Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model

Abstract

The pseudoscalar particles pions, kaons and the $\eta$-particle are considerably lighter than the other hadrons such as protons or neutrons. Their lightness was understood as a consequence of approximate chiral symmetry breaking. This led to current algebra, a way to express the relations imposed by the symmetry breaking. It was realized by Weinberg that because of their low mass, it is possible to formulate a purely pionic (effective) field theory at experimental energies, which carries all information on the (non-perturbative) dynamics, symmetries, and their spontaneous breaking of quantum chromodynamics (QCD) and allows for systematic calculations of observables. In this review, we trace these developments and present recent activities in this field. We make the connection to other effective theories, more generally introduced by Wilson, as approximate field theories at low energies. Indeed, principles and paradigms introduced first for pions have become ubiquitous in particle physics and the standard model. Lastly, we turn to the latest development where the present (fundamental) standard model itself is considered as an effective field theory of a - yet to be formulated - even more fundamental theory. We also discuss important techniques that were developed in order to turn chiral perturbation theory into a predictive framework and briefly review some connections between lattice QCD and chiral perturbation theory (ChPT).

56 pages, 2 figures. Accepted for publication in the Indian Journal of Physics

References in corpus (31)

• Heavy quarkonium: progress, puzzles, and opportunities
• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• Measurement of the permanent electric dipole moment of the neutron
• Mesonic low-energy constants
• Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 experiment
• Expansion by regions: revealing potential and Glauber regions automatically
• Geometric approach to asymptotic expansion of Feynman integrals
• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• Cusps in K --> 3 pi decays
• The decay $\eta \to 3\pi$: study of the Dalitz plot and extraction of the quark mass ratio $Q$
• Rescattering effects in eta {\to} 3pi decays
• Analytic three-loop static potential
• Flavor Anomalies in Heavy Quark Decays
• The proton radius: From a puzzle to precision
• The proton radius (puzzle?) and its relatives
• The Massive O(N) Non-linear Sigma Model at High Orders
• On the Development of Effective Field Theory
• Constraints on the $\omega \pi$ form factor from analyticity and unitarity
• Basics of Resonance Chiral Theory
• Soft-collinear gravity beyond the leading power
• Chiral logarithms to five loops
• The expansion by regions in pi K scattering
• Brief history of the pion-nucleon sigma term
• Leading Chiral Logarithms for Pion Form Factors to Arbitrary Number of Loops
• Chiral Lagrangians for mesons with a single heavy quark
• Chiral Effective Theory Methods and their Application to the Structure of Hadrons from Lattice QCD
• The Pion Mass and Decay Constant at Three Loops in Two-Flavour Chiral Perturbation Theory
• Leading logarithms for the nucleon mass
• The 27-plet contributions to the CP-conserving $K\to \pi l^{+}{l}^{-}$ decays
• An Analytic Approach to Sunset Diagrams in Chiral Perturbation Theory: Theory and Practice
• Consistency tests of AMPCALCULATOR and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial based approach