RECORD
Fixed points in the evolution of neutrino mixings
High Energy Physics - Phenomenology · Submitted 5 Oct 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We identify fixed points in the equations for mixing angles, which can be reached during the evolution for several mass patterns and give $\sin^22\theta_{sol}=\sin^22\theta_{atm}\sin^2\theta_3/ (\sin^2\theta_{atm}\cos^2\theta_3 + \sin^2\theta_3)^2$, consistently with the present experimental information.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We derive the renormalization group equations for the neutrino masses and mixing angles in explicit form and discuss the possible classes of their solutions. We identify fixed points in the equations for mixing angles, which can be reached during the evolution for several mass patterns and give $\sin^22\theta_{sol}=\sin^22\theta_{atm}\sin^2\theta_3/ (\sin^2\theta_{atm}\cos^2\theta_3 + \sin^2\theta_3)^2$, consistently with the present experimental information. Further experimental test of this relation is of crucial interest. Moreover, we discuss the stability of quantum corrections to neutrino mass squared differences. Several interesting mass patterns show stability in the presence of fixed point solutions for the angles.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We derive the renormalization group equations for the neutrino masses and mixing angles in explicit form and discuss the possible classes of their solutions. | contribution 0.72 | 0.95 | 0.07 | asserted 0.99 |
| s1 | We identify fixed points in the equations for mixing angles, which can be reached during the evolution for several mass patterns and give $\sin^22\theta_{sol}=\sin^22\theta_{atm}\sin^2\theta_3/ (\sin^2\theta_{atm}\cos^2\theta_3 + \sin^2\theta_3)^2$, consistently with the present experimental information. | result 0.97 | 0.94 | 0.74 | asserted 0.63 |
| s2 | Further experimental test of this relation is of crucial interest. | future work 0.99 | 0.09 | 0.10 | asserted 0.88 |
| s3 | Moreover, we discuss the stability of quantum corrections to neutrino mass squared differences. | contribution 0.98 | 0.83 | 0.06 | unclear 0.50 |
| s4 | Several interesting mass patterns show stability in the presence of fixed point solutions for the angles. | result 0.97 | 0.84 | 0.15 | asserted 0.97 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We derive the renormalization group equations for the neutrino masses and mixing angles in explicit form and discuss the possible classes of their solutions. We identify fixed points in the equations for mixing angles, which can be reached during the evolution for several mass patterns and give $\sin^22\theta_{sol}=\sin^22\theta_{atm}\sin^2\theta_3/ (\sin^2\theta_{atm}\cos^2\theta_3 + \sin^2\theta_3)^2$, consistently with the present experimental information. Further experimental test of this relation is of crucial interest. Moreover, we discuss the stability of quantum corrections to neutrino mass squared differences. Several interesting mass patterns show stability in the presence of fixed point solutions for the angles.
Human review
References
How the literature uses it
13 arXiv papers cite this in 16 sentences
Papers citing it · 8 sentences without a confident label
Uses its method or tool 3 papers
-
The evolution of neutrino mass matrix $M^_ν$ from $Λ^_μτ$ down to $Λ^_EW$ through the one-loop RGE in MSSM can be expressed as [ref]
RGE-induced $\mu$-$\tau$ symmetry breaking: an analysis of the latest T2K results · Theoretical set-up · 0.98
-
To obtain the RGE for $U$, we adopt the procedure first introduced in Ref. [ref] for the renormalisation of the Cabbibo-Kobayashi-Maskawa mixing matrix, and later used for the neutrino case [ref] .
Running effects on neutrino parameters and l_i -> l_j gamma predictions in the triplet-extended MSSM · Running of the neutrino masses and mixing matrix · 1.00
-
After integrating Eq. (3.79), we get [ref] [equation] at $Λ^_EW$, where $I^_τ≃Diag {1, 1, 1-Δ^_τ}$ and [equation] Given $Λ^_FS∼10^14$ GeV, for example, $I^_α$ changes from 0.9 to 0.8 and $Δ^_τ$ changes from 0.002 to 0.044 when $tanβ$ varies from 10 to 50.
A review of mu-tau flavor symmetry in neutrino physics · RGE-induced $μ$-$τ$ symmetry breaking effects · 0.87
Cites it as background 5 papers
-
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
-
Specific features of the evolution, like the stability of mixing angles and masses [ref] , possible occurrence of fixed points [ref] , evolution of nearly degenerate Majorana neutrinos [ref] , the generation of large mixing angles from small angles at the high scale [ref] , or radiative generation of $U_e3$ starting from zero value at high scale [ref] , have been explored.
Renormalization group evolution of neutrino mixing parameters near $\theta_{13} = 0$ and models with vanishing $\theta_{13}$ at the high scale · Introduction · 0.97
-
The phenomenological implications have been discussed, e.g., in [ref] , demonstrating that one-loop quantum effects can have a strong impact on scenarios with degenerate neutrinos, leading to quasi-fixed points in the infrared for the elements of the leptonic mixing matrix, and generating a mass splitting between the initially degenerate eigenvalues.
Quantum effects on neutrino parameters from a flavored gauge boson · Introduction · 0.84
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.