High Energy Physics - Phenomenology · arXiv:hep-ph/9409309 v1 · submitted 14 Sep 1994
QCD Factors a1 and a2 Beyond Leading Logarithms Versus Factorization in Non-Leptonic Heavy Meson Decays
The paper says
“We point out that a1 for B-decays depends very weakly on $\Lms$, μ and the choice of the renormalization scheme.”
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Abstract
We calculate the QCD factors a1 and a2, entering the tests of factorization in non-leptonic heavy meson decays, beyond the leading logarithmic approximation in three renormalization schemes (NDR, HV, DRED). We investigate their μ–dependence and the renormalization scheme dependence. We point out that a1 for B-decays depends very weakly on $\Lms$, μ and the choice of the renormalization scheme. For $\Lms^{(5)}=225\pm85~MeV$ and 4 GeV ≤ μ ≤ 8 GeV we find a1 = 1.01 ± 0.02 in accordance with phenomenology. The $\Lms$, μ and scheme dependences of a2 are on the other hand sizable. Interestingly, for the NDR scheme we find a2NDR = 0.20 ± 0.05, in the ball park of recent phenomenological results and substantially larger than leading order estimates. However a2HV = 0.16 ± 0.05 and a2DRED = 0.15 ± 0.05. Implications of these findings for the tests of factorization in B-decays and D-decays are critically discussed.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.73 · human participants 0.01 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.95 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We calculate the QCD factors $a_1$ and $a_2$, entering the tests of factorization in non-leptonic heavy meson decays, beyond the leading logarithmic approximation in three renormalization schemes (NDR, HV, DRED). | contribution 1.00 | 0.96 | 0.07 | asserted 0.99 |
| We investigate their $\mu$--dependence and the renormalization scheme dependence. | contribution 0.97 | 0.91 | 0.03 | asserted 0.72 |
| We point out that $a_1$ for B-decays depends very weakly on $\Lms$, $\mu$ and the choice of the renormalization scheme. | result 1.00 | 0.88 | 0.21 | asserted 1.00 |
| For $\Lms^{(5)}=225\pm85~MeV$ and $4~GeV\leq\mu\leq 8~GeV$ we find $a_1=1.01\pm0.02$ in accordance with phenomenology. | result 1.00 | 0.97 | 0.17 | asserted 1.00 |
| The $\Lms$, $\mu$ and scheme dependences of $a_2$ are on the other hand sizable. | result 1.00 | 0.86 | 0.14 | asserted 1.00 |
| Interestingly, for the NDR scheme we find $a_2^{NDR}=0.20\pm0.05$, in the ball park of recent phenomenological results and substantially larger than leading order estimates. | result 0.99 | 0.96 | 0.19 | asserted 0.99 |
| However $a_2^{HV}=0.16\pm0.05$ and $a_2^{DRED}=0.15\pm0.05$. | result 1.00 | 0.95 | 0.09 | asserted 1.00 |
| Implications of these findings for the tests of factorization in B-decays and D-decays are critically discussed. | interpretation 0.99 | 0.67 | 0.08 | unclear 0.70 |
What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from simulation or computation 0.73
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,494 input tokens, $0.0003 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
Cited by 4 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Unitary $KK$ and $K\pi$ inputs for an amplitude analysis of the $D^+ \to K^-K^+\pi^+$ decay hep-ph · Nov 2026
- Using $B^0_s\to D_s^\mp K^\pm$ Decays as a Portal to New Physics hep-ph · Sep 2021
- $A_{\textrm{CP}}[D_{(s)}^{0,+} \to V \gamma]$ from Large ${\cal O}_8$ hep-ph · Oct 2012
- Unravelling theoretical challenges in understanding $B_c$ meson decay hep-ph · Nov 2024
How the literature uses it
10 arXiv papers cite this in 17 sentences
Papers citing it · 10 sentences without a confident label
Uses its method or tool 1 paper
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Therefore, for the description of such processes, we use the approximation of the infinite number of colors ($N_c→∞$) proposed in Ref [ref] .
Exclusive semileptonic and nonleptonic $J/\psi$ decays · INTRODUCTION · 0.87
Uses its data or values 4 papers
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Theoretically, Ref. [ref] obtained $a_1=1.31(19)$ and $a_2$ ranging between $-0.55(15)$ and $-0.60(22)$, depending on the chosen renormalization scheme.
A combined study of hadronic $D^+\to K^-\pi^+\pi^+$ and $D_s^+\to K^+K^+\pi^-$ decays by means of the analysis of semileptonic $D^+\to K^-\pi^+ \ell^+\nu_\ell$ decays · Naïve factorization in decays · 0.96
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For the QCD factors $a_1,2$ we use the phenomenological values $a_1=1.2±0.1$ and $a_2=-0.5±0.1$, obtained from different analyses of two-body $D$ meson decays [ref] .
K pi form factors, final state interactions and D+ -> K- pi+ pi+ decays · Theoretical framework · 0.97
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For these factors we use the phenomenological values [equation] obtained from different analyses of two-body $D$ meson decays [ref] .
Kpi form factors and final state interactions in D+ --> K- pi+ pi+ decays · Theoretical framework · 0.92
Cites it as background 1 paper
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In naive factorisation, $a_NF^(q)=a_1$, where $a_1$ represents the appropriate combination of Wilson coefficient functions of the current-current operators[For a detailed discussion, see Ref. [ref] .].
Anatomy of $B\rightarrow D\bar{D}$ Decays · Information from Semileptonic Decays · 0.84
Challenges and discussion
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