gaugecoupling

Gauge coupling refers to the parameter that sets the strength of the interaction between matter fields and gauge bosons in a gauge theory. In a gauge theory, interactions are introduced through the covariant derivative D_μ = ∂_μ + i g A_μ^a T^a, where g is the gauge coupling for that gauge group; A_μ^a is the gauge field and T^a are the group generators. Different factors in a product gauge group have their own couplings.

In the Standard Model there are three gauge groups: U(1)_Y, SU(2)_L, and SU(3)_c, with couplings g1, g2, g3; the physical electromagnetic coupling e is obtained from g1 and g2 by electroweak mixing. These couplings are often expressed through fine-structure constants α_i = g_i^2/(4π).

Moreover, the values of the gauge couplings depend on energy scale μ; this running is described by renormalization group equations. At higher energies, non-Abelian couplings like SU(3) can become weaker (asymptotic freedom), while the Abelian coupling can behave differently depending on the theory. In many beyond-Standard-Model theories, the running couplings tend to meet at a common value at a high energy (gauge coupling unification).

Experimentally, the couplings are measured in scattering processes; typical references are α_em ≈ 1/137 at low energies and α_s ≈ 0.118 at the Z mass, with α1, α2, α3 defined with a particular normalization. Gauge coupling is a central concept in predicting interactions, symmetry breaking, and unification in particle physics.