Analogs of noninteger powers in general analytic QCD

Abstract

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 negative semiaxis of the Q2-plane (where q2 ≡ −Q2 is the momentum squared), thus reflecting correctly the analytic structure of the spacelike observables. The minimal analytic model (MA, also called APT) of Shirkov and Solovtsov removes the nonphysical cut (at positive Q2) of the usual pQCD coupling and keeps the pQCD cut discontinuity of the coupling at negative Q2 unchanged. In order to evaluate in MA the physical QCD quantities whose perturbation expansion involves noninteger powers of the pQCD coupling, a specific method of construction of MA analogs of noninteger pQCD powers was developed by Bakulev, Mikhailov and Stefanis (BMS). We present a construction, applicable now in any analytic QCD model, of analytic analogs of noninteger pQCD powers; this method generalizes the BMS approach obtained in the framework of MA. We need to know only the discontinuity function of the analytic coupling (the analog of the pQCD coupling) along its cut in order to obtain the analytic analogs of the noninteger powers of the pQCD coupling, as well as their timelike (Minkowskian) counterparts. As an illustration, we apply the method to the evaluation of the width for the Higgs decay into the pair.