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On-shell renormalization of the mixing matrices in Majorana neutrino theories
High Energy Physics - Phenomenology · Submitted 22 Feb 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We generalize a recently proposed on-shell approach to renormalize the Cabibbo-Kobayashi-Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism.
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The abstract, sentence by sentence
We generalize a recently proposed on-shell approach to renormalize the Cabibbo-Kobayashi-Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. Also, the texture zero in the neutrino mass matrix is preserved.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We generalize a recently proposed on-shell approach to renormalize the Cabibbo-Kobayashi-Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. | contribution 1.00 | 0.91 | 0.30 | asserted 1.00 |
| s1 | An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. | result 0.94 | 0.77 | 0.23 | asserted 1.00 |
| s2 | Also, the texture zero in the neutrino mass matrix is preserved. | result 0.98 | 0.77 | 0.14 | asserted 1.00 |
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The paper
Original abstract
We generalize a recently proposed on-shell approach to renormalize the Cabibbo-Kobayashi-Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. Also, the texture zero in the neutrino mass matrix is preserved.
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References
How the literature uses it
6 arXiv papers cite this in 15 sentences
Papers citing it · 5 sentences without a confident label
Uses its method or tool 2 papers
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We follow the approach in [ref] .
On the On-Shell Renormalization of Fermion Masses, Fields, and Mixing Matrices at 1-loop · 1-loop rotation · 1.00
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By Autonne–Takagi matrix factorization,[ An explicit proof of this theorem may be found, e.g., in Appendix B of Ref. [ref] .] the complex, symmetric $N×N$ matrix $M^'0$ may be transformed into a real, diagonal matrix $M^0$ with nonnegative entries,[ In this paper, summation over repeated indices is not implied in the absence of summation symbols.] [equation] via a single unitary matrix $U_-$, as $M^0=U_-M^'0U_-^T$.
Propagator mixing renormalization for Majorana fermions · Unrenormalized dressed propagator matrix · 0.84
Compares with it 1 paper
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This allows for the comparison of divergent parts with [ref] for the quarks in the SM, for the comparison with [ref] in case of Majorana neutrinos and the corresponding mixing matrix while also providing new results.
On the On-Shell Renormalization of Fermion Masses, Fields, and Mixing Matrices at 1-loop · Introduction · 1.00
Cites it as background 3 papers
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As for the flavor mixing matrices of Majorana fermions, various renormalization prescriptions have been proposed at one loop for the case of stability [ref] .
Propagator mixing renormalization for Majorana fermions · Introduction · 0.99
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For lepton or neutrino mass matrices also [ref] proposed useful renormalization conditions allowing gauge independent results.
Electroweak corrections to Neutralino and Chargino decays into a W-boson in the (N)MSSM · Introduction · 0.85
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Related aspects in the onshell scheme are discussed, albeit in different contexts, for example, in Refs. [ref] .
Baryon Asymmetry from the Decay and Scattering of a Majorana Fermion Pair Coupled to Quarks · Renormalization of the $Χ_n Χ̅_m$ 2-point function · 0.97
What it cites · 15 sentences without a confident label
Builds on 1 paper
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The aim of this paper is to generalize the on-shell renormalization of the CKM matrix recently proposed in Ref. [ref] to extensions of the SM in which the lepton sector contains Majorana neutrinos.
Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix · Introduction · 0.98
Uses the method or tool of 1 paper
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Following the approach of Ref. [ref] , the analysis of external-leg corrections leads to two classes of contributions: (i) terms proportional to the virtual-fermion propagator $i/(-m_f^')$ with gauge-independent cofactors not involving $$, where $m_f^'$ stands generically for the mass of the virtual fermion; (ii) terms in which the virtual propagator is cancelled in both the diagonal and off-diagonal amplitudes.
Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix · Self-energy corrections to an external leg · 0.92
Compares with 1 paper
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At this point, we should emphasize that Eq. ([ref]) is the same as that for up-type quarks, given in Eq. (29) of Ref. [ref] , up to particle changes.
Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix · Outgoing charged lepton · 0.96
Cites as background 2 papers
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In fact, this problem has been the object of several interesting studies over the last two decades [ref] .
Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix · Introduction · 0.95
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In fact, this problem has been the object of several interesting studies over the last two decades [ref] .
Fermion Mixing Renormalization and Gauge Invariance · Introduction · 0.95
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