Can a Linear Sigma Model Describe Walking Gauge Theories at Low Energies?

¹ Sloane Physics Laboratory Yale University New Haven, CT 06520, USA
² Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
³ Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

^* Speaker, e-mail: andrew.gasbarro@yale.edu. Acknowledgments: This work is carried out as a part of the Lattice Strong Dynamics Collaboration (LSD). This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office ofWorkforce Development for Teachers and Scientists, Office of Science Graduate Student Research (SCGSR) program. The SCGSR program is administered by the Oak Ridge Institute for Science and Education (ORISE) for the DOE. ORISE is managed by ORAU under contract number DE-SC0014664. A.G. thanks Lawrence Livermore National Laboratory and Lawrence Berkeley National Laboratory for hospitality during the completion of this work. He also thanks James Ingoldby and LSD members George Fleming, Thomas Appelquist, Pavlos Vranas, and Richard Brower for many useful discussions.

Published online: 26 March 2018

Abstract

In recent years, many investigations of confining Yang Mills gauge theories near the edge of the conformal window have been carried out using lattice techniques. These studies have revealed that the spectrum of hadrons in nearly conformal ("walking") gauge theories differs significantly from the QCD spectrum. In particular, a light singlet scalar appears in the spectrum which is nearly degenerate with the PNGBs at the lightest currently accessible quark masses. This state is a viable candidate for a composite Higgs boson. Presently, an acceptable effective field theory (EFT) description of the light states in walking theories has not been established. Such an EFT would be useful for performing chiral extrapolations of lattice data and for serving as a bridge between lattice calculations and phenomenology. It has been shown that the chiral Lagrangian fails to describe the IR dynamics of a theory near the edge of the conformal window. Here we assess a linear sigma model as an alternate EFT description by performing explicit chiral fits to lattice data. In a combined fit to the Goldstone (pion) mass and decay constant, a tree level linear sigma model has a Χ²/d.o.f. = 0.5 compared to Χ²/d.o.f. = 29.6 from fitting nextto-leading order chiral perturbation theory. When the 0++ (σ) mass is included in the fit, Χ²/d.o.f. = 4.9. We remark on future directions for providing better fits to the σ mass.