Tantalizing dilaton tests from a near-conformal EFT

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.Comment: 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 figure

Can a light Higgs impostor hide in composite gauge models?

The frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group is investigated. In previous studies the chiral condensate and the mass spectrum were shown to be consistent with chiral symmetry breaking ($\chi$SB) at vanishing fermion mass. The recently reported $\beta$-function is not inconsistent with this observation, suggesting that the model is very close to the conformal window and a light "Higgs impostor" could emerge as a composite state. In this work we describe the methodology and preliminary results of studying the emergence of the light composite scalar with $0^{++}$ quantum numbers.Comment: 7 pages, Proceedings of the 31st International Symposium on Lattice Field Theory - LATTICE 2013 06

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

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

The chiral condensate from the Dirac spectrum in BSM gauge theories

The eigenvalues of the Dirac operator at finite volume encode whether or not chiral symmetry is spontaneously broken in a massless theory. We apply this framework in a particular BSM context, namely SU(3) gauge theory with N_f=2 massless flavors in the 2-index symmetric (sextet) representation. Our first results are at a single lattice spacing. We find that both the density of near-zero eigenvalues and the renormalization group invariant mode number indicate spontaneous symmetry breaking. Quantitatively, there is a discrepancy between the determination of the fermion condensate in the chiral limit via the eigenvalue spectrum and the determinations from direct measurements of the chiral condensate and the GMOR relation. We comment on possible explanations of this discrepancy and further refinements of this study.Comment: 7 pages, Proceedings of the 31st International Symposium on Lattice Field Theory - LATTICE 201

Extended investigation of the twelve-flavor β\beta-function

We report new results from high precision analysis of an important BSM gauge theory with twelve massless fermion flavors in the fundamental representation of the SU(3) color gauge group. The range of the renormalized gauge coupling is extended from our earlier work {Fodor:2016zil} to probe the existence of an infrared fixed point (IRFP) in the $\beta$-function reported at two different locations, originally in {Cheng:2014jba} and at a new location in {Hasenfratz:2016dou}. We find no evidence for the IRFP of the $\beta$-function in the extended range of the renormalized gauge coupling, in disagreement with {Cheng:2014jba,Hasenfratz:2016dou}. New arguments to guard the existence of the IRFP remain unconvincing {Hasenfratz:2017mdh}, including recent claims of an IRFP with ten massless fermion flavors {Chiu:2016uui,Chiu:2017kza} which we also rule out. Predictions of the recently completed 5-loop QCD $\beta$-function for general flavor number are discussed in this context.Comment: 7 pages, 9 figure

Spectroscopy of the BSM sextet model

As part of our ongoing lattice study of SU(3) gauge theory with two flavors of fermions in the two-index symmetric representation (the sextet model), we present the current status of the pseudoscalar particle spectrum. We use a mixed action approach based on the gradient flow to control lattice artifacts, allowing a simultaneous extrapolation to the chiral and continuum limits. We find strong evidence that the pseudoscalar is a Goldstone boson state, with spontaneously broken chiral symmetry and a non-zero Goldstone decay constant in the chiral limit. In agreement with our study of the gauge coupling $\beta$ function, we find the sextet model appears to be a near-conformal gauge theory and serves as a prototype of the composite Higgs BSM template.Comment: 8 pages, 6 figures, Proceeding of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Weakly coupled conformal gauge theories on the lattice

Results are reported for the beta-function of weakly coupled conformal gauge theories on the lattice, SU(3) with Nf=14 fundamental and Nf=3 sextet fermions. The models are chosen to be close to the upper end of the conformal window where perturbation theory is reliable hence a fixed point is expected. The study serves as a test of how well lattice methods perform in the weakly coupled conformal cases. We also comment on the 5-loop beta-function of two models close to the lower end of the conformal window, SU(3) with Nf=12 fundamental and Nf=2 sextet fermions.Comment: 8 pages, 20 figures, Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai

Conformal finite size scaling of twelve fermion flavors

Extended simulation results and their analysis are reported in a strongly coupled gauge theory with twelve fermion flavors in the fundamental SU(3) color representation. The conformality of the model is probed using mass deformed conformal finite size scaling (FSS) theory driven by the fermion mass anomalous dimension. Two independent conformal FSS fitting procedures are used in the analysis. The first one deploys physics motivated scaling functions, complemented by a second fitting procedure with spline based general B-forms for the scaling functions. The results at fixed gauge coupling show unresolved problems with the conformal hypothesis.Comment: 7 pages, Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australi

The sextet gauge model, light Higgs, and the dilaton

The frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group is investigated \cite{Fodor:2012ty}. The chiral condensate and the mass spectrum are consistent with chiral symmetry breaking at vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper \cite{DeGrand:2012yq} which could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing \beta -function is not in conflict with chiral symmetry breaking reported here. A light Higgs impostor could emerge as the dilaton from spontaneous symmetry breaking of scale invariance or, without the dilaton mechanism, as a composite state.Comment: 7 pages, Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australi