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Simple On-Shell Renormalization Framework for the Cabibbo-Kobayashi-Maskawa Matrix
High Energy Physics - Theory · Submitted 5 Dec 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Diagonalization of the complete mass matrices leads then to an explicit expression for the CKM counterterm matrix, which is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are non-singular in the limit in which any two fermions become mass degenerate.
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The abstract, sentence by sentence
We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix at the one-loop level. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, and to adjust non-diagonal mass counterterm matrices to cancel all the divergent sm contributions, and also their finite parts subject to constraints imposed by the hermiticity of the mass matrices. It is also shown that the proof of gauge independence and finiteness of the remaining one-loop corrections to W -> q_i + anti-q_j reduces to that in the unmixed, single-generation case. Diagonalization of the complete mass matrices leads then to an explicit expression for the CKM counterterm matrix, which is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are non-singular in the limit in which any two fermions become mass degenerate.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix at the one-loop level. | contribution 1.00 | 0.95 | 0.23 | asserted 1.00 |
| s1 | It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, and to adjust non-diagonal mass counterterm matrices to cancel all the divergent sm contributions, and also their finite parts subject to constraints imposed by the hermiticity of the mass matrices. | method 0.98 | 0.93 | 0.16 | asserted 1.00 |
| s2 | It is also shown that the proof of gauge independence and finiteness of the remaining one-loop corrections to W -> q_i + anti-q_j reduces to that in the unmixed, single-generation case. | result 0.87 | 0.88 | 0.16 | asserted 1.00 |
| s3 | Diagonalization of the complete mass matrices leads then to an explicit expression for the CKM counterterm matrix, which is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are non-singular in the limit in which any two fermions become mass degenerate. | result 0.96 | 0.92 | 0.56 | asserted 1.00 |
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The paper
Original abstract
We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix at the one-loop level. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, and to adjust non-diagonal mass counterterm matrices to cancel all the divergent sm contributions, and also their finite parts subject to constraints imposed by the hermiticity of the mass matrices. It is also shown that the proof of gauge independence and finiteness of the remaining one-loop corrections to W -> q_i + anti-q_j reduces to that in the unmixed, single-generation case. Diagonalization of the complete mass matrices leads then to an explicit expression for the CKM counterterm matrix, which is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are non-singular in the limit in which any two fermions become mass degenerate.
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References
How the literature uses it
6 arXiv papers cite this in 15 sentences
Papers whose main result relates to this one's
States the same result 3 papers
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Diagonalization of the complete mass matrix leads to an explicit CKM counterterm matrix, which automatically satisfies all the following important properties: it is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are non-singular in the limit in which any two fermions become mass degenerate.
Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix · 1.00
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Diagonalization of the latter then leads to explicit expressions for the CKM counterterm matrix, which are gauge independent, preserve unitarity, and lead to renormalized amplitudes that are non-singular in the limit in which any two quarks become mass degenerate.
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It leads to a CKM matrix counterterm which is gauge parameter independent and satisfies the unitarity constraint, and renormalized physical amplitudes which are gauge parameter independent and smooth in quark mass difference.
Papers citing it · 7 sentences without a confident label
Uses its method or tool 2 papers
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An explicit expression for $δm_ii^'$ in the SM can be obtained by using Eq. (21) of Ref. [ref] , which provides the Feynman amplitude $M_ii^'^(1)$ corresponding to Fig. [ref] in the $R_ξ$ gauges.
A Novel Formulation of Cabibbo-Kobayashi-Maskawa Matrix Renormalization · Introduction · 0.86
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We renormalize the bare Lagrangian of the top sector based on the on-shell wave function renormalization scheme [ref] , largely following the method of Ref. [ref] .
Loop Induced Single Top Partner Production and Decay at the LHC · Wavefunction and Mass Renormalization of Top Partner · 1.00
Compares with it 1 paper
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A comparative analysis of the calculations of the $W$-boson hadronic widths in various CKM renormalization schemes, including the ones proposed here and in Refs. [ref] , is presented in Ref. [ref] .
A Novel Formulation of Cabibbo-Kobayashi-Maskawa Matrix Renormalization · Introduction · 0.91
Cites it as background 5 papers
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Recently, a new approach to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) matrix [ref] at the one-loop level in the Standard Model (SM) framework was proposed [ref] .
A Novel Formulation of Cabibbo-Kobayashi-Maskawa Matrix Renormalization · Introduction · 0.85
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In the sequel, various proposals were made for a gauge-parameter-independent renormalization of the quark-mixing matrix [ref] .
Renormalization of mixing angles · Introduction · 0.90
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For the special case of the CKM matrix different methods were discussed in the literature: [ref] proposed to set the momenta of the non-diagonal entries of the quark self-energies to zero, [ref] suggested new variants of renormalization in particular for the mixing matrices themselves partially based on physical processes which allows one to get gauge independent decay widths.
Electroweak corrections to Neutralino and Chargino decays into a W-boson in the (N)MSSM · Introduction · 0.88
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