Tantalizing dilaton tests from a near-conformal EFT

Abstract

The dilaton low-energy effective field theory (EFT) of an emergent light scalar is probed in the paradigm of strongly coupled near-conformal gauge theories. These studies are motivated by models which exhibit small $\beta$-functions near the conformal window (CW), perhaps with slow scale-dependent walking and a light scalar with $0^{++}$ quantum numbers. We report our results from the hypothesis of a dilaton inspired EFT analysis with two massless fermions in the two-index symmetric (sextet) representation of the SU(3) color gauge group. With important caveats in our conclusions, conformal symmetry breaking entangled with chiral symmetry breaking would drive the near-conformal infrared behavior of the theory predicting characteristic dilaton signatures of the light scalar from broken scale invariance when probed on relevant scales of fermion mass deformations. From a recently reasoned choice of the dilaton potential in the EFT description~\cite{Golterman:2016lsd} we find an unexpectedly light dilaton mass in the chiral limit at $m_d/f_{\pi }=1.56(28)$, set in units of the pion decay constant $f_{\pi }$. Subject to further statistical and systematic tests of continued post-conference analysis, this result is significantly lower than our earlier estimates from less controlled extrapolations of the light scalar (the $\sigma$-particle) to the massless fermion limit of chiral perturbation theory. We also discuss important distinctions between the dilaton EFT analysis and the linear $\sigma$-model without dilaton signatures. For comparative reasons, we comment on dilaton tests from recent work with fermions in the fundamental representation with $n_f=8$ flavors.

14 pages, 34 figures, Proceedings of the 36th International Symposium on Lattice Field Theory (Lattice 2018), July 22-28, 2018, East Lancing, USA; elimination of some fit redundancies with minor changes in related figures

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