Case studies of near-conformal β-functions

We present updated results for the non-perturbative β-function of SU(3) gauge theories with N_f = 12 or 10 massless flavors in the fundamental rep or N_f = 2 in the sextet rep, measured with staggered fermions. New data at finer lattice spacing and our previously introduced method, the infinitesimal β-function, strengthen the case that the N_f = 12 model has no infrared fixed point up to g² = 7.2. We show how underestimated cutoff dependence in one domain wall study for N_f = 10 has been corrected, which is now consistent with staggered results showing a monotonically increasing β-function. A consistent theme is that too small volumes can lead to apparent fixed points which vanish towards the continuum limit. We also apply the infinitesimal β-function method to the N_f = 10 model, finding consistent behavior with the finite-step β-function. Ongoing simulations and analysis for the sextet model confirm our previous results from weak to strong coupling with a non-zero β-function throughout, in quantitative difference to Wilson fermion simulations [14].