Abstract
We study an effective field theory (EFT) describing the interaction of an approximate dilaton with a set of pseudo-Nambu-Goldstone bosons (pNGBs). The EFT is inspired by, and employed to analyse, recent results from lattice calculations that reveal the presence of a remarkably light singlet scalar particle. We adopt a simple form for the scalar potential for the EFT, which interpolates among earlier proposals. It describes departures from conformal symmetry, by the insertion of a single operator at leading order in the EFT. To fit the lattice results, the global internal symmetry is explicitly broken, producing a common mass for the pNGBs, as well as a further, additive deformation of the scalar potential. We discuss sub-leading corrections arising in the EFT from quantum loops. From lattice measurements of the scalar and pNGB masses and of the pNGB decay constant, we extract model parameter values, including those that characterise the scalar potential. The result includes the possibility that the conformal deformation is clearly non-marginal. The extrapolated values for the decay constants and the scalar mass would then be not far below the current lattice-determined values.
Highlights
Lattice studies of SUð3Þ gauge theories with matter field content consisting of Nf 1⁄4 8 fundamental (Dirac) fermions [1,2,3,4,5], as well as Nf 1⁄4 2 symmetric 2-index (Dirac) fermions [6,7,8,9,10], have reported evidence of the presence in the spectrum of a light scalar, singlet particle, at least in the accessible range of fermion masses
We develop further the framework we adopted in Refs. [11,12], by assuming that the strongly coupled dynamics of the underlying nearly conformal gauge theory is captured by a dilaton effective field theory (EFT) satisfying the following conditions
It may be natural to postulate that the scale-breaking quantity m2d=f2d depends itself on Nf in a manner emerging from the underlying gauge theory [13,30], but this requires moving outside the framework of the EFT
Summary
Lattice studies of SUð3Þ gauge theories with matter field content consisting of Nf 1⁄4 8 fundamental (Dirac) fermions [1,2,3,4,5], as well as Nf 1⁄4 2 symmetric 2-index (Dirac) fermions (sextets) [6,7,8,9,10], have reported evidence of the presence in the spectrum of a light scalar, singlet particle, at least in the accessible range of fermion masses. [11,12] we analyzed lattice data in terms of an effective field theory (EFT) framework that extends the field content of the chiral Lagrangian It includes a dilaton field χ, together with the pseudo-NambuGoldstone-boson (pNGB) fields π, along the lines discussed in Refs. Potential at large field excursions to be compatible with a simple power law, VðχÞ ∝ χp with p close to 4 [12] By combining this result with the lattice measurement of the scalar mass, we estimated the ratio of decay constants of the dilaton and the pNGBs, finding roughly f2π=f2d ∼ 0.1. For both of the two gauge theories, the dilaton EFT fared remarkably well when used at the tree level.
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