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In contrast to the coupling parameter in the usual perturbative QCD (pQCD),the coupling parameter in the analytic QCD models has cuts only on the negativesemiaxis of the Q^2-plane (where q^2 = -Q^2 is the momentum squared), thusreflecting correctly the analytic structure of the spacelike observables. TheMinimal Analytic model (MA, named also APT) of Shirkov and Solovtsov removesthe nonphysical cut (at positive Q^2) of the usual pQCD coupling and keeps thepQCD cut discontinuity of the coupling at negative Q^2 unchanged. In order toevaluate in MA the physical QCD quantities whose perturbation expansioninvolves noninteger powers of the pQCD coupling, a specific method ofconstruction of MA analogs of noninteger pQCD powers was developed by Bakulev,Mikhailov and Stefanis (BMS). We present a construction, applicable now in anyanalytic QCD model, of analytic analogs of noninteger pQCD powers; this methodgeneralizes the BMS approach obtained in the framework of MA. We need to knowonly the discontinuity function of the analytic coupling (the analog of thepQCD coupling) along its cut in order to obtain the analytic analogs of thenoninteger powers of the pQCD coupling, as well as their timelike (Minkowskian)counterparts. As an illustration, we apply the method to the evaluation of thewidth for the Higgs decay into b+(bar b) pair.

Analogs of noninteger powers in general analytic QCD