Linear Sigma EFT for Nearly Conformal Gauge Theories

Abstract

We construct a generalized linear sigma model as an effective field theory (EFT) to describe nearly conformal gauge theories at low energies. The work is motivated by recent lattice studies of gauge theories near the conformal window, which have shown that the lightest flavor-singlet scalar state in the spectrum ($\sigma$) can be much lighter than the vector state ($\rho$) and nearly degenerate with the PNGBs ($\pi$) over a large range of quark masses. The EFT incorporates this feature. We highlight the crucial role played by the terms in the potential that explicitly break chiral symmetry. The explicit breaking can be large enough so that a limited set of additional terms in the potential can no longer be neglected, with the EFT still weakly coupled in this new range. The additional terms contribute importantly to the scalar and pion masses. In particular, they relax the inequality $M_{\sigma }^2\ge 3M_{\pi }^2$, allowing for consistency with current lattice data.

arXiv comment9 pages, 1 figure, published version

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Cited by in corpus (13)

• Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors
• Crawling technicolor
• Application of dilaton chiral perturbation theory to $N_f=8$, $\mathrm{SU}(3)$ spectral data
• Chiral effective theories with a light scalar at one loop
• Lattice studies of the $Sp(4)$ gauge theory with two fundamental and three antisymmetric Dirac fermions
• Explorations beyond dilaton chiral perturbation theory in the eight-flavor SU(3) gauge theory
• Lattice Gauge Theory for Physics Beyond the Standard Model
• Gravitational Waves from Walking Technicolor
• Goldstone Boson Scattering with a Light Composite Scalar
• Gravitational tests of electroweak relaxation
• Dilaton in scalar QFT: a no-go theorem in $4-\epsilon$ and $3-\epsilon$ dimensions
• Studies of Conformal Behavior in Strongly Interacting Quantum Field Theories
• Soft pion scattering in infrared-conformal gauge-fermion theories