Introduction to Chiral Perturbation Theory

Abstract

An introduction to the basic ideas and methods of Chiral Perturbation Theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.Comment: 46 pages, 4 figures (appended at the end), CERN-TH.6978/9

Testing mu = 0 on the lattice

“…The results agree (by design) with the picture that all terms in L 4 are consistent with the values obtained by integrating out light resonances, and are inconsistent with m u = 0[30]. In particular, a conventional estimate of this kind gives[33,34,35,36] 10 3 L 8 ≈ 0.9 ± 0.3, 10 3 L 7 ≈ (−0.4 ± 0.2), while the hypothesis m u = 0 would require 10 3 L 8 = −0.4 ± 0.3, and 10 3 L 7 = 0.2 ± 0.2.Thus any method which can directly determine the L's, even with errors as large as 100%, can distinguish between these two possibilities.3 m u on the latticeSimulating QCD on a lattice is, in principle, the most reliable way of determining quantities which are not predicted from symmetry alone. For instance, although it is only possible to constrain ratios of light quark masses phenomenologically, recent lattice computations of the hadron spectrum have suggested an absolute range for the strange quark mass[37,38,39,40,41,42,43,44,45,46] and the parameter B.…”

Portal Effective Theories. A framework for the model independent description of light hidden sector interactions

“…In this case, the only non-vanishing external currents are L µ , R µ , M , and Θ, and the resulting χPT Lagrangian is well established, see e.g. the discussions in [105,109,149,[183][184][185][186][187]197]. Afterwards, we consider the EW and UV suppressed contributions and use the spurion approach to construct the novel contributions with general spacetime dependent currents S ω , Γ, H x , and H x .…”

“…For more details, see e.g. the general introductions to χPT in [184][185][186][187]. In the SM, the spurion approach neglects contributions to the χPT Lagrangian that are generated from diagrams with virtual photon exchanges.…”

“…Operators that count as order ∂ 2 n c contain only a single quark-flavour trace. In the absence of explicit symmetry breaking due to the mass-like current M , the only available operator of this type is [105,109,149,[183][184][185][186][187]197]…”

Just a Taste: Lectures on Flavor Physics

“…For some reviews see[78][79][80][81] or more recent reviews on modern versions of this idea[82,83]. Additionally, older-style textbooks such as Cheng & Li[58] or Donoghue et al[42] give very nice introductions.…”