Abstract
The effective charges motivated method is applied to the relation between pole and M̅S̅-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors nl, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to π2 effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the t-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the b-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.
Highlights
It is well-known that the masses of charm, bottom and top-quarks are one of the most important QCD parameters, which are relevant for processing different data, obtained at LHC and Tevatron
In order to study whether there may be extra theoretical ambiguities in the results of applications of the widely spreaded infrared renormalon (IRR) approach, recently used in [? ] to analyze the uncertainties of the asymptotic QCD predictions for the coefficients of heavy quark masses relation, we will compare in Sec.5 its outcomes with the five and six-loop estimates of the same terms, obtained by means not related to the IRR-approach ECH-inspired methods
Defining the ECH aes f f (s) for the quantity T (s)/mq(s) and the corresponding βe f ffunction with coefficients βne f f, fixed by the replacements φn → φnM = tnM/t1M in Eqs.(????), one can get the estimates for coefficients tnM, ECH direct of pole-running heavy quark mass relation directly in the Minkowskian region after using the ansatz βenf f = βn at n ≥ 2
Summary
It is well-known that the masses of charm, bottom and top-quarks are one of the most important QCD parameters, which are relevant for processing different data, obtained at LHC and Tevatron. ] to analyze the uncertainties of the asymptotic QCD predictions for the coefficients of heavy quark masses relation, we will compare in Sec. its outcomes with the five and six-loop estimates of the same terms, obtained by means not related to the IRR-approach ECH-inspired methods. Defining the ECH aes f f (s) for the quantity T (s)/mq(s) and the corresponding βe f f (aes f f )function with coefficients βne f f , fixed by the replacements φn → φnM = tnM/t1M in Eqs.(????), one can get the estimates for coefficients tnM, ECH direct of pole-running heavy quark mass relation directly in the Minkowskian region after using the ansatz βenf f = βn at n ≥ 2. This demonstrates compatibility of the estimates for heavy quark mass relations coefficients, obtained by applying ECH-inspired procedure both in the Euclidean and Minkowskian regions
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