One-loop effective Lagrangian for low-energy multigluon processes in arbitrary dimensions

Abstract

This study has been motivated by a reconsideration of the photon-photon scattering generalizing known results to arbitrary dimensional spacetime and any number of scattering photons. This abelian problem naturally leads one to consider its nonabelian analog: the multigluon scattering process in arbitrary dimensions. Unlike its abelian counterpart however, the multigluon interaction is not a feeble process since the gluon coupling constant g is significantly larger than the electronic charge e. Also, multigluon scattering will be mediated not only by meson and fermion virtual particle loops but by vector and ghost particles as well, quite apart from the tree level contributions. These new features are of course due to the inherent nonlinearity of the nonabelian field strength tensor, F_μν = ∂_μA_ν − ∂_νA_μ − ig[A_μ,A_ν], where the gauge field A_μ, possesses a nontrivial internal symmetry, A_μ = T^aA^a_μ with the generators T^a satisfying [T^a, T^b] = if^abcT^c. 
In this study, we focus on the evaluation of the one-loop effective Lagrangian for multigluon processes in arbitrary dimensions under the assumption that the background fields are strong but slowly varying. This means that invariants which involve covariant derivatives of the background fields are deemed much smaller when compared to invariants formed from the fields themselves of the same mass dimensionality.