Analogs of noninteger powers in general analytic QCD

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 Q^2-plane (where q^2 = -Q^2 is the momentum squared), thus reflecting correctly the analytic structure of the spacelike observables. The Minimal Analytic model (MA, named also APT) of Shirkov and Solovtsov removes the nonphysical cut (at positive Q^2) of the usual pQCD coupling and keeps the pQCD cut discontinuity of the coupling at negative Q^2 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 b+(bar b) pair.Comment: 29 pages, 5 figures; sections II and III extended, appendix B is ne

Single Cut Integration

We present an analytic technique for evaluating single cuts for one-loop integrands, where exactly one propagator is taken to be on shell. Our method extends the double-cut integration formalism of one-loop amplitudes to the single-cut case. We argue that single cuts give meaningful information about amplitudes when taken at the integrand level. We discuss applications to the computation of tadpole coefficients.Comment: v2: corrected typo in abstrac

Infinite temperature limit of meson spectral functions calculated on the lattice

We analyze the cut-off dependence of mesonic spectral functions calculated at finite temperature on Euclidean lattices with finite temporal extent. In the infinite temperature limit we present analytic results for lattice spectral functions calculated with standard Wilson fermions as well as a truncated perfect action. We explicitly determine the influence of `Wilson doublers' on the high momentum structure of the mesonic spectral functions and show that this cut-off effect is strongly suppressed when using an improved fermion action.Comment: 25 pages, 8 figure