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Wolfenstein Parametrization at Higher Order: Seeming Discrepancies and Their Resolution
High Energy Physics - Phenomenology · Submitted 5 Jun 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that most of the discrepancies can be naturally resolved by a proper redefinition of the numerically small (of order $\lambda$) parameters.
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The abstract, sentence by sentence
In different Wolfenstein parametrizations derived from different exact parametrizations of the Cabibbo-Kobayashi-Maskawa matrix, we explicitly study seeming discrepancies between the matrix elements at the higher order of the expansion parameter $\lambda$. A systematic way of resolving the seeming discrepancies is proposed. We find that most of the discrepancies can be naturally resolved by a proper redefinition of the numerically small (of order $\lambda$) parameters. Our approach is further applied to the cases for the Wolfenstein-{\it like} parametrizations, such as the Qin-Ma parametrization.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In different Wolfenstein parametrizations derived from different exact parametrizations of the Cabibbo-Kobayashi-Maskawa matrix, we explicitly study seeming discrepancies between the matrix elements at the higher order of the expansion parameter $\lambda$. | contribution 0.82 | 0.89 | 0.05 | asserted 0.97 |
| s1 | A systematic way of resolving the seeming discrepancies is proposed. | contribution 0.68 | 0.82 | 0.12 | asserted 0.96 |
| s2 | We find that most of the discrepancies can be naturally resolved by a proper redefinition of the numerically small (of order $\lambda$) parameters. | result 1.00 | 0.96 | 0.81 | asserted 1.00 |
| s3 | Our approach is further applied to the cases for the Wolfenstein-{\it like} parametrizations, such as the Qin-Ma parametrization. | contribution 0.94 | 0.88 | 0.05 | asserted 0.99 |
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The paper
Original abstract
In different Wolfenstein parametrizations derived from different exact parametrizations of the Cabibbo-Kobayashi-Maskawa matrix, we explicitly study seeming discrepancies between the matrix elements at the higher order of the expansion parameter $\lambda$. A systematic way of resolving the seeming discrepancies is proposed. We find that most of the discrepancies can be naturally resolved by a proper redefinition of the numerically small (of order $\lambda$) parameters. Our approach is further applied to the cases for the Wolfenstein-{\it like} parametrizations, such as the Qin-Ma parametrization.
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References
How the literature uses it
19 arXiv papers cite this in 23 sentences
Papers citing it · 20 sentences without a confident label
Uses its data or values 2 papers
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Firstly, we collect the input parameters used in this work as below [ref] [equation] The branching ratios used in this paper are taken from the Particle Data Group [ref] [equation] As for the universal nonfactorizable parameters, we use the results fitted in Ref. [ref] , which are based on the factorization-assisted topological-amplitudes approach [equation] In order to see physics more transparently, we use the Wolfenstein parametrization of the CKM matrix elements, which imaginary part satisfy the unitarity relation to order $λ^5$ [ref] [equation] with $λ$, $A$, $ρ$ and $η$ are the real parameters.
Study of CP Violation in $D^{\pm}\rightarrow K^{\ast}(892)^{0} \pi^{\pm} + \bar{K}^{\ast }(892)^{0}\pi^{\pm}\rightarrow K_{S,L}^{0}\pi^0 \pi^{\pm}$ Decays · Input parameters · 0.97
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One has been found in Ref. [ref] : [equation] A global fit of the CKM matrix gives: $λ≃0.225$, $f ≃0.75$, $h̅ ≃1.35$ and the `maximal' phase $δ_QM ≃90^o$.
Second Generation of 'Miranda Procedure' for CP Violation in Dalitz Studies of B (\& D \& \tau) Decays · CKM Matrix Parametrization through $O( λ^6)$ · 0.90
Cites it as background 1 paper
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Within the SM, for CP asymmetries in charm decays one has to go to the CKM matrix through order $λ^6$ in the Wolfenstein parametrization [ref] and understand the differences between other parameterizations [ref] .
Model-Independent Analysis of CP Violation in Charmed Meson Decays · Decay amplitudes and CP asymmetries · 0.84
What it cites · 9 sentences without a confident label
Compares with 1 paper
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These relations are in agreement with those obtained in [ref] except for some higher order $λ$ corrections.
Remarks on the Qin-Ma Parametrization of Quark Mixing Matrix · Introduction · 0.99
Cites as background 3 papers
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A new Wolfenstein-like parametrization has been advocated recently by Qin and Ma (QM) [ref] in which the three angles are substituted by the parameters $λ, f$ and $h$ while the phase parameter $δ$ is still kept.
A new simple form of quark mixing matrix · Introduction · 0.84
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It was pointed out [ref] that as in any perturbative expansion, high order terms in $λ$ are not unique in the Wolfenstein parametrization, though the nonuniqueness of the high order terms does not change the physics.
Waiting for the Top Quark Mass, K^+ --> \pi^+ \nu \bar\nu, B_s^0-\bar{B}_s^0 Mixing and CP Asymmetries in B-Decays · Introduction · 0.81
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(Of course, the freedom of rotating the phase of quark fields will render the parametrization of the quark mixing matrix infinitely many.) Among them, the most popular ones are the KM, CK and Fritzsch-Xing (FX) [ref] parametrizations.
Flavor Symmetries and the Description of Flavor Mixing · Introduction · 0.92
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