Abstract
The appearance of a light composite $0^+$ scalar resonance in nearly conformal gauge-fermion theories motivates further study of the low energy structure of these theories. To this end, we present a nonperturbative lattice calculation of s-wave scattering of Goldstone bosons in the maximal-isospin channel in SU(3) gauge theory with $N_f=8$ light, degenerate flavors. The scattering phase shift is measured both for different values of the underlying fermion mass and for different values of the scattering momentum. We examine the effect of a light flavor-singlet scalar (reported in earlier studies) on Goldstone boson scattering, employing a dilaton effective field theory (EFT) at the tree level. The EFT gives a good description of the scattering data, insofar as the magnitude of deviations between EFT and lattice data are no larger than the expected size of next-to-leading order corrections in the EFT.
Highlights
The near-conformality of the gauge theory and the observed spectrum reported in previous publications [13,14] lead us to interpret the lattice results in terms of an effective field theory (EFT) including a light singlet scalar interpreted as an approximate dilaton, along with the pseudo-Nambu–Goldstone boson (PNGB) [30–33]
We have considered the maximal isospin s-wave scattering of PNGBs in a nearly conformal gauge theory known to possess a light scalar state
We have investigated the possibility that the light scalar, being nearly degenerate with the PNGBs on the gauge ensembles considered, may play a significant role in ππ scattering
Summary
Despite considerable numerical effort to date, little is known from direct lattice calculation about the light scalar resonance beyond its mass. For these studies, work is ongoing to control lattice artifacts [10] and finite-volume effects [26] and to push closer to the chiral limit [14]. We instead probe the physics of the light singlet scalar through the lattice computation of pseudo-Nambu–Goldstone boson (PNGB) scattering at low energies. The near-conformality of the gauge theory and the observed spectrum reported in previous publications [13,14] lead us to interpret the lattice results in terms of an effective field theory (EFT) including a light singlet scalar interpreted as an approximate dilaton, along with the PNGBs [30–33].
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