Light scalar meson and decay constant in SU(3) gauge theory with eight dynamical flavors

The SU(3) gauge theory with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>N</a:mi><a:mi>f</a:mi></a:msub><a:mo>=</a:mo><a:mn>8</a:mn></a:math> nearly massless Dirac fermions has long been of theoretical and phenomenological interest due to the near-conformality arising from its proximity to the conformal window. One particularly interesting feature is the emergence of a relatively light, stable flavor-singlet scalar meson <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>σ</c:mi><c:mo stretchy="false">(</c:mo><c:msup><c:mi>J</c:mi><c:mrow><c:mi>P</c:mi><c:mi>C</c:mi></c:mrow></c:msup><c:mo>=</c:mo><c:msup><c:mn>0</c:mn><c:mrow><c:mo>+</c:mo><c:mo>+</c:mo></c:mrow></c:msup><c:mo stretchy="false">)</c:mo></c:math> in contrast to the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>N</g:mi><g:mi>f</g:mi></g:msub><g:mo>=</g:mo><g:mn>2</g:mn></g:math> theory QCD. In this work, we study the finite-volume dependence of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>σ</i:mi></i:math> meson correlation function computed in lattice gauge theory and determine the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>σ</k:mi></k:math> meson mass and decay constant extrapolated to the infinite-volume limit. We also determine the infinite-volume mass and decay constant of the flavor-nonsinglet scalar meson <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>a</m:mi><m:mn>0</m:mn></m:msub></m:math>. Published by the American Physical Society 2024