Effective field theory approach to trans-TeV supersymmetry: covariant matching, Yukawa unification and Higgs couplings

Dismissing traditional naturalness concerns while embracing the Higgs boson mass measurement and unification motivates careful analysis of trans-TeV supersymmetric theories. We take an effective field theory (EFT) approach, matching the Minimal Supersymmetric Standard Model (MSSM) onto the Standard Model (SM) EFT by integrating out heavy superpartners, and evolving MSSM and SMEFT parameters according to renormalization group equations in each regime. Our matching calculation is facilitated by the recent covariant diagrams formulation of functional matching techniques, with the full one-loop SUSY threshold corrections encoded in just 30 diagrams. Requiring consistent matching onto the SMEFT with its parameters (those in the Higgs potential in particular) measured at low energies, and in addition requiring unification of bottom and tau Yukawa couplings at the scale of gauge coupling unification, we detail the solution space of superpartner masses from the TeV scale to well above. We also provide detailed views of parameter space where Higgs coupling measurements have probing capability at future colliders beyond the reach of direct superpartner searches at the LHC.Comment: 59 pages, 8 figures; v2: references and minor clarifications adde

Covariant diagrams for one-loop matching

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed "covariant diagrams." The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.Comment: 54 pages, 8 tables; v2: matches published versio

Effective Field Theory Approaches to Particle Physics Beyond the Standard Model

This dissertation covers applications of effective field theory (EFT) ideas and techniques to the study of particle physics beyond the Standard Model (SM). The recent discovery of the Higgs boson without other new physics discoveries hints at the possibility that additional exotic states that couple to SM particles, if they exist, are not in the neighborhood of the electroweak scale. In this case, precision measurements of SM processes offer an important indirect probe of heavy new physics that is complementary to direct searches for new particles at high energy colliders, and EFT becomes the tool of choice to bridge a vast range of new physics ideas and experimental observation. We start with a discussion of the precision analyses program, reviewing the analysis framework and the status of electroweak precision tests. The Higgs boson discovery has added a new module to this program, and we point out new issues related to heavy quark masses that must be taken into account in future precision studies of the Higgs boson. Various approaches exist in the literature to extract information about new physics from precision analyses. Two examples are oblique parameters and triple gauge couplings (TGCs). We critically examine these conventional approaches in the EFT framework. In particular, we clarify that the applicability of oblique parameters is restricted to universal theories at leading order, and we find that TGCs no longer serve as a general parameterization of new physics effects in W boson pair production with recent LHC data. In both cases, EFT provides a consistent framework to rectify and extend the oversimplified conventional approaches, in order to take full advantage of high energy data to learn about new physics. We next turn to the subject of EFT matching, i.e. deriving a low energy EFT by integrating out heavy degrees of freedom from an ultraviolet theory. We develop a diagrammatic framework to carry out covariant functional matching calculations in a systematic manner. In contrast to conventional Feynman diagram methods, our approach avoids the detour of computing correlation functions, and meanwhile preserves gauge covariance and simplifies calculations. Finally, we apply this new technique to trans-TeV supersymmetry, and show that future precision Higgs measurements can probe scenarios of Yukawa unification featuring heavy superpartners beyond direct LHC reach.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143937/1/zzkevin_1.pd

Establishing the Isolated Standard Model

The goal of this article is to initiate a discussion on what it takes to claim "there is no new physics at the weak scale," namely that the Standard Model (SM) is "isolated." The lack of discovery of beyond the SM (BSM) physics suggests that this may be the case. But to truly establish this statement requires proving all "connected" BSM theories are false, which presents a significant challenge. We propose a general approach to quantitatively assess the current status and future prospects of establishing the isolated SM (ISM), which we give a reasonable definition of. We consider broad elements of BSM theories, and show many examples where current experimental results are not sufficient to verify the ISM. In some cases, there is a clear roadmap for the future experimental program, which we outline, while in other cases, further efforts -- both theoretical and experimental -- are needed in order to robustly claim the establishment of the ISM in the absence of new physics discoveries.Comment: 10 pages, 2 figures, 1 tabl