Abstract
We develop an effective-field-theory (EFT) framework to analyze the spectra emerging from lattice simulations of a large class of confining gauge theories. Simulations of these theories, for which the light-fermion count is not far below the critical value for transition to infrared conformal behavior, have indicated the presence of a remarkably light singlet scalar particle. We incorporate this particle by including a scalar field in the EFT along with the Nambu-Goldstone bosons (NGB’s), and discuss the application of this EFT to lattice data. We highlight the feature that data on the NGB’s alone can tightly restrict the form of the scalar interactions. As an example, we apply the framework to lattice data for an SU(3) gauge theory with eight fermion flavors, concluding that the EFT can describe the data well.
Highlights
JHEP07(2017)[035] descend from the underlying, confining gauge theory with m = 0, and we expect them to have values set by the confinement scale
The latter arise from the spontaneous breaking of chiral symmetry, and the former, to the extent that it can be interpreted as a dilaton, arises from the spontaneous breaking of conformal symmetry
The purely scalar part of the EFT consists of a kinetic term along with a potential arising from the explicit breaking of conformal symmetry in the underlying theory, which we take to be small: Ld
Summary
The low-energy EFT is built from the scalar field χ and a set of NGB fields πa The latter arise from the spontaneous breaking of chiral symmetry, and the former, to the extent that it can be interpreted as a dilaton, arises from the spontaneous breaking of conformal symmetry. The purely scalar part of the EFT consists of a kinetic term along with a potential arising from the explicit breaking of conformal symmetry in the underlying theory, which we take to be small: Ld. We assume that the potential has a minimum at some value fd, and that it is comparatively shallow, so that the mass md of the fluctuations around the minimum satisfies md 4πfd. The first is a weakly-coupled potential such as the one appearing in the standard model It can arise from the deformation of an underlying conformal field theory (CFT) by relevant operators. The shifted VEV will, through eq (2.4), re-scale the NGB kinetic term, and the NGB decay constant
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