The Bogoliubov Renormalization Group in Theoretical and Mathematical Physics

Shirkov, D. V.

doi:10.1007/3-540-44482-3_10

Cited by 5 publications

(8 citation statements)

References 45 publications

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“…We recast the running mass m(Q 2 ) in terms of the RG-invariant massm . The analytical continuation was similar to the much studied Euclidean to Minkowskian continuation for the e + e − R-ratio [29][30][31][32][33][34][35][36][37][38][39][40]. The presence of an anomalous dimension complicated the analysis slightly.…”

Section: Discussionmentioning

confidence: 60%

“…Because of the absence of the Ward identity Z 1 = Z 2 present in the vector case, and the inevitable involvement of the quark mass anomalous dimension, the analysis amd combinatorics was considerably more complicated. An all-orders large-N f result for the anomalous mass dimension γ m was obtained in (39,40), and thanks to the remarkable identity (20) relating insertions into twoloop skeleton diagrams to the anomalous dimension, it was possible to obtain the all-orders large-N f result for the coefficient function of R S in (51)- (53). As in the vector case the Borel transform of (44) and (45) contained UV and IR renormalons.…”

Section: Discussionmentioning

confidence: 99%

“…The continuation is essentially the same as that involved in the vector case for the analytical continuation of the Adler D-function to the QCD R-ratio. The effects of analytical continuation have been much studied [29]- [40] in attempts to improve the convergence of the QCD perturbation series by resumming an infinite subset of analytical continuation terms at each order in perturbation theory. Such resummation may be accomplished conveniently by representing the continuation as a contour integral around a circle in the complex −Q 2 plane (for one of the first discussion of this realization of the contour-improved technique see Ref.…”

Section: Analytic Continuation Of Fractional Powers Of α Smentioning

confidence: 99%

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Renormalons and multi-loop estimates in scalar correlators, Higgs decay and quark-mass sum rules

2001

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The single renormalon-chain contribution to the correlator of scalar currents in QCD is calculated in the MS-scheme in the limit of a large number of fermions, N f . At n-loop order we find that in the MS-scheme the factorial growth of the perturbative coefficients due to renormalons takes over almost immediately in the euclidean region. The essential differences between the large-order growth of perturbative coefficients in the present scalar case, and in the previously-studied vector case are analysed. In the timelike region a stabilization of the corresponding perturbative series for the imaginary part, with n-loop behaviour S n /[log(s/Λ 2 )] n−1 , where S n is essentially constant for n ≤ 6, is observed. Only for n ≥ 7 does one discern the factorial growth and alternations of sign. We use the new all-orders results to scrutinize the performance of multiloop estimates , using a largeβ 0 = (11N c − 2N f )/12 approximation, the so-called "naive nonabelianization" procedure, and within the effective charges approach. The asymptotic behaviour of perturbative coefficients, in both large-N f and large-N c limits, is analysed both in the spacelike and timelike regions. A contour-improved resummation technique in the time-like region is developed. Some subtleties connected with scheme-dependence are analysed , and illustrated using results in the MS and V -schemes. The all-orders series under investigation are summed up with the help of the Borel resummation method. The results obtained are relevant to the analysis of the theoretical uncertainties in the 4-loop extractions of the running and invariant s-quark masses from QCD sum rules, and in calculations of the Higgs boson decay width into a quark-antiquark pair.

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Section: Discussionmentioning

confidence: 60%

Section: Discussionmentioning

confidence: 99%

Section: Analytic Continuation Of Fractional Powers Of α Smentioning

confidence: 99%

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Renormalons and multi-loop estimates in scalar correlators, Higgs decay and quark-mass sum rules

2001

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“…The evolution equation for the polarization function can be directly obtained from the fundamental concept of the scheme-invariant charge [17,18], defined through…”

Section: Notation and Generalitiesmentioning

confidence: 99%

The relation between the QED charge renormalized in and on-shell schemes at four loops, the QED on-shell β-function at five loops and asymptotic contributions to the muon anomaly at five and six loops

et al. 2013

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In this paper we compute the four-loop corrections to the QED photon selfenergy Π(Q 2 ) in the two limits of q = 0 and Q 2 → ∞. These results are used to explicitly construct the conversion relations between the QED charge renormalized in on-shell(OS) and MS scheme. Using these relations and results of Baikov et al. [1] we construct the momentum dependent part of Π(Q 2 , m, α) at large Q 2 at five loops in both MS and OS schemes. As a direct consequence we arrive at the full result for the QED β-function in the OS scheme at five loops. These results are applied, in turn, to analytically evaluate a class of asymptotic contributions to the muon anomaly at five and six loops.

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“…Questions arise whether analytic versions of both types of couplings may exist for which the above expressions could be connected. We shall see in the next step how this goal can, indeed, be achieved using non-power-series (functional) expansions within APT [12,14,18,19,20,37,38,75,76].…”

Section: Conceptual Essentials Of Analytic Perturbation Theorymentioning

confidence: 99%

Fractional analytic perturbation theory in Minkowski space and applicationto Higgs boson decay into abb¯pair

Bakulev¹,

Михайлов²,

Stefanis

2007

Phys. Rev. D

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We work out and discuss the Minkowski version of Fractional Analytic Perturbation Theory (MFAPT) for QCD observables, recently developed and presented by us for the Euclidean region. The original analytic approach to QCD, initiated by Shirkov and Solovtsov, is summarized and relations to other proposals to achieve an analytic strong coupling are pointed out. The developed framework is applied to the Higgs boson decay into a bb pair, using recent results for the massless correlator of two quark scalar currents in the MS scheme. We present calculations for the decay width within MFAPT including those non-power-series contributions that correspond to the O α 3 sterms, taking also into account evolution effects of the running coupling and the b-quark-mass renormalization. Comparisons with previous results within standard QCD perturbation theory are performed and the differences are pointed out. The interplay between effects originating from the analyticity requirement and the analytic continuation from the spacelike to the timelike region and those due to the evolution of the heavy-quark mass is addressed, highlighting the differences from the conventional QCD perturbation theory.

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The Bogoliubov Renormalization Group in Theoretical and Mathematical Physics

Cited by 5 publications

References 45 publications

Renormalons and multi-loop estimates in scalar correlators, Higgs decay and quark-mass sum rules

Renormalons and multi-loop estimates in scalar correlators, Higgs decay and quark-mass sum rules

The relation between the QED charge renormalized in and on-shell schemes at four loops, the QED on-shell β-function at five loops and asymptotic contributions to the muon anomaly at five and six loops

Fractional analytic perturbation theory in Minkowski space and applicationto Higgs boson decay into abb¯pair

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