Dilaton Chiral Perturbation Theory - Determining Mass and Decay Constant of Technidilaton on the Lattice

Abstract

We propose a scale-invariant chiral perturbation theory of the pseudo-Nambu-Goldstone bosons of the chiral symmetry (pion "pi") as well as the scale symmetry (dilaton "phi") for the large N_f QCD. The resultant dilaton mass M_phi reads M_phi^2= m_phi^2 + (3-gamma_m)(1+gamma_m)/4 (2 N_f F_pi^2/F_phi^2) m_pi^2 + (chiral log corrections), where m_phi, m_pi, gamma_m, F_pi and F_phi are the dilaton mass in the chiral limit, the pion mass, mass anomalous dimension, decay constants of pi and phi, respectively. The chiral extrapolation of the lattice data on M_phi^2 vs m_pi^2 plot then simultaneously determines (m_phi, F_phi) of the technidilaton in the walking technicolor with gamma_m =~1. The chiral logarithmic corrections are explicitly given.