Abstract
The spectrum of light bound states in an SU(2) gauge theory with two flavors of fundamentally charged fermions is investigated by solving the Bethe-Salpeter equations in the respective channels within a 3PI-type (i.e., beyond rainbow-ladder) truncation including self-consistently a correspondingly truncated fermion--gauge-boson vertex. Remarkable differences with respect to the meson spectrum of an SU(3) gauge theory are found although in our approach these are not as pronounced as indicated by some recent respective investigations within lattice gauge field theory.
Highlights
Understanding the physics of bound states in generic gauge field theories is for several reasons of interest
Some technical issues related to solving for the fermion–gauge boson vertex are deferred to the Appendix
A remark is in order: All Yang-Mills input is taken from DS calculations which were originally performed for QCD, i.e., for an SU(3) gauge theory
Summary
Understanding the physics of bound states in generic gauge field theories is for several reasons of interest. An SU(2) gauge theory with two fundamentally charged Dirac fermions has been studied on the lattice [73,74,75,76,77] because it provides the simplest field theoretical realization of a unified theory of a composite Goldstone boson Higgs and technicolor [78] Such a theory might serve as a template for aspects of dynamical electroweak symmetry breaking as well as the SIMP scenario for dark matter. In this investigation, light fermion-anti-fermion (“mesons”) and fermion-fermion (bosonic two-color “baryons”) bound states are studied in an SU(2) gauge theory with two fundamentally charged fermions within a beyond-rainbowladder (BRL) truncation to the respective Dyson-Schwinger (DS) and Bethe-Salpeter (BS) equations. Some technical issues related to solving for the fermion–gauge boson vertex are deferred to the Appendix
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