Meson structure in a relativistic many-body approach

Area of Science:

• Quantum Chromodynamics (QCD)
• Many-Body Physics
• Hadron Spectroscopy

Background:

• Understanding the meson spectrum and vacuum structure is fundamental in particle physics.
• Chiral symmetry plays a critical role in the properties of light mesons, particularly the pion.
• Previous studies on glueballs showed less pronounced differences between theoretical frameworks.

Purpose of the Study:

• To present results from a relativistic many-body analysis of the meson spectrum using an effective QCD Hamiltonian.
• To comparatively study Bardeen-Cooper-Schrieffer (BCS), Tamm-Dancoff Approximation (TDA), and Random Phase Approximation (RPA) treatments.
• To gain insight into vacuum condensate structure, chiral symmetry, and meson mass splittings.

Main Methods:

• Extensive relativistic many-body analysis.
• Utilization of a realistic effective Quantum Chromodynamics (QCD) Hamiltonian.
• Comparative numerical study of BCS, Tamm-Dancoff (TDA), and Random Phase Approximation (RPA) methods.

Main Results:

• Significant quantitative differences were computed between TDA and RPA for the light quark sector.
• The pion emerges as a Goldstone boson exclusively within the RPA treatment.
• New insights into vacuum condensate structure and meson spin, orbital, and flavor mass splitting contributions were obtained.

Conclusions:

• The choice of theoretical framework (TDA vs. RPA) significantly impacts the description of the light meson spectrum.
• The Random Phase Approximation (RPA) is essential for correctly describing the pion's properties as a Goldstone boson.
• This work provides a deeper understanding of chiral symmetry breaking and its consequences for meson properties.