Ⅱ-6. Particle Physics

RIKEN Accel. Prog. Rep. 50 (2017)

Light scalar resonance from lattice simulation of SU(3) gauge theorywith eight light fermions†∗1,∗2[forthe LSD
LSD Collaboration
Collaboration]
E.
E. T.
T. Neil
Neil∗1,∗2
for theStudying the properties of strongly-coupled gauge
theories with a large number of fermions has been an
area of active research using lattice gauge theory techniques in recent years1) . The screening of the gauge
force by the presence of Nf light fermions is known totrigger a phase transition as Nf increases, with conﬁnement and chiral symmetry breaking disappearing as
the theory becomes scale invariant at long distances.
Near the transition, such a theory can be conﬁning(and therefore a useful candidate for the constructionof composite Higgs models), but exhibit novel dynamical features associated with the onset of scale invariance.
Lattice gauge theory provides an ideal method tostudy these non-perturbative theories numerically. We
consider an SU(3) gauge theory with Nf = 8 degenerate light fermions, charged under the fundamental
representation. An earlier study of this same theory
by the LatKMI collaboration2) revealed evidence for avery light scalar resonance with J P C = 0++ quantum
numbers. This is qualitatively diﬀerent from QCD,
where the lightest scalar resonance is heavy enough todecay into two pions.
Our lattice simulations are carried out with annHYP-smeared staggered fermion action, and a plaquette gauge action which includes an adjoint plaquette term to reduce lattice artifacts associated with3)3)
a lattice phase
phase transitiontransition.
. WeWe use
use standard
standard latlattice spectroscopy techniques to calculate the resonancemasses and decay constants. For the 0++ meson state,
the fermion-line-disconnected contribution to the twopoint correlation function is important, for which weemploy the method of dilution with U (1) stochastic
sources. We simulate the theory at relatively lightfermion masses, with the ratio Mρ /Mπ ≈ 2.1 at ourlightest point shown, requiring a 643 × 128 lattice volume in order to control ﬁnite-volume systematic effects.
One of the main results of our simulation is shownin ﬁgure 1, which gives the resonance masses as afunction of the input fermion mass am. Over a wide
range of input masses, the 0++ resonance is seen tobe nearly degenerate with the pion, and both resonances are becoming light compared to the ρ and otherheavier states seen in the spectrum. This conﬁrms theLatKMI result2) and demonstrates that the degeneracy
between the 0++ and π states persists even to rather†∗1∗2

Condensed from the article in Phys. Rev. D 93 no. 11,114514 (2016)
RIKEN Nishina Center
Department of Physics, University of Colorado, Boulder- 135 -Fig. 1. Spectrum of the SU(3) Nf = 8 theory in latticeunits, obtained from our simulations. The states shown
are the lightest resonance in the pseudoscalar (π), scalar(0++ ), vector (ρ), axial vector (a1 ), and nucleon (N )channels. Error bars are shown for all results, but areoften smaller than the size of the symbols used. The
0++ and π states are seen to be near-degenerate overa wide range of input fermion masses am and wellseparated from the rest of the spectrum.

light fermion masses, approaching the chiral limit ofthe theory.
The separation of the 0++ and π states relative tothe rest of the spectrum, which stands in stark contrast to the familiar case of QCD, raises the questionof whether there is an eﬀective ﬁeld theory (EFT) containing both the 0++ and π degrees of freedom which
can describe the low-energy dynamics of the Nf = 8system. Identifying a novel EFT that contains a light
scalar degree of freedom could provide a completely
new approach to the construction of composite Higgs
models, and might help to deepen our understandingof the conﬁning-conformal transition in many-fermion
gauge theories as well. As a next step in our studyof this theory, lattice calculations of π − π scattering
are now underway, which will help to distinguish thepossible EFT descriptions of this intriguing system.
References
1) T. DeGrand, Rev. Mod. Phys. 88 (2016), 015001.
2) Y. Aoki et al. (LatKMI Collaboration): Phys. Rev. D89(2014), 111502.
3) A. Cheng, A. Hasenfratz, and D. Schaich, Phys. Rev. D85(2012), 094509.