Recent developments in chiral perturbation theory

Abstract

I review recent developments in chiral perturbation theory (CHPT) which is the effective field theory of the standard model below the chiral symmetry breaking scale. The effective chiral Lagrangian formulated in terms of the pseudoscalar Goldstone bosons (π, K, η) is briefly discussed. It is shown how one can gain insight into the ratios of the light quark masses and to what extent these statements are modelindependent. A few selected topics concerning the dynamics and interactions of the Goldstone bosons are considered. These are ππ and πK scattering, some non-leptonic kaon decays and the problem of strong pionic final state interactions. CHPT also allows to make precise statements about the temperature dependence of QCD Green functions and the finite size effects related to the propagation of the (almost) massless pseudoscalar mesons. A central topic is the inclusion of matter fields, baryon CHPT. The relativistic and the heavy fermion formulation of coupling the baryons to the Goldstone fields are discussed. As applications, photo-nucleon processes, the πN Σ-term and non-leptonic hyperon decays are presented. Implications of the spontaneously broken chiral symmetry on the nuclear forces and meson exchange currents are also described. Finally, the use of effective field theory methods in the strongly coupled Higgs sector and in the calculation of oblique electroweak corrections is touched upon.

Y(3940),Z(3930), and theXMolina1, Oset2 2009Phys. Rev. D

“…Some approximations were made there which make the formalism handy and reliable, by neglecting the three-momentum of the vector mesons with respect to their masses. It is interesting to see that with this approximation one obtains [39] from the hidden gauge approach the chiral local Lagrangians which are used to study the interaction of pseudoscalar mesons among themselves and the pseudoscalar mesons with vector mesons and with baryons [42,43,44,45]. …”

Chiral symmetry amplitudes in the S-wave isoscalar and isovector channels and the σ, f0(980), a0(980) scalar mesons

“…Another different approach to the meson-meson scattering is chiral perturbation theory [29,30,31,32].…”

“…We start from the standard chiral Lagrangian in lowest order of chiral perturbation theory (χP T ) L 2 which contains the most general low energy interactions of the pseudoscalar meson octet [29][30][31][32] in this order. This Lagrangian will provide the potentials which will be used in the coupled channel scattering equations.…”

“…The physical amplitudes as a function of s (real variable) are given by the expressions in eqs. (30). However, in order to explore the position of the poles of the scattering amplitudes one must take into account the analytical structure of these amplitudes in the different Riemann sheets.…”

The Standard Model prediction for ε′/ε

“…As indicated in figure 1, below the resonance region one can use global symmetry considerations to define another Effective Field Theory in terms of the QCD Goldstone bosons (π, K, η). The Chiral Perturbation Theory (χPT) formulation of the Standard Model [28][29][30][31][32] is an ideal framework to describe the pseudoscalar-octet dynamics, through a perturbative expansion in powers of momenta and light quark masses over the chiral symmetry breaking scale (Λ χ ∼ 1 GeV). Chiral symmetry fixes the allowed χPT…”