Scale-dependent mass anomalous dimension from Dirac eigenmodes

Abstract

We investigate the eigenmodes of the massless Dirac operator to extract the scale-dependent fermion mass anomalous dimension gamma_m(mu). By combining simulations on multiple lattice volumes, and when possible several gauge couplings, we are able to measure the anomalous dimension across a wide range of energy scales. The method that we present is universal and can be applied to any lattice model of interest, including both conformal or chirally broken systems. We consider SU(3) lattice gauge theories with Nf=4, 8 and 12 light or massless fermions. The 4-flavor model behaves as expected for a QCD-like system and demonstrates that systematic effects are manageable in practical lattice calculations. Our 12-flavor results are consistent with the existence of an infrared fixed point, at which we predict the scheme-independent mass anomalous dimension gamma_m^*=0.32(3). For the 8-flavor model we observe a large anomalous dimension across a wide range of energy scales. Further investigation is required to determine whether Nf=8 is chirally broken and walking, or if it possesses a strongly-coupled conformal fixed point.Comment: Version to be published in JHE

Massive holographic QCD in the Veneziano limit

“…This supports the idea that x = x c can be located by extracting γ * from the meson masses on the lattice. In fact, recent lattice results for γ * in the conformal window report very low values [75,107] that are in apparent contradiction of the curves in figure 8. Recall however that the model has not been tuned to fit any QCD data yet.…”

Lattice tests of beyond standard model dynamics

“…An issue with using this method is that the exponent depends on the range of eigenvalues used to measure it. The authors of Cheng et al (2013) combine the intermediate and large eigenvalues to construct a "scale dependent mass anomalous dimension," whose scale in energy space is given by λ itself, and whose extrapolation to small λ gives the actual y m (assuming, of course, that the system studied is truly conformal). They are able to compare and contrast a confining theory (SU (3) with N f = 4 fundamentals) with a slowly running one (SU (3) with N f = 12 fundamentals), which they identify as conformal.…”

The running coupling of 8 flavors and 3 colors

“…These studies agreed in their conclusion that the model is outside the conformal window and spontaneous chiral symmetry breaking takes place. In [7] the mass anomalous dimension was investigated but a definite conclusion whether the model is inside or outside the conformal window could not be drawn from the data. In any case conformal behavior was not ruled out.…”