The three-loop on-shell renormalization of QCD and QED

Melnikov, Kirill; Ritbergen, T. van

doi:10.1016/s0550-3213(00)00526-5

Cited by 172 publications

(199 citation statements)

References 38 publications

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“…3 (i). We need, therefore, the constant Z 2,OS (ǫ, µ 2 /m 2 ) at the two-loop level, that was computed in [26,27]. We use the result of [27] and we express it in terms of the renormalized MS coupling α S , finding:…”

Section: Two-loop Countertermmentioning

confidence: 99%

Two-loop QCD corrections to the heavy quark form factors: the vector contributions

et al. 2005

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Section: Two-loop Countertermmentioning

confidence: 99%

Two-loop QCD corrections to the heavy quark form factors: the vector contributions

et al. 2005

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“…At the end one arrives at a small set of integrals -so-called master integrals -which actually have to be evaluated. In [126,182] the considerations of [183] have been extended and the missing master integrals have been evaluated. The technique used for the computation is based on the hard-mass procedure for large M which represents the on-shell integrals in terms of a power series in q 2 /M 2 .…”

Section: The Relation Between the Ms And On-shell Quark Massmentioning

confidence: 99%

“…for q 2 = M 2 , can be reduced to known mathematical constants. For explicit examples we refer to [182]. At the end of this section we will list the analytical result for z m (µ) obtained in [126].…”

Section: The Relation Between the Ms And On-shell Quark Massmentioning

confidence: 99%

Results and techniques of multi-loop calculations

Steinhauser

2002

Physics Reports

100

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In this review some recent multi-loop results obtained in the framework of perturbative Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore the connection to observables involving a scalar Higgs boson is worked out in detail. An all-order low energy theorem is derived which establishes a relation between the coefficient functions in the hadronic Higgs decay and the decoupling constants. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order α 4 s and α 3 s , respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Padé approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass-dependence. In particular, we concentrate on the evaluation of the total cross section for the production of hadrons in e + e − annihilation. The knowledge of the complete mass dependence at order α 2 s has triggered a bunch of theory-driven analyses of the hadronic contribution to the electromagnetic coupling evaluated at high energy scales. The status is summarized in this review. In a further application four-loop diagrams are considered which contribute to the order α 2 QED corrections to the µ decay. Its relevance for the determination of the Fermi constant G F is discussed. Finally the calculation of the three-loop relation between the MS and on-shell quark mass definitions is presented and physical applications are given. To complete the presentation, some technical details are presented in the Appendix, where also explicit analytical results are listed.

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“…[11,12,21,22]. In fact, in [21,22], another problem was considered: the evaluation of threeloop renormalization constants, for which master integrals are almost the same, up to one additional master integral. This three-loop evaluation was typically performed up to transcendentality weight five, with some exceptions where some master integrals were expanded in ǫ up to weight four.…”

Section: Introductionmentioning

confidence: 99%

Analytic epsilon expansion of three-loop on-shell master integrals up to four-loop transcendentality weight

Lee

Smirnov

2011

J. High Energ. Phys.

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We evaluate analytically higher terms of the ǫ-expansion of the threeloop master integrals corresponding to three-loop quark and gluon form factors and to the three-loop master integrals contributing to the electron g−2 in QED up to the transcendentality weight typical to four-loop calculations, i.e. eight and seven, respectively. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin-Barnes representation, and the PSLQ algorithm.

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The three-loop on-shell renormalization of QCD and QED

Cited by 172 publications

References 38 publications

Two-loop QCD corrections to the heavy quark form factors: the vector contributions

Two-loop QCD corrections to the heavy quark form factors: the vector contributions

Results and techniques of multi-loop calculations

Analytic epsilon expansion of three-loop on-shell master integrals up to four-loop transcendentality weight

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