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

Fael, Matteo; Schönwald, Kay; Steinhauser, Matthias

doi:10.1007/jhep10(2020)087

Cited by 29 publications

(20 citation statements)

References 44 publications

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“…[31] but we consider the internal charm mass effects beyond the linear approximation in m c /m 1S using the results in ref. [32]. For the charm quark, we use the relation between the pole and the MS masses up to the O(α 3 s ) order [33,34,35,36,37,38,39,40].…”

Section: Determination Of |V Cb |mentioning

confidence: 99%

Determination of $|V_{cb}|$ using N$^3$LO perturbative corrections to $Γ(B \to X_c \ell ν)$ and 1S masses

Hayashi,

Sumino,

Takaura

2022

Preprint

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We determine |V cb | using the third-order perturbative series for the inclusive semileptonic B decay width and for the masses of the bottomonium 1S states. We use the masses of η b (1S) and Υ(1S) as short-distance masses and point out that there is a sizable difference of |V cb | between the two 1S mass schemes. This is the dominant error of our determination and stems from insufficiency to describe theoretically the observed mass splitting of the bottomonium 1S states. We also study the significance of the O(Λ 2 MS ) non-perturbative effects in HQET with respect to the current perturbative accuracy. Our result |V cb | = 0.0425( 11) is consistent with the PDG value determined from the inclusive decays and has a slightly larger error. G m 2 b + O((Λ MS /m b ) 3 ) . (1)

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Section: Determination Of |V Cb |mentioning

confidence: 99%

Determination of $|V_{cb}|$ using N$^3$LO perturbative corrections to $Γ(B \to X_c \ell ν)$ and 1S masses

Hayashi,

Sumino,

Takaura

2022

Preprint

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“…In contrast, one may argue [32] that the bottom pole to MS mass conversion factor should be expressed in terms of α (3) s (m b ) rather than the four-flavour coupling α (4) s (m b ). For the two-and three-loop coefficients, for which the mass dependence is known [41][42][43], this substitution indeed renders the charm mass effect almost negligible. A quantitative investigation of bottom and charm mass effects on the top pole mass series was undertaken in [20,44].…”

Section: Internal Quark Mass Effectsmentioning

confidence: 98%

Pole mass renormalon and its ramifications

Beneke

2021

Eur. Phys. J. Spec. Top.

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I review the structure of the leading infrared renormalon divergence of the relation between the pole mass and the $$\overline{\mathrm{MS}}$$ MS ¯ mass of a heavy quark, with applications to the top, bottom and charm quark. That the pole quark mass definition must be abandoned in precision computations is a well-known consequence of the rapidly diverging series. The definitions and physics motivations of several leading renormalon-free, short-distance mass definitions suitable for processes involving nearly on-shell heavy quarks are discussed.

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“…(1.4)) it is possible to obtain analytic results in terms of iterated integrals. We use the same techniques already discussed for the calculation at O(α 3 s ) [31] and presented in ref. [37].…”

Section: Ms-os Relation At Four Loops: Analytic Resultsmentioning

confidence: 99%

“…The first three letters define the harmonic polylogarithms, the following two letters are also needed for the calculation at O(α 3 s ) [31] while the last two cyclotomic letters are needed for the n m • n l colour factors at O(α 4 s ). The application of this algorithm to the example in eq.…”

Section: Jhep09(2021)152mentioning

confidence: 99%

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

Cited by 29 publications

References 44 publications

Determination of $|V_{cb}|$ using N$^3$LO perturbative corrections to $Γ(B \to X_c \ell ν)$ and 1S masses

Determination of $|V_{cb}|$ using N$^3$LO perturbative corrections to $Γ(B \to X_c \ell ν)$ and 1S masses

Pole mass renormalon and its ramifications

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

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