Status of Chiral-Scale Perturbation Theory

Chiral-scale perturbation theory χPTσ has been proposed as an alternative to chiral SU(3)L × SU (3)R perturbation theory which explains the ∆I = 1/2 rule for kaon decays. It is based on a low- energy expansion about an infrared fixed point in three-flavor QCD. In χ PTσ , quark condensation ⟨q ̄q⟩vac ̸= 0 induces nine Nambu-Goldstone bosons: π,K,η and a QCD dilaton σ which we identify with the f0(500) resonance. Partial conservation of the dilatation and chiral currents constrains low-energy constants which enter the effective Lagrangian of χ PTσ . These constraints allow us to obtain new phenomenological bounds on the dilaton decay constant via the coupling of σ/f0 to pions, whose value is known precisely from dispersive analyses of ππ scattering. Improved predictions for σ → γγ and the σNN coupling are also noted. To test χPTσ for kaon decays, we revive a 1985 proposal for lattice methods to be applied to K → π on-shell