High-precision four-loop mass and wave function renormalization in QED

Laporta, S.

doi:10.1016/j.physletb.2020.135264

Cited by 4 publications

(10 citation statements)

References 31 publications

(38 reference statements)

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“…Let us consider the structure of the ratio M l /m l (m 2 l ) in more details. Using the U (1)-limit of the results of the diagram calculations [1,2,[4][5][6][7] and [17] of the coefficients t M k performed within the SU (N c ) theory with their decomposition into the Casimir operators (or the recent four-loop results of the explicit numerical computations [72]), it is possible to get the on-shell-MS mass relation for the charged leptons in QED in the O(a 4 ) approximation: where a = α(m 2 l )/π is the QED coupling constant defined in the MS-scheme and N l is the number of the massless charged leptons. The first four-loop N l -independent (the N ldependent one as well) term in the curly braces corresponds to the abelian U (1)-limit of the results of the semi-analytical calculations [17] carried out for the case of the SU (N c ) theory with n l massless quarks.…”

Section: Resultsmentioning

confidence: 99%

“…The first four-loop N l -independent (the N ldependent one as well) term in the curly braces corresponds to the abelian U (1)-limit of the results of the semi-analytical calculations [17] carried out for the case of the SU (N c ) theory with n l massless quarks. The second one follows from the recent high-precision (about 1100 digits) four-loop computations of the on-shell mass renormalization constant Z OS m performed in QED in [72] (see also [109] where the wave function renormalization constant Z OS 2 was also found) for the case of N l = 0. It is worth emphasizing that the results of [72] are in very good agreement with the ones following from [17].…”

Section: Resultsmentioning

confidence: 99%

“…The second one follows from the recent high-precision (about 1100 digits) four-loop computations of the on-shell mass renormalization constant Z OS m performed in QED in [72] (see also [109] where the wave function renormalization constant Z OS 2 was also found) for the case of N l = 0. It is worth emphasizing that the results of [72] are in very good agreement with the ones following from [17].…”

Section: Resultsmentioning

confidence: 99%

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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

Kataev

Molokoedov

2020

Eur. Phys. J. C

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The 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.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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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

Kataev

Molokoedov

2020

Eur. Phys. J. C

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“…Setting C F ¼ T F ¼ d FF ¼ 1 and C A ¼ d FA ¼ 0 we see that our four-loop result is indeed gauge invariant and is given by where α ¼ α ðn f Þ ðMÞ; L QED ¼ P i¼0;1;2;3;l L i is the ε 0 term in Z ð4Þ 2 of Eq. 26in [14]. Its numerical value is given in Eq.…”

Section: The Qed and Bloch-nordsieck Heavy-lepton Fieldsmentioning

confidence: 99%

Matching the heavy-quark fields in QCD and HQET at four loops

et al. 2020

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The QCD/HQET matching coefficient for the heavy-quark field is calculated up to four loops. It must be finite; this requirement produces analytical results for some terms in the four-loop on-shell heavy-quark field renormalization constant which were previously only known numerically. The effect of a nonzero lighter-flavor mass is calculated up to three loops. A class of on-shell integrals with two masses is analyzed in detail. By specifying our result to QED, we obtain the relation between the electron field and the Bloch-Nordsieck field with four-loop accuracy.

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“…Within QCD, analytic results for both renormalization constants are available up to three loops [2][3][4][5][6][7][8][9]. At four-loop order [10][11][12][13] semi-analytic methods were used. Starting from two loops there are contributions with closed quark loops, which can either be massless, have the mass of the external quark (m 1 ), or have a different mass (m 2 ).…”

Section: Introduction and Notationmentioning

confidence: 99%

Exact results for $$ {Z}_m^{\mathrm{OS}} $$ and $$ {Z}_2^{\mathrm{OS}} $$ with two mass scales and up to three loops

Fael

Schönwald

Steinhauser

2020

J. High Energ. Phys.

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We consider the on-shell mass and wave function renormalization constants $$ {Z}_m^{\mathrm{OS}} $$ Z m OS and $$ {Z}_2^{\mathrm{OS}} $$ Z 2 OS up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters $$ \sqrt{1-{\tau}^2} $$ 1 − τ 2 and $$ \sqrt{1-{\tau}^2}/\tau $$ 1 − τ 2 / τ which extends the findings from ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order $$ \mathcal{O} $$ O (ϵ2) and $$ \mathcal{O} $$ O (ϵ) at two- and three-loop order which are crucial ingredients for a future four-loop calculation. Compact results for the expansions around the zero-mass, equal-mass and large-mass cases allow for a fast high-precision numerical evaluation.

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High-precision four-loop mass and wave function renormalization in QED

Cited by 4 publications

References 31 publications

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

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

Matching the heavy-quark fields in QCD and HQET at four loops

Exact results for $$ {Z}_m^{\mathrm{OS}} $$ and $$ {Z}_2^{\mathrm{OS}} $$ with two mass scales and up to three loops

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