QCD non-leading corrections to weak decays as an application of regularization by dimensional reduction

Altarelli, Guido; Curci, G; Martinelli, G.; Petrarca, S.

doi:10.1016/0550-3213(81)90473-9

Cited by 292 publications

(245 citation statements)

References 32 publications

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“…Equating A full and A eff in Eqs. (12) and (13) at a scale µ 0 translates into the following identity [24] …”

Section: General Structurementioning

confidence: 99%

“…After the pioneering Leading Order (LO) calculation of the O(α n s L n ) contributions [8], the resummation of the O(α n s L n−1 ) logarithms has been completed more than ten years ago and subsequently confirmed by several groups. The main components of the perturbative Next-to-Leading Order (NLO) calculation are i) the one-loop O(α s ) corrections to the relevant Wilson coefficient functions [9][10][11] and ii) the two-loop O(α 2 s ) Anomalous Dimension Matrix (ADM) describing the mixing of the associated physical operators [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Effective Hamiltonian for non-leptonic decays at NNLO in QCD

2005

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We compute the effective hamiltonian for non-leptonic |∆F | = 1 decays in the standard model including next-to-next-to-leading order QCD corrections. In particular, we present the complete three-loop anomalous dimension matrix describing the mixing of currentcurrent and QCD penguin operators. The calculation is performed in an operator basis which allows to consistently use fully anticommuting γ 5 in dimensional regularization at an arbitrary number of loops. The renormalization scheme dependences and their cancellation in physical quantities is discussed in detail. Furthermore, we demonstrate how our results are transformed to a different basis of effective operators which is frequently adopted in phenomenological applications. We give all necessary two-loop constant terms which allow to obtain the three-loop anomalous dimensions and the corresponding initial conditions of the two-loop Wilson coefficients in the latter scheme. Finally, we solve the renormalization group equation and give the analytic expressions for the low-energy Wilson coefficients relevant for non-leptonic B meson decays beyond next-to-leading order in both renormalization schemes.

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“…Equating A full and A eff in Eqs. (12) and (13) at a scale µ 0 translates into the following identity [24] …”

Section: General Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effective Hamiltonian for non-leptonic decays at NNLO in QCD

2005

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“…The coefficients h ± w are known to two loops in perturbation theory [40], while h m remain undetermined. In Eq.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Probing the chiral weak Hamiltonian at finite volumes

Hernández¹,

Laine²

2006

J. High Energy Phys.

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Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants could be determined at finite volumes by matching the non-perturbatively measured three-point correlation functions between the weak Hamiltonian and two left-handed flavour currents, to analytic predictions following from chiral perturbation theory. Here we complete the analytic side in two respects: by inspecting how small ("ǫ-regime") and intermediate or large ("p-regime") quark masses connect to each other, and by including in the discussion the two leading ∆I = 1/2 operators. We show that the ǫ-regime offers a straightforward strategy for disentangling the coefficients of the ∆I = 1/2 operators, and that in the p-regime finite-volume effects are significant in these observables once the pseudoscalar mass M and the box length L are in the regime M L < ∼ 5.0. July 20061 pilar.hernandez@ific.uv.es 2

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“…The sum over the quarks q runs over the active flavours at the scale µ. Note that we use here the labeling of the operators as given in [7,8] which differs from [1]- [3] by the interchange 1 ↔ 2. Q 1 and Q 2 are the so-called current-current operators, Q 3−6 the QCD-penguin operators and Q 7−10 the electroweak penguin operators.…”

Section: Effective Hamiltonianmentioning

confidence: 99%

“…Similarly, the renormalization scheme dependence of C i (µ) cancels the one of Q i (µ) . It should be stressed that these cancellations involve generally several terms in the expansion (1).…”

Section: Introductionmentioning

confidence: 99%

Non-leptonic two-body B decays beyond factorization

2000

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We present a general scheme and scale independent parameterization of two-body non-leptonic B decay amplitudes which includes perturbative QCD corrections as well as final state interactions in a consistent way. This parameterization is based on the Next-to-Leading effective Hamiltonian for non-leptonic B decays and on Wick contractions in the matrix elements of the local operators. Using this parameterization, and making no dynamical assumption, we present a classification of two-body B decay channels in terms of the parameters entering in the decay amplitudes. This classification can be considered as the starting point for a model-independent analysis of non-leptonic B decays and of CP violating asymmetries. We also propose, on the basis of the large N expansion, a possible hierarchy among the different effective parameters. We discuss the strategy to extract the most important effective parameters from the experimental data. Finally, we establish a connection between our parameterization and the diagrammatic approach which is widely used in the literature.

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QCD non-leading corrections to weak decays as an application of regularization by dimensional reduction

Cited by 292 publications

References 32 publications

Effective Hamiltonian for non-leptonic decays at NNLO in QCD

Effective Hamiltonian for non-leptonic decays at NNLO in QCD

Probing the chiral weak Hamiltonian at finite volumes

Non-leptonic two-body B decays beyond factorization

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