Nonperturbative contributions in an analytic running coupling of QCD

In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all Q > Λ they are shown to be represented in the form of an expansion in inverse powers of Euclidean momentum squared. The expansion coefficients are calculated for different numbers of active quark flavors nf and for different number of loops taken into account. On basis of the stated expansion the effective method for precise calculation of the analytic running coupling can be developed. PACS number(s): 12.38.Aw, 12.38.Lg It is widely believed that nonphysical singularities of the perturbation theory in the infrared region of QCD should be canceled by the nonperturbative contributions. The nonperturbative contributions arise quite naturally in an analytic approach [1] — [5] to QCD. The idea of the approach goes back to Refs. [6, 7] devoted to the nonphysical ghost pole problem in QED. In recent papers [2, 3] it is suggested to solve the ghost pole problem in QCD demanding the running coupling constant be analytic in Q (Q is the Euclidean momentum squared). As a result of the procedure, instead of the one-loop expression α s (Q ) = (4π/b0)/ ln(Q /Λ) taking into account the leading logarithms and having the ghost pole at Q = Λ, one obtains new expression α an (Q ) = 4π b0 [ 1 ln(Q2/Λ2) + Λ Λ2 −Q2 ] . (1) Eq. (1) is an analytic function in the complex Q-plane with a cut along the negative real semiaxis. The pole of the perturbative running coupling at Q = Λ is canceled by the nonperturbative contribution (Λ ' μ exp{−4π/(b0αan(μ))} at αan(μ) → 0) and the value α an (0) = 4π/b0 appeared to be finite and independent of the normalization conditions (independent of Λ). The most important feature of the procedure is the stability property [2, 3] of the value of the ”analytically improved” running coupling constant at Electronic address: [email protected]