Cumulant and factorial moments in perturbative gluodynamics

Multiparticle production and quantum chromodynamics

“…This astonishing qualitative prediction [40] of the new type of the moments behaviour has been confirmed in experiment (for the very first time in Ref. [86]) as in e + e − (see Fig.…”

“…The Taylor series expansion leads [40] immediately, as will be shown below, to the perturbation theory series in the exponent of the physically measurable quantities. It implies the summation of some specific subseries of the purely perturbative expansion in the coupling strength for this particular characteristics.…”

“…After that, the derivatives over u of both sides considered at u = 1 lead in a natural way to the prediction [40,41,79] concerning the behaviour of the ratio H q = K q /F q . At asymptotically high energies, this ratio as a function of the rank q is predicted to behave 11 as q −2 .…”

“…For the running coupling strength (8), they have been solved only in the perturbative theory approach. The systematical method, proposed in [40], consists in using the Taylor series expansion of the expressions under the integral sign. It results in the modified perturbative expansion of the physically measurable quantities.…”

“…Using the Taylor series expansion [40] of n at large y in Eqns (17), (18) with (20), (21) and equating the terms of the same order in γ 0 in both sides, one gets the coefficients a i , r i shown in the Table 1 (r 0 = 9/4). …”