Analogs of noninteger powers in general analytic QCD

Details Analogs of noninteger powers in general analytic QCD Analogs of noninteger powers in general analytic QCD

2011-06-21

arxiv.org/abs/1106.4275v2

Physics

High Energy Physics

High Energy Physics - Phenomenology

21 pages, 5 figures; new references ([7-11, 14-15]) added

Scientific paper

We present a method of evaluation, in any analytic QCD, of physical quantities whose perturbative expansion involves noninteger powers of the perturbative QCD (pQCD) coupling parameter. In contrast to the pQCD coupling parameter, the analytic QCD coupling parameter has cuts only on the negative semiaxis of the Q^2-plane (where q^2 = -Q^2 is the momentum squared), thus reflecting correctly the analytic structure of the spacelike observables as dictated by causality in quantum field theories. It turns out that we need to know only the discontinuity function along this cut in order to obtain the analog of the noninteger power of spacelike pQCD coupling parameter, as well as its timelike counterpart.

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