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Probing the gluon self-interaction in light mesons.

Christian S Fischer¹, Richard Williams

¹Institute for Nuclear Physics, Darmstadt University of Technology, 64289 Darmstadt, Germany.

Physical Review Letters

|October 2, 2009

Summary

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We studied light meson properties using Dyson-Schwinger and Bethe-Salpeter equations. Our findings suggest gluon self-interaction and pion cloud effects cancel nonperturbatively in the rho meson mass.

Area of Science:

* Quantum Chromodynamics (QCD) and Hadron Physics.
* Theoretical Nuclear and Particle Physics.

Background:

* Understanding light meson properties is crucial for testing fundamental theories of strong interactions.
* Previous models often simplify the complex interactions within mesons, particularly the role of gluon self-interactions.

Purpose of the Study:

* To investigate the masses and decay constants of light mesons.
* To explicitly include non-Abelian contributions from gluon self-interaction to the quark-gluon vertex.
* To assess the impact of gluon self-interaction on meson properties beyond the rainbow-ladder approximation.

Main Methods:

* Coupled system of Dyson-Schwinger and Bethe-Salpeter equations.
* Construction of a Bethe-Salpeter kernel satisfying the axial-vector Ward-Takahashi identity.

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* Numerical solution of all equations in the complex plane, including full momentum dependencies.

Main Results:

* Calculated masses and decay constants for light mesons.
* Observed indications of a nonperturbative cancellation between gluon self-interaction and pion cloud effects in the rho meson mass.
* Demonstrated the influence of gluon self-interaction on meson properties.

Conclusions:

* The study provides a more comprehensive theoretical framework for light meson properties.
* The cancellation effect in the rho meson mass highlights the importance of nonperturbative dynamics.
* Results pave the way for further investigations into QCD phenomena.