scholarly journals On the relation between pole and running heavy quark masses beyond the four-loop approximation

2018 ◽  
Vol 191 ◽  
pp. 04005 ◽  
Author(s):  
A. L. Kataev ◽  
V. S. Molokoedov
Keyword(s):  
Heavy Quark ◽  
Perturbative Qcd ◽  
Mass Relation ◽  
Coupling Constant ◽  
Quark Masses ◽  
Asymptotic Nature ◽  
Asymptotic Expressions ◽  
Loop Approximation ◽  
Euclidean Region ◽  
Direct Calculations

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.

scholarly journals Heavy quark masses from sum rules in four-loop approximation

2007 ◽  
Vol 778 (1-2) ◽  
pp. 192-215 ◽  
Author(s):  
Johann H. Kühn ◽  
Matthias Steinhauser ◽  
Christian Sturm
Keyword(s):  
Heavy Quark ◽  
Sum Rules ◽  
Quark Masses ◽  
Loop Approximation

scholarly journals Multiloop contributions to the on-shell-$$ \overline{{\mathrm{MS}}}$$ heavy quark mass relation in QCD and the asymptotic structure of the corresponding series: the updated consideration

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
A. L. Kataev ◽  
V. S. Molokoedov
Keyword(s):  
Heavy Quark ◽  
Mass Relation ◽  
Normalization Factor ◽  
Asymptotic Structure ◽  
Quark Masses ◽  
Heavy Quark Mass ◽  
Seventh Order ◽  
Order Of Magnitude ◽  
Effective Charges ◽  
Asymptotic Character

AbstractThe asymptotic structure of the QCD perturbative relation between the on-shell and $$\overline{{\mathrm{MS}}}$$ 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-$$\beta _0$$ β 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.

scholarly journals Erratum to: On the relation between pole and running heavy quark masses beyond the four-loop approximation

2018 ◽  
Vol 191 ◽  
pp. 04013
Author(s):  
A. L. Kataev ◽  
V. S. Molokoedov
Keyword(s):  
Heavy Quark ◽  
Full Text ◽  
Quark Masses ◽  
Loop Approximation

Citations in the original article are corrupted due to error made by Editors QUARKS-2018. See the Full text with correct citations in PDF file.

AN IMPROVED ONE-LOOP ANALYSIS OF THE λϕ4 THEORY AT FINITE TEMPERATURE

1987 ◽  
Vol 02 (03) ◽  
pp. 713-728 ◽  
Author(s):  
SWEE-PING CHIA
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Coupling Constant ◽  
Loop Analysis ◽  
Temperature Dependent ◽  
Effective Coupling ◽  
Loop Approximation ◽  
The One ◽  
Dependent Mass

The λϕ4 theory with tachyonic mass is analyzed at T ≠ 0 using an improved one-loop approximation in which each of the bare propagators in the one-loop diagram is replaced by a dressed propagator to take into account the higher loop effects. The dressed propagator is characterized by a temperature-dependent mass which is determined by a self-consistent relation. Renomalization is found to be necessarily temperature-dependent. Real effective potential is obtained, giving rise to real effective mass and real coupling constant. For T < Tc, this is achieved by first shifting the ϕ field by its zero-temperature vacuum expectation value. The effective coupling constant is found to exhibit the striking behavior that it approaches a constant nonzero value as T → ∞.

scholarly journals OPERATOR-PRODUCT EXPANSION AND ANALYTICITY

1999 ◽  
Vol 14 (30) ◽  
pp. 4819-4840
Author(s):  
JAN FISCHER ◽  
IVO VRKOČ
Keyword(s):  
Operator Product Expansion ◽  
Deflection Angle ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Operator Product ◽  
Coupling Constant ◽  
Expectation Value ◽  
Euclidean Region ◽  
The Deflection Angle ◽  
Class Of Functions

We discuss the current use of the operator-product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the Euclidean region, we observe how the bound varies with increasing deflection from the Euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane down to the Minkowski region is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions considered. The results obtained are discussed in connection with calculations of the coupling constant αs from the τ decay.

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