Mathematica and Fortran programs for various analytic QCD couplings

Understand

We outline here the motivation for the existence of analytic QCD models, i.e., QCD frameworks in which the running coupling $A(Q^2)$ has no Landau singularities.

• The analytic (holomorphic) coupling $A(Q^2)$ is the analog of the underlying pQCD coupling $a(Q^2) \equiv \alpha_s(Q^2)/\pi$, and any such $A(Q^2)$ defines an analytic QCD model.
• We present the general construction procedure for the couplings $A_{\nu}(Q^2)$ which are analytic analogs of the powers $a(Q^2)^{\nu}$.
• Three analytic QCD models are presented.