Generalized factorization in non-leptonic two-body B-decays: A critical look

Andrzej J. Buras; Luca Silvestrini

doi:10.1016/S0550-3213(99)00022-X

Generalized factorization in non-leptonic two-body B-decays: A critical look

Andrzej J. Buras, Luca Silvestrini

Chair of Theoretical Elementary Particle Physics

Technical University of Munich

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

We reanalyze critically the generalized factorization hypothesis in non-leptonic two-body B-decays discussed recently by several authors. In particular we address the determination of the factorization scale μ_f and of the non-perturbative parameters ξ^NF₁(m_b) and ξ^NF₂(m_b) which are supposed to measure non-factorizable contributions to hadronic matrix elements with ξ^NF_i(μ_f) = 0. We emphasize that both μ_f and ξ^NF_i(m_b) are renormalization scheme dependent and we demonstrate analytically and numerically that for any chosen scale μ_f = O(m_b) it is possible to find a renormalization scheme for which ξ^NF₁(μ_f) = ξ^NF₂(μ_f) = 0. The existing data indicate that such "factorization schemes" differ from the commonly used schemes NDR and HV. Similarly we point out that the recent extractions of the effective number of colours N^eff from two-body non-leptonic B-decays while μ and renormalization scheme independent suffer from gauge dependences and infrared dependences.

Original language	English
Pages (from-to)	293-308
Number of pages	16
Journal	Nuclear Physics, Section B
Volume	548
Issue number	1-3
DOIs	https://doi.org/10.1016/S0550-3213(99)00022-X
State	Published - 24 May 1999

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title = "Generalized factorization in non-leptonic two-body B-decays: A critical look",

abstract = "We reanalyze critically the generalized factorization hypothesis in non-leptonic two-body B-decays discussed recently by several authors. In particular we address the determination of the factorization scale μf and of the non-perturbative parameters ξNF1(mb) and ξNF2(mb) which are supposed to measure non-factorizable contributions to hadronic matrix elements with ξNFi(μf) = 0. We emphasize that both μf and ξNFi(mb) are renormalization scheme dependent and we demonstrate analytically and numerically that for any chosen scale μf = O(mb) it is possible to find a renormalization scheme for which ξNF1(μf) = ξNF2(μf) = 0. The existing data indicate that such {"}factorization schemes{"} differ from the commonly used schemes NDR and HV. Similarly we point out that the recent extractions of the effective number of colours Neff from two-body non-leptonic B-decays while μ and renormalization scheme independent suffer from gauge dependences and infrared dependences.",

author = "Buras, \{Andrzej J.\} and Luca Silvestrini",

note = "Funding Information: Two-body non-leptonic B-decays play an important role in the phenomenology of weak decays not only probing the structure of weak interactions corrected by short distance QCD effects but also providing some insight into the non-perturbative phenomena related to long distances. The increasing experimental information on these decays, in particular from the CLEO detector, stimulated recently several new theoretical analyses of these decays. The most extensive analyses of this type are based on the factorization * Supported by the German Bundesministefium fiir Bildung and Forschung under contract 06 TM 874 and by the DFG project Li 519/2-2.",

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T1 - Generalized factorization in non-leptonic two-body B-decays

T2 - A critical look

AU - Buras, Andrzej J.

AU - Silvestrini, Luca

N1 - Funding Information: Two-body non-leptonic B-decays play an important role in the phenomenology of weak decays not only probing the structure of weak interactions corrected by short distance QCD effects but also providing some insight into the non-perturbative phenomena related to long distances. The increasing experimental information on these decays, in particular from the CLEO detector, stimulated recently several new theoretical analyses of these decays. The most extensive analyses of this type are based on the factorization * Supported by the German Bundesministefium fiir Bildung and Forschung under contract 06 TM 874 and by the DFG project Li 519/2-2.

PY - 1999/5/24

Y1 - 1999/5/24

N2 - We reanalyze critically the generalized factorization hypothesis in non-leptonic two-body B-decays discussed recently by several authors. In particular we address the determination of the factorization scale μf and of the non-perturbative parameters ξNF1(mb) and ξNF2(mb) which are supposed to measure non-factorizable contributions to hadronic matrix elements with ξNFi(μf) = 0. We emphasize that both μf and ξNFi(mb) are renormalization scheme dependent and we demonstrate analytically and numerically that for any chosen scale μf = O(mb) it is possible to find a renormalization scheme for which ξNF1(μf) = ξNF2(μf) = 0. The existing data indicate that such "factorization schemes" differ from the commonly used schemes NDR and HV. Similarly we point out that the recent extractions of the effective number of colours Neff from two-body non-leptonic B-decays while μ and renormalization scheme independent suffer from gauge dependences and infrared dependences.

AB - We reanalyze critically the generalized factorization hypothesis in non-leptonic two-body B-decays discussed recently by several authors. In particular we address the determination of the factorization scale μf and of the non-perturbative parameters ξNF1(mb) and ξNF2(mb) which are supposed to measure non-factorizable contributions to hadronic matrix elements with ξNFi(μf) = 0. We emphasize that both μf and ξNFi(mb) are renormalization scheme dependent and we demonstrate analytically and numerically that for any chosen scale μf = O(mb) it is possible to find a renormalization scheme for which ξNF1(μf) = ξNF2(μf) = 0. The existing data indicate that such "factorization schemes" differ from the commonly used schemes NDR and HV. Similarly we point out that the recent extractions of the effective number of colours Neff from two-body non-leptonic B-decays while μ and renormalization scheme independent suffer from gauge dependences and infrared dependences.

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Generalized factorization in non-leptonic two-body B-decays: A critical look

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