Hadronic bound states in SU(2) from Dyson-Schwinger equations

Area of Science:

• Quantum Chromodynamics (QCD) and related gauge theories.
• Theoretical particle physics and hadron spectroscopy.
• Computational physics and numerical simulations.

Background:

• The Dyson-Schwinger/Bethe-Salpeter formalism is a powerful tool for studying the properties of hadrons.
• The rainbow-ladder truncation is a common approximation used in QCD, but its applicability to other gauge theories is questionable.
• SU(2) gauge theories with fundamental fermions provide a simpler yet non-trivial testing ground for theoretical methods.

Purpose of the Study:

• To calculate the ground state spectrum of hadrons in an SU(2) gauge theory with two fundamental fermions.
• To assess the validity of the rainbow-ladder truncation in this specific SU(2) theory.
• To develop and apply a more sophisticated truncation scheme for improved accuracy.

Main Methods:

• Utilizing the Dyson-Schwinger/Bethe-Salpeter formalism in Euclidean spacetime.
• Implementing a novel truncation at the level of the quark-gluon vertex Dyson-Schwinger equation.
• Comparing results with existing lattice QCD studies for validation.

Main Results:

• Demonstrating the inadequacy of the rainbow-ladder truncation for the studied SU(2) gauge theory.
• Achieving good agreement between the novel truncation method and lattice QCD results for the hadron spectrum.
• Providing a more reliable theoretical framework for investigating strongly interacting gauge theories.

Conclusions:

• The rainbow-ladder approximation is not universally applicable to all strongly interacting gauge theories.
• Advanced truncation techniques, such as including the quark-gluon vertex Dyson-Schwinger equation, are necessary for accurate predictions in generic gauge theories.
• This work highlights the importance of method selection for reliable results in theoretical particle physics.