Abstract
The asymptotic structure of the QCD perturbative relation between the on-shell and overline{{mathrm{MS}}} heavy quark masses is studied. We estimate the five and six-loop contributions to this relation by three different techniques. First, the effective charges motivated approach in two variants is used. Second, the results following from the large-beta _0 approximation are analyzed. Finally, the consequences of applying the asymptotic renormalon-based formula are investigated. We show that all approaches lead to corrections which are qualitatively consistent in order of magnitude. Their sign-alternating character in powers of the number of massless quarks is demonstrated. We emphasize that there is no contradiction in the behavior of the fine structure of the renormalon-based estimates with other approaches if one use the detailed information about the normalization factor included in the renormalon asymptotic formula. The obtained five- and six-loop estimates indicate that in the case of the b-quark the asymptotic character of the studied relation manifests itself above the fourth order of PT, whereas for the t-quark it starts to reveal itself after the seventh order. This allows to conclude that like the running masses, the pole masses of the b and especially t-quark in principle may be used in the phenomenologically-oriented studies.
Highlights
Where m0,q, Mq and mq are the bare, pole and MS-scheme running masses respectively
MS m contain the traces of ultraviolet divergences in the form of poles and are represented by the perturbation theory (PT) series in powers of the coupling constant of the strong interaction depending on the scale parameter μ and defined in the corresponding subtraction scheme
Comparing the magnitudes of the estimated leading terms in nl, obtained by us in two variants of the ECH-method and with help of the infrared renormalon (IRR)-based formula, we conclude that the results (31c–31d) in more extent corresponds to the known coefficients t5M,4 and t6M,5
Summary
Where m0,q , Mq and mq are the bare, pole and MS-scheme running masses respectively. The renormalization mass constants. In this perturbative expression mq (s) is the MS-scheme running mass of heavy quark, normalized at the scale μ2 = s in the time-like region and tk are the dimensionless coefficients of this spectral function.. 544133.68 344053.30 201430.55 β(as) and γm(as) (9a–10d), the analogous expressions for contributions Δk respect the alternation of signs in powers of nl that is typical to the two, three and four-loop coefficients tkM )-ratio, typical to the on-shell renormalization scheme, we note that it is really worth to treat these special terms with care
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
