RECORD
Third Family Corrections to Tri-bimaximal Lepton Mixing and a New Sum Rule
High Energy Physics - Phenomenology · Submitted 29 Nov 2007
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule 's = r cos delta + 2/3 a' (where s, r, a describe the deviations of solar, reactor and atmospheric mixing angles from their tri-bimaximal values, and 'delta' is the observable Dirac CP phase) which is stable under all leading order third family wave-function corrections, as well as Cabibbo-like charged lepton mixing effects.
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 investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. At leading order both sorts of corrections can be subsumed into a single universal parameter. For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule 's = r cos delta + 2/3 a' (where s, r, a describe the deviations of solar, reactor and atmospheric mixing angles from their tri-bimaximal values, and 'delta' is the observable Dirac CP phase) which is stable under all leading order third family wave-function corrections, as well as Cabibbo-like charged lepton mixing effects.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. | contribution 0.99 | 0.87 | 0.06 | asserted 0.59 |
| s1 | Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. | background 0.96 | 0.11 | 0.02 | hedged possibility 0.82 |
| s2 | At leading order both sorts of corrections can be subsumed into a single universal parameter. | result 0.52 | 0.58 | 0.07 | asserted 0.95 |
| s3 | For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule 's = r cos delta + 2/3 a' (where s, r, a describe the deviations of solar, reactor and atmospheric mixing angles from their tri-bimaximal values, and 'delta' is the observable Dirac CP phase) which is stable under all leading order third family wave-function corrections, as well as Cabibbo-like charged lepton mixing effects. | result 0.95 | 0.90 | 0.92 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- 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 investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. At leading order both sorts of corrections can be subsumed into a single universal parameter. For hierarchical neutrinos, this leads to a new testable lepton mixing sum rule 's = r cos delta + 2/3 a' (where s, r, a describe the deviations of solar, reactor and atmospheric mixing angles from their tri-bimaximal values, and 'delta' is the observable Dirac CP phase) which is stable under all leading order third family wave-function corrections, as well as Cabibbo-like charged lepton mixing effects.
Human review
References
How the literature uses it
21 arXiv papers cite this in 42 sentences
Papers citing it · 31 sentences without a confident label
Builds on it 1 paper
-
Regarding the tri-bimaximal mixing example, we go beyond the analysis of [ref] by considering CN corrections in a realistic class of SU(3) flavour symmetry models and by providing additional details regarding the derivation of the CN results and of the procedure of combining CN corrections with corrections from renormalisation group (RG) running and Cabibbo-like charged lepton mixing contributions (i.e. regarding the there proposed stable mixing sum rule).
Third Family Corrections to Quark and Lepton Mixing in SUSY Models with non-Abelian Family Symmetry · Introduction · 1.00
Uses its method or tool 2 papers
-
Using the approximate formulae of [ref] , we can obtain estimates for the mixing angles of the MNS mixing matrix as
From Flavour to SUSY Flavour Models · The Lepton Sector · 1.00
-
Taking $Y^e ≈diag(0,0,y_τ)$ and $Y^ν≈diag(0,0,y_ν_3)$, one finds, to leading log approximation, that there is a single parameter which governs the RG corrections to all the mixing angles given by [ref] : [equation] Assuming tri-bimaximal neutrino mixing at the GUT scale, the low energy scale parameters are then given approximately by: [equation]
Deviations from Tri-bimaximal Mixing: Charged Lepton Corrections and Renormalization Group Running · Justification of the numerical approach · 0.85
Uses its data or values 1 paper
-
$< g r a p h i c s >$ Corrections to the tri-bimaximal neutrino mixing due to canonical normalisation (taken from [ref] ).
Third Family Corrections to Quark and Lepton Mixing in SUSY Models with non-Abelian Family Symmetry · Canonical normalisation corrections to tri-bimaximal neutrino mixing · 0.95
Compares with it 2 papers
-
Combining them we find the improved sum rule s≈rcosδ+ 2/3a (1-2m_2^ν/m_3^νcosα_2) which, compared to [ref] , includes next-to-leading correction to $s$ of the form $O( a m_2/m_3)$.
Perturbative Estimates of Lepton Mixing Angles in Unified Models · Other Limits, Applications and Sum Rules · 0.85
-
It is remarkable that Eq.([ref]) belongs to a set of well-known leptonic mixing sum rules [ref] , and the same results have been obtained in Ref. [ref] .
Adjoint SUSY $SU(5)$ Grand Unified Model with $S_4$ Flavor Symmetry · Down type quarks and charged leptons sector · 0.91
Cites it as support 1 paper
-
Furthermore, since $θ^e_13∼θ^e_23∼0$, two sum rules for lepton mixing are respected [ref] .
SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry · Down quark and charged lepton sector · 0.97
Cites it as background 3 papers
-
However it should also be noted that the above predictions are valid at the GUT scale and are subject to renormalisation group (RG) [ref] and canonical normalisation (CN) [ref] corrections.
A Grand Delta(96) x SU(5) Flavour Model · Predictions for PMNS Mixing · 0.82
-
[ref] ), or from the next order in small angle expansion for the charged lepton mixing effects.
Large neutrino mixing angle \theta_{13}^{MNS} and quark-lepton mass ratios in unified flavour models · Predictions for $θ_13$ · 0.80
-
In general one can expect corrections coming from renormalisation group (RG) running [ref] as well as canonical normalisation corrections [ref] .
A to Z of Flavour with Pati-Salam · Numerical results for neutrino masses and lepton mixing · 0.85
What it cites · 7 sentences without a confident label
Cites as background 3 papers
-
Many models attempt to reproduce this as a theoretical prediction [ref] .
Deviations from Tri-bimaximal Neutrino Mixing in Type-II Seesaw and Leptogenesis · Introduction · 0.95
-
Many models attempt to reproduce this as a theoretical prediction [ref] .
U_{PMNS} = U_ell^dagger U_nu · Introduction · 0.95
-
Many models attempt to reproduce this as a theoretical prediction [ref] .
Near Tribimaximal Neutrino Mixing with Delta(27) Symmetry · Introduction · 0.95
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.