Chiral-Scale Perturbation Theory and the Renormalization Group

Chiral-Scale Perturbation Theory and the Renormalization Group
Rod Crewther, U. Adelaide
Date and time: Fri, Jan 22, 2016 - 2:15pm
Location: LGRT 1033
Category: ACFI Seminar
Abstract:
Three-flavor chiral perturbation theory with t,b,c quarks decoupled tests the infrared limit of three-flavor QCD. The standard theory chiPT_3 (before being unitarised) assumes that there is no infrared fixed point alpha_IR. If alpha_IR exists, we get chiral-scale perturbation theory chiPT_sigma about a scale-invariant theory where the quark condensate is also a scale condensate with nine Nambu-Goldstone (NG) bosons: a massless 0^{++} dilaton sigma (f_0(500) in the real world) as well as pi, K, eta. Unlike electroweak and gravitational "dilatons", this dilaton is of the original type: in the scale-invariant limit, the vacuum breaks scale invariance and non-NG particles such as baryons retain their masses. The effective Lagrangian for chiPT_sigma is the standard one modified by sigma-dependent terms and factors required to give the correct dimensions, and can be systematically extended to include higher-order and electroweak corrections. The most important result is a neat explanation of the Delta I = 1/2 puzzle for kaon decays; we propose to test it on the lattice via K --> pi with both on shell. The dynamical electroweak analogue of our dilaton yields a Higgs boson with a small mass proportional to beta'(4 + beta'), where beta' is the slope of the beta function at the infrared fixed point.