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Running Neutrino Masses, Mixings and CP Phases: Analytical Results and Phenomenological Consequences
High Energy Physics - Phenomenology · Submitted 26 May 2003
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We derive simple analytical formulae for the renormalization group running of neutrino masses, leptonic mixing angles and CP phases, which allow an easy understanding of the running.
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The abstract, sentence by sentence
We derive simple analytical formulae for the renormalization group running of neutrino masses, leptonic mixing angles and CP phases, which allow an easy understanding of the running. Particularly for a small angle theta_13 the expressions become very compact, even when non-vanishing CP phases are present. Using these equations we investigate: (i) the influence of Dirac and Majorana phases on the evolution of all parameters, (ii) the implications of running neutrino parameters for leptogenesis, (iii) changes of the mass bounds from WMAP and neutrinoless double beta decay experiments, relevant for high-energy mass models, (iv) the size of radiative corrections to theta_13 and theta_23 and implications for future precision measurements.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We derive simple analytical formulae for the renormalization group running of neutrino masses, leptonic mixing angles and CP phases, which allow an easy understanding of the running. | contribution 0.94 | 0.96 | 0.42 | asserted 1.00 |
| s1 | Particularly for a small angle theta_13 the expressions become very compact, even when non-vanishing CP phases are present. | result 0.79 | 0.86 | 0.10 | asserted 1.00 |
| s2 | Using these equations we investigate: (i) the influence of Dirac and Majorana phases on the evolution of all parameters, (ii) the implications of running neutrino parameters for leptogenesis, (iii) changes of the mass bounds from WMAP and neutrinoless double beta decay experiments, relevant for high-energy mass models, (iv) the size of radiative corrections to theta_13 and theta_23 and implications for future precision measurements. | contribution 0.99 | 0.92 | 0.16 | asserted 0.90 |
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The paper
Original abstract
We derive simple analytical formulae for the renormalization group running of neutrino masses, leptonic mixing angles and CP phases, which allow an easy understanding of the running. Particularly for a small angle theta_13 the expressions become very compact, even when non-vanishing CP phases are present. Using these equations we investigate: (i) the influence of Dirac and Majorana phases on the evolution of all parameters, (ii) the implications of running neutrino parameters for leptogenesis, (iii) changes of the mass bounds from WMAP and neutrinoless double beta decay experiments, relevant for high-energy mass models, (iv) the size of radiative corrections to theta_13 and theta_23 and implications for future precision measurements.
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References
How later papers used it
67 later papers cite it
4 later papers by other authors are listed below: 4 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool.
Uses its method or tool 5 of 10 papers with this label · 1 by the same authors
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In order to do this we use the REAP 11.4 Mathematica package [ref] .
One String to Rule Them All: Neutrino Masses and Mixing Angles (2019) · RGE Evolution to the Electroweak Scale · 0.98
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Wrote down the renormalization group equations for leptonic mixing angles in the MSSM in the leading order approximation.
Breaking of the tetra-maximal neutrino mixing pattern (2019) · 0.84 · paraphrased: the licence does not allow quoting
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Followed its procedure to expand the renormalization group equations to leading order in the small mixing angle theta_13.
Running effects on neutrino parameters and l_i -> l_j gamma predictions in the triplet-extended MSSM (2009) · 1.00 · paraphrased: the licence does not allow quoting
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Calculated the mixing angles for the accepted points as a second step.
Neutrino mass hierarchy and the origin of leptonic flavor mixing from the right-handed sector (2011) · 0.93 · paraphrased: the licence does not allow quoting
By the same authors
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For the contribution of the 33 element of the neutrino Yukawa matrix $y_ν_3$ we took the light neutrino mass $m_ν_3≈50.14$meV and computed its RG evolution from the low scale up to the right-chiral neutrino mass scale $M_3$ (which we also varied in the MCMC analysis) according to the following (1-loop) equation [ref] : [equation] where $α=-3g_2^2+2(y_τ^2+y_μ^2+y_e^2)+6(y_t^2+y_b^2+y_c^2+y_s^2+y_u^2+y_d^2)+λ$, $θ_13$ and $θ_23$ are the PMNS-mixing angles, and $λ$ is the SM Higgs self-coupling.
