LambdaQCD

Lambda_QCD (Λ_QCD) is the QCD scale parameter that characterizes the energy level at which the strong interaction becomes nonperturbative. It is not a particle but a parameter that emerges through the renormalization group evolution in quantum chromodynamics, particularly when a renormalization scheme such as MS-bar is used. The classical QCD Lagrangian has no intrinsic scale, but quantum corrections introduce one via dimensional transmutation.

In perturbation theory, the running coupling α_s(Q^2) decreases at high energies (asymptotic freedom) and grows as Q approaches Λ_QCD, signaling confinement. At leading order, α_s(Q^2) ≈ 4π/(β0 ln(Q^2/Λ_QCD^2)), with β0 = 11 − 2/3 n_f and n_f the number of active quark flavors; higher-loop terms refine this relation.

Values of Λ_QCD are scheme- and flavor-dependent. In the MS-bar scheme, typical estimates are Λ_MSbar^(5) on the order of 210–230 MeV and Λ_MSbar^(3) around 330–350 MeV, though exact numbers vary with the input for α_s and the data set used.

Role in physics includes setting the scale for nonperturbative phenomena such as confinement, hadron masses, and chiral symmetry breaking. Λ_QCD provides a common scale for comparing experimental results with lattice QCD calculations, where it helps convert dimensionless lattice outputs into physical units.

Notes: Because Λ_QCD depends on the renormalization scheme and the active flavor content, its numerical value is not universal. It is determined from experimental data through global fits of α_s and related observables.