A new method for the beta function in the chiral symmetry broken phase

Abstract

We describe a new method to determine non-perturbatively the beta function of a gauge theory using lattice simulations in the p-regime of the theory. This complements alternative measurements of the beta function working directly at zero fermion mass and bridges the gap between the weak coupling perturbative regime and the strong coupling regime relevant to the mass spectrum of the theory. We apply this method to $\mathrm{SU}(3)$ gauge theory with two fermion flavors in the 2-index symmetric (sextet) representation. We find that the beta function is small but non-zero at the renormalized coupling value $g^2=6.7$, consistent with our previous independent investigation using simulations directly at zero fermion mass. The model continues to be a very interesting explicit realization of the near-conformal composite Higgs paradigm which could be relevant for Beyond Standard Model phenomenology.

8 pages, 7 figures; Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain

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• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• The perturbative QCD gradient flow to three loops

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• Dislocations under gradient flow and their effect on the renormalized coupling
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Non-perturbative decoupling of massive fermions
• Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors
• Applications of the Perturbative Gradient Flow