Nucleon decay in a minimal non-SUSY GUT with predicted quark-lepton Yukawa ratios (2021) (same authors) · Viability of the GUT scale Yukawa ratios $y_τ/y_b = 3/2$ and $y_μ/y_s = 9/2$ · 0.96
How the literature uses it
57 arXiv papers cite this in 102 sentences
Papers citing it · 64 sentences without a confident label
Builds on it 1 paper
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As a practical application of these one-loop RGEs, we take the type-I SEFT for example and further derive the explicit expressions of the one-loop RGEs for the physical parameters involved in the charged- and neutral-current interactions of leptons, like those done for the type-I SEFT with only the Weinberg operator [ref] .
Complete One-loop Renormalization-group Equations in the Seesaw Effective Field Theories · Introduction · 0.96
Uses its method or tool 8 papers
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Considering the leading order approximation, we write down the renormalization group equations for leptonic mixing angles in the MSSM [ref] as
Breaking of the tetra-maximal neutrino mixing pattern · Spontaneous Breaking of TMM · 0.84
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Setting the small Majorana phases to zero and with $δ_MNS ≈90^∘$, we can estimate in leading order [ref] [equation] where $μ$ is the renormalisation scale.
Measurable Neutrino Mass Scale in A4 x SU(5) · Renormalisation Group Corrections · 0.82
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According to [ref] , the mass effects may be to a good degree approximated by universal multiplicative factors, e.g., [equation] where the hat denotes seesaw-scale quantities, see Section [ref].
Leptogenesis in the minimal flipped $SU(5)$ unification · Experimental inputs · 0.93
Uses its data or values 1 paper
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This evolution effect will be, in the first approximation, accounted for by a simple multiplication of their low-scale values ($m_i$) by a common $r$-factor, i.e., [equation] where $r ∼1.32$ (cf. Ref. [ref] and Appendix [ref]).
Leptogenesis in the minimal flipped $SU(5)$ unification · The seesaw · 0.91
Compares with it 3 papers
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As can be observed, the running of masses is quite substantial in Type-III seesaw, as compared to the SM, the MSSM [ref] , or the Type-I seesaw [ref] .
Renormalization group evolution of neutrino masses and mixing in the Type-III seesaw mechanism · Illustrative examples of RG running of masses and mixing · 1.00
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Not surprisingly, the results for $θ̇_ij^ν$ agree with those obtained for the MSSM in Ref. [ref] .
Running effects on neutrino parameters and l_i -> l_j gamma predictions in the triplet-extended MSSM · RGEs for the neutrino masses, mixing angles and CP-violating phases · 0.97
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We made full parameter scan via the RG evolution of the Majorana neutrinos with non-zero Majorana phases and show the correlations between the Majorana phases and “neutrino less double beta decay mass” $m_e e$ to be different compared to previous analyses [ref] where a few data points at unification scale were used.
Majorana phases in high-scale mixings unification hypotheses · Summary and Outlook · 0.92
Cites it as support 4 papers
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However, since the neutrino mass receives negligible RG running effect [ref] , the neutrino mass eigen-fields can be treated universally during the whole process.
Neutrino CP Measurement in the Presence of RG Running with Mismatched Momentum Transfers · Vacuum Oscillation with RG Running and Zero-Distance Effect · 0.98
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For such a hierarchical neutrino spectrum, the RGE running in the neutrino parameters can be considered negligible to a good approximation [ref] .
Order and Anarchy hand in hand in 5D SO(10) · Fitting the fermion mass spectrum: a viability test · 0.99
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The renormalization of the neutrino mass can be neglected for the normal hierarchy case [ref] .
Analysis of right-handed Majorana neutrino mass in an $SU(4) \times SU(2)_{L} \times SU(2)_{R}$ Pati--Salam model with democratic texture · Analysis of the right-handed Majorana neutrino mass matrix · 0.97
Cites it as background 16 papers
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RG Running and Zero-Distance Effect – In the presence of RG running, the Dirac CP phase $δ_D$ can possess scale dependence parametrized by its $β$ function [ref] , as follows: [equation] where $μ^2$ is the renormalization scale.
Testing the RG Running of the Leptonic Dirac CP Phase with Reactor Neutrinos · Introduction · 0.96
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The analysis of how $U_PMNS$ changes with the RG running has already extensively performed [ref] in the context of SM and MSSM.
Running Effects on Lepton Mixing Angles in Flavour Models with Type I Seesaw · Flavour symmetries and RGE effects · 0.96
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The RG equations (RGEs) for the Weinberg operator [ref] , which describes Majorana neutrino masses in SM effective field theory (SMEFT), have been calculated at 1-loop order in [ref] and recently at 2-loop order in [ref] ; phenomenological implications have been studied in [ref] .
Running of neutrino mass parameters in the Zee model · Introduction · 0.98
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