Soft-Collinear Effective Theory

The lectures that appear within this chapter provide an introduction to soft-collinear effective theory (SCET). It begins by discussing resummation for soft-photon effects in QED, including soft photons in electron–electron scattering and the expansion of loop integrals and the method of regions event-shape variables. It then covers SCET specifically, including the method of regions for the Sudakov form factor, effective Lagrangians, the vector current in SCET, and resummation by renormalization group (RG) evolution. It covers applications of SCET in jet physics, describes the characteristic feature in jet processes of Sudakov logarithms, and discusses factorization for the event-shape variable thrust and factorization and resummation for jet cross sections.

Effective Theory Approach to Direct Detection of Dark Matter

It is now certain that dark matter exists in the Universe. However, we do not know its nature, nor are there dark matter candidates in the standard model of particle physics or astronomy However, weakly interacting massive particles (WIMPs) in models beyond the standard model are one of the leading candidates available to provide explanation. The dark matter direct detection experiments, in which the nuclei recoiled by WIMPs are sought, are one of the methods to elucidate the nature of dark matter. This chapter introduces an effective field theory (EFT) approach in order to evaluate the nucleon–WIMP elastic scattering cross section.

Effective Field Theory of Large-Scale Structure

The lectures featured in this chapter review the observables relevant to the large-scale structure (LSS) of our Universe. The chapter introduces an effective field theory (EFT) that allows us to analytically describe the growth of fluctuations into the non-linear era, with uncertainties better controlled than in classical linear perturbation theory. Topics covered in the chapter include random fields in three-dimensional space, Fourier space conventions, the shape of the matter power spectrum, Gaussian random fields, estimators and cosmic variance, dynamics in the Newtonian regime, a perturbative solution of the fluid equations, the EFT approach, the Lagrangian perturbation theory, biased tracers, and redshift space distortions.

Effective Field Theories for Nuclear and (Some) Atomic Physics

These lectures are a pedagogical—not comprehensive—introduction to the applications of effective field theory (EFT) in the context of nuclear and atomic physics. A common feature of these applications is the interplay between non-perturbative physics (needed at leading order to produce non-relativistic bound states and resonances) and controlled perturbative corrections (crucial for predictive power). The essential ideas are illustrated with the simplest nuclear EFT, pionless EFT, which contains only contact interactions and, with minor changes, can be adapted to certain atomic systems. This EFT exploits the two-body unitarity limit, where renormalization leads to discrete scale invariance in systems of three and more bodies. Remarkably complex structures then arise from very simple leading-order interactions. It briefly describes some of the challenges and rewards of including long-range forces—pion exchange in chiral EFT for nuclear systems or Van der Waals forces between atoms.

Effective Field Theory with Nambu–Goldstone Modes

These lectures provide an introduction to the low-energy dynamics of Nambu–Goldstone fields, which associated with some spontaneous (or dynamical) symmetry breaking, using the powerful methods of effective field theory. The generic symmetry properties of these massless modes are described in detail and two very relevant phenomenological applications are worked out: chiral perturbation theory, the low-energy effective theory of QCD, and the (non-linear) electroweak effective theory. The similarities and differences between these two effective theories are emphasized, and their current status is reviewed. Special attention is given to the short-distance dynamical information encoded in the low-energy couplings of the effective Lagrangians. The successful methods developed in QCD could help us to uncover fingerprints of new physics scales from future measurements of the electroweak effective theory couplings.

Effective Field Theories for Heavy Quarks: Heavy Quark Effective Theory and Heavy Quark Expansion

The heavy quark effective theory (HQET) and the heavy quark expansion (HQE) have developed into the standard tools in heavy-flavour physics. The lectures in this chapter introduce the basics of the approach and illustrates the methods by discussing some of their phenomenological applications. The chapter covers construction of the HQET Lagrangian, symmetries of HQET, HQET at one loop, and HQET applications to phenomenology. It also discusses HQE inclusive decays, operator product expansion (OPE), tree-level results, HQE parameters, QCD corrections, and end-point regions. It concludes by reiterating the enormous impact that both HQET and the HQE have had on particle physics phenomenology.

Introduction to Effective Field Theories and Inflation

The lecture notes presented in this chapter provide an introduction to inflationary cosmology with an emphasis on some of the ways effective field theories (EFTs) are used in its analysis. Topics covered in the chapter include introduction to cosmological backgrounds and fluctuations, including a brief discussion of inflationary models; general relativity as an effective theory; new issues raised by cosmology for EFTs, such as time-dependent backgrounds; and power-counting in cosmological EFTs. It also discusses issues surrounding the existence in the universe of both dark matter and dark energy, and the broader controversial question of their existence. It touches on the Hot Big Bang theory of cosmology, and the various types of particles believed to be 'elementary' at the temperatures of interest.

Renormalization Theory and Effective Field Theories

Chapter 1 features lectures that review the formalism of renormalization in quantum field theories with special regard to effective quantum field theories. While renormalization theory is part of every advanced course on quantum field theory, for effective theories some more advanced topics become particularly important. These topics include the renormalization of composite operators, operator mixing under scale evolution, and the resummation of large logarithms of scale ratios. The lectures from this course thus set the basis for any systematic study of the techniques and applications of effective field theories and offer an introduction for the reader to the content within this book.

Solutions to Problems at Les Houches Summer School on EFT

This final chapter provides details of worked solutions to the various problems set by the lecturers during the course of the school; some of these problems appear within the chapters of this book. This chapter also contains further exercises that were added after the school are not solved here; these are left as a challenge for the enterprising reader. Problems run the range of topics covered. These problems and solutions are associated with topics that include the introduction to EFT, renormalization theory, nuclear and atomic physics, Nambu–Goldstone modes, inflation, and large-scale structure, and how each topic relates to EFTs.

Effective Theories for Quark Flavour Physics

The purpose of the lectures that appear within this chapter is to provide the reader with an idea of how we can probe new physics with quark flavour observables using effective theory techniques. It begins by providing a concise review of the quark flavour structure of the standard model. Then it introduces the effective Hamiltonian for quark weak decays. Following on, it then considers the effective Hamiltonian for ?F=2 transitions in the standard model and beyond. It discusses how meson–anti–meson mixing and CP violation can be described in terms of the ?F=1 and ?F=2 effective Hamiltonians. Finally, it presents the Unitarity Triangle Analysis and discusses how very stringent constraints on new physics can be obtained from ?F=2 processes.