + Z Pµ. Example applications can be found in Section 6.4.3........................... 113 6.4 (From [60]) Additional building blocks of covariant diagrams when Dirac fermions are involved in matching, as derived in Section 6.3.4. These are used when the quadratic operator for fermionic fields is not squared like in Eq. (6.60). Example applications can be found in Sections 6.4.4 and 6.4.5.. 113 6.5 (From [60]) List of universal coefficients in terms of the master integrals de- fined in Eq. (6.67) (Column 1). The UOLEA master formula for one-loop matching reported in [56] is reproduced by adding up traces of the operators in Column 2 with the corresponding universal coefficients, and multiplying the overall factor −ics; see Eq. (6.68). The covariant diagrams used to com- pute each universal coefficient are listed in Column 3. See AppendixB for expressions of the universal coefficients in terms of heavy particle masses. 122 6.6 (From [60]) Summary of the results in Eq. (6.96) for mixed heavy-light con- tributions to one-loop matching for the scalar triplet model. The SM gauge coupling-independent terms for the three operators OT ; OH ; OR in Eq. (6.89) are computed (in the MS scheme). 127 vi 7.1 (From [132]) Heavy fields 'H in the MSSM, their gauge quantum numbers, and conjugate fields (which appear on the left side of QUV). 153 7.2 (From [132]) Light fields 'L in the MSSM, their gauge quantum numbers, and conjugate fields (which appear on the left side of QUV). Primed Weyl fermion fields are unphysical auxiliary fields, to be set to zero at the end of the calculation.