threegluon

Threegluon refers to the interaction among three gluons, a feature allowed by the non-Abelian nature of quantum chromodynamics (QCD). In QCD, gluons carry color charge and can interact with themselves, unlike photons in quantum electrodynamics. The threegluon interaction arises from the SU(3) gauge symmetry and is encoded in the QCD Lagrangian through the non-Abelian field strength tensor.

The field strength is F^a_{mu nu} = partial_mu A^a_nu - partial_nu A^a_mu + g_s f^{abc} A^b_mu A^c_nu, where A^a_mu are gluon fields, g_s is the strong coupling, and f^{abc} are the SU(3) structure constants. The term -1/4 F^a_{mu nu} F^{a mu nu} contains both three-gluon and four-gluon vertices. The threegluon vertex is proportional to f^{abc} and involves a particular combination of Lorentz indices and gluon momenta, reflecting the gauge structure.

In perturbative QCD, the threegluon vertex is described by a Feynman rule, typically written as Gamma^{abc}_{mu nu lambda}(p, q, r) = i g_s f^{abc} [ g_{mu nu} (p - q)_lambda + g_{nu lambda} (q - r)_mu + g_{lambda mu} (r - p)_nu ], with p, q, r the incoming momenta satisfying p + q + r = 0. The exact form can vary with convention, but the important point is the dependence on f^{abc} and the Lorentz-coupled tensor structure.

Significance of the threegluon interaction includes gluon self-coupling, its contribution to the running of the strong coupling constant, and its role in processes producing multi-jet events and in non-perturbative phenomena such as confinement. The threegluon vertex works alongside the four-gluon vertex, both arising from the non-Abelian gauge symmetry of QCD.