Minimal subtraction and the decoupling of heavy quarks for arbitrary values of the gauge parameter

Wetzel, Werner

doi:10.1016/0550-3213(82)90038-4

Cited by 54 publications

(81 citation statements)

References 7 publications

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“…In Ref. [51] the decoupling constant for α s has been computed at the two-loop order. The crucial idea of the method is based on the fact that the decoupling theorem [48] works in momentum subtraction schemes.…”

Section: Decoupling Of Heavy Particlesmentioning

confidence: 99%

“…In order to make the decoupling explicit the two-loop result of [51] is needed. However, it turned out that after expressing the decay rate in terms of effective parameters the top quark did not decouple.…”

Section: Decoupling Of Heavy Particlesmentioning

confidence: 99%

“…It can be performed in a more or less complicated way. As it is even nowadays highly non-trivial to apply the methods of [51] and [52] at order α 3 s , we developed a procedure which relates the n-loop decoupling constants of Eq. (3.4) to n-loop massive one-scale integrals.…”

Section: Construction Of An Effective Lagrangian In Qcdmentioning

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: Decoupling Of Heavy Particlesmentioning

confidence: 99%

Section: Decoupling Of Heavy Particlesmentioning

confidence: 99%

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Results and techniques of multi-loop calculations

Steinhauser

2002

Physics Reports

100

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“…h is integrated out. Specifically, one constructs an effective n l -flavour theory by requiring consistency with the full n f -flavour theory at the heavy-quark threshold µ (n f ) = O(m h ) [4,5]. This leads to nontrivial matching conditions between the couplings and light-quark masses of the two theories.…”

Section: Introductionmentioning

confidence: 99%

“…Starting at next-to-next-to-leading (two-loop) order, they are broken by finite corrections, of O(α 2 s ), as was noticed in the pioneering works of Refs. [4,5]. The relations between the couplings and light-quark masses of the full and effective theories are called decoupling relations; the proportionality constants that appear in these relations are denoted decoupling constants, ζ g and ζ m .…”

Section: Introductionmentioning

confidence: 99%

Decoupling relations to O(αs3) and their connection to low-energy theorems

1998

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If quantum chromodynamics (QCD) is renormalized by minimal subtraction (MS), at higher orders, the strong coupling constant α s and the quark masses m q exhibit discontinuities at the flavour thresholds, which are controlled by so-called decoupling constants, ζ g and ζ m , respectively. Adopting the modified MS (MS) scheme, we derive simple formulae which reduce the calculation of ζ g and ζ m to the solution of vacuum integrals. This allows us to evaluate ζ g and ζ m through three loops. We also establish low-energy theorems, valid to all orders, which relate the effective couplings of the Higgs boson to gluons and light quarks, due to the virtual presence of a heavy quark h, to the logarithmic derivatives w.r.t. m h of ζ g and ζ m , respectively. Fully exploiting present knowledge of the anomalous dimensions of α s and m q , we thus calculate these effective couplings through four loops. Finally, we perform a similar analysis for the coupling of the Higgs boson to photons.

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Higgs decay into massive b-quarks at NNLO QCD in the nested soft-collinear subtraction scheme

Behring

Bizon

2020

J. High Energ. Phys.

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We present a fully differential description of a decay of a scalar Higgs boson into massive b-quarks valid at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics (QCD). We work within the nested soft-collinear subtraction scheme extended to accommodate massive partons. We include the loop-induced contribution involving a Higgs coupling to a top quark. We test our calculation against results existing in the literature, comparing the predictions for the total decay width and jet rates.

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Minimal subtraction and the decoupling of heavy quarks for arbitrary values of the gauge parameter

Cited by 54 publications

References 7 publications

Results and techniques of multi-loop calculations

Results and techniques of multi-loop calculations

Decoupling relations to O(αs3) and their connection to low-energy theorems

Higgs decay into massive b-quarks at NNLO QCD in the nested soft-collinear subtraction scheme

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