Light scalar meson and decay constant in SU(3) gauge theory with eight dynamical flavors
R. C. Brower, Evan K. Owen, C. Rebbi, Chris Culver, David Schaich, K. K. Cushman, George Fleming, Andrew Gasbarro, Anna Hasenfratz, Ethan T. Neil, James Ingoldby, Xiao-Yong Jin, J. C. Osborn, Enrico Rinaldi, Pavlos Vranas, E. Weinberg, Oliver Witzel
Abstract
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