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

Grozin, Andrey; Marquard, Peter; Smirnov, Alexander V.; Smirnov, Vladimir A.; Steinhauser, Matthias

doi:10.1103/physrevd.102.054008

Cited by 5 publications

(2 citation statements)

References 57 publications

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“…Whereas the two-loop results are still quite compact (see, e.g., eqs. (15) and 28of ref. [1]), the threeloop expressions are too big to be printed.…”

Section: Results and Conclusionmentioning

confidence: 93%

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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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“…Whereas the two-loop results are still quite compact (see, e.g., eqs. (15) and 28of ref. [1]), the threeloop expressions are too big to be printed.…”

Section: Results and Conclusionmentioning

confidence: 93%

“…[3,4] and [1] at two-and three-loop orders (see also refs. [14,15]). In this work we re-consider these contributions to Z OS m and Z OS 2 up to threeloop order and provide analytic results including O( ) terms.…”

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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A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the $$ \overline{\mathrm{MS}} $$-pole quark mass relation

Fael

Lange

Schönwald

et al. 2021

J. High Energ. Phys.

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We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter x and the dimension d, in the whole kinematic range of x. The method is based on differential equations, which, however, do not require any special form, and series expansions around singular and regular points. This method provides results well suited for fast numerical evaluation and sufficiently precise for phenomenological applications. We apply the approach to four-loop on-shell integrals and compute the coefficient function of eight colour structures in the relation between the mass of a heavy quark defined in the $$ \overline{\mathrm{MS}} $$ MS ¯ and the on-shell scheme allowing for a second non-zero quark mass. We also obtain analytic results for these eight coefficient functions in terms of harmonic polylogarithms and iterated integrals. This allows for a validation of the numerical accuracy.

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