Effective pion mass term and the trace anomaly

Recently, we developed an effective theory of pions and a light dilatonic meson for gauge theories with spontaneously broken chiral symmetry that are close to the conformal window. The pion mass term in this effective theory depends on an exponent y. We derive the transformation properties under dilatations of the renormalized fermion mass and use this to rederive y = 3 -gamma(m)*, where gamma(m)* is the fixed-point value of the mass anomalous dimension at the sill of the conformal window. This value for y is consistent with the trace anomaly of the underlying near-conformal gauge theory.