The pole mass in perturbative QCD

Tarrach, R.

doi:10.1016/0550-3213(81)90140-1

Cited by 455 publications

(358 citation statements)

References 10 publications

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“…In numerical form it reads [164] 32) where ω = √ s − M is the only dimensionful quantity in the effective theory and L ω = ln(µ 2 /ω 2 ). The tilde and the prime remind that the quantity on the left-hand side of Eq.…”

Section: Heavy-light Current Correlatorsmentioning

confidence: 99%

“…where the coefficients γ m,i are known up to the four-loop order [32,33,34,15,16] For the computation of γ m one has to know the quark mass renormalization constant in the MS scheme, Z m , which relates the bare mass, m 0 , to the renormalized one through…”

Section: Global Infra-red Re-arrangement and The Quark Anomalous Dimementioning

confidence: 99%

“…For the relation between the MS and on-shell quark mass one finds up to three loops [32,123,124,125,126] …”

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confidence: 99%

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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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Section: Heavy-light Current Correlatorsmentioning

confidence: 99%

Section: Global Infra-red Re-arrangement and The Quark Anomalous Dimementioning

confidence: 99%

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Results and techniques of multi-loop calculations

Steinhauser

2002

Physics Reports

100

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“…They are computed and parameterized in the so-called matching scheme, which has been introduced in [35] and specified in appendix B of [15] (see also [32] for another detailed discussion). Our formulae for all relevant operators below refer to the two-flavour theory and are based on their anomalous dimensions known up to three-loop order in continuum perturbation theory [39][40][41][42][43][44][45][46][47][48][49][50][51], to be combined with the matching coefficients between QCD and the effective theory up to two loops [2,43,[52][53][54], see appendix B of [15]. In order to judge the impact of the order of the perturbative expansion on this comparison between QCD and HQET, introduced by the conversion functions C X as far as they enter the observables under study, we evaluate the C X including the two-loop and three-loop anomalous dimensions (together with the respective matching coefficients in one-and two-loop accuracy) separately.…”

Section: B Conversion Functionsmentioning

confidence: 99%

Non-perturbative tests of continuum HQET through small-volume two-flavour QCD

Fritzsch

Garrón

Heitger

2016

J. High Energ. Phys.

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Abstract:We study the heavy quark mass dependence of selected observables constructed from heavy-light meson correlation functions in small-volume two-flavour lattice QCD after taking the continuum limit. The light quark mass is tuned to zero, whereas the range of available heavy quark masses m h covers a region extending from around the charm to beyond the bottom quark mass scale. This allows entering the asymptotic mass-scaling regime as 1/m h → 0 and performing well-controlled extrapolations to the infinite-mass limit. Our results are then compared to predictions obtained in the static limit of continuum Heavy Quark Effective Theory (HQET), in order to verify non-perturbatively that HQET is an effective theory of QCD. While in general we observe a nice agreement at the per cent level, we find it to be less convincing for the small-volume pseudoscalar decay constant when perturbative matching is involved.

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“…For α s , given the value α s (M t ), which we get from the running of the RGE's from the unification to the M t scale, we can compute Λ QCD at M t using the approximate solution for α s in the SM [36] Later using the same formula we can extrapolate α s at M Z . To compute the top quark pole mass we use [37] M pol t = M t (M t ) 1 + 4 3π α 3 (M t )…”

Section: Acknowledgementsmentioning

confidence: 99%

Unification of gauge couplings and the tau-neutrino mass in supergravity without R parity

et al. 2000

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Minimal R-parity violating supergravity predicts a value for α s (M Z ) smaller than in the case with conserved the R-parity, and therefore closer to the experimental world average. We show that the R-parity violating effect on the α s prediction comes from the larger two-loop b-quark Yukawa contribution to the renormalization group evolution of the gauge couplings which characterizes R-parity violating supergravity. The effect is correlated to the tau neutrino mass and is sensitive to the initial conditions on the soft supersymmetry breaking parameters at the unification scale. We show how a few percent effect on α s (M Z ) may naturally occur even with ν τ masses as small as indicated by the simplest neutrino oscillation interpretation of the atmospheric neutrino data from Super-Kamiokande.

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The pole mass in perturbative QCD

Cited by 455 publications

References 10 publications

Results and techniques of multi-loop calculations

Results and techniques of multi-loop calculations

Non-perturbative tests of continuum HQET through small-volume two-flavour QCD

Unification of gauge couplings and the tau-neutrino mass in supergravity without R parity

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