REVIEW
Grand unification of $\mu-\tau$ Symmetry
High Energy Physics - Phenomenology · Submitted 2 Mar 2006 · 23 references
Pith's verdict: Interesting GUT attempt at mu-tau symmetry, but the stated symmetry doesn't generate the mass textures used in the fit.
T0 · AI review
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Referee report
The paper
The paper claims
A supersymmetric SU(5) grand unified model can obey μ-τ symmetry and still fit all fermion masses, predicting a nonzero θ13 that is correlated with θ23.
The reading
What carries the argument
The load-bearing object is a discrete $\mu$-$\tau$ exchange symmetry imposed on the SU(5) superpotential: $F_\mu\leftrightarrow F_\tau$, $(h,\bar h)\leftrightarrow(h,\bar h)$, and $(H,\bar H)\to(-H,-\bar H)$, with all other fields singlets. This forces the neutrino mass matrix into the form with equal (2,3) and (3,2) entries and equal (2,2) and (3,3) entries, so in the exact limit $\theta_{13}=0$ and $\theta_{23}$ is maximal. The same symmetry constrains the down-quark and charged-lepton matrices via the 5 and 45 Higgs couplings, so the fitted $U_l$ carries the symmetry breaking into the neutrino sector. Neutrino masses come from the type-II seesaw through the 15-dimensional Higgs, and a one-loop gluino-squark correction to the (1,1) entry of the down-quark mass matrix repairs the otherwise too-small $m_d$. Those ingredients combine into the predicted nonzero $\theta_{13}$ and nonmaximal $\theta_{23}$.
Extended reading notes
Core claim
The central claim is that an apparently purely leptonic symmetry, the exchange of the muon and tau generations, can be promoted to a symmetry of a complete quark-lepton unified theory. In the exact limit, the neutrino mass matrix in the flavor basis has equal off-diagonal entries, so $\theta_{13}=0$ and $\theta_{23}=\pi/4$. Once embedded in SU(5), the same symmetry forces specific textures on the down-quark and charged-lepton mass matrices through the 5 and 45 Higgs couplings. Fitting the GUT-scale fermion masses fixes a left-handed charged-lepton mixing matrix $U_l$, and the relations $\sin\theta_{13}=|U_{l21}-U_{l31}|/\sqrt{2}$ and $\tan\theta_{23}=|U_{l22}-U_{l32}|/|U_{l23}-U_{l33}|$ convert the quark-lepton unified structure into small deviations from the symmetric limit. Typical fits give $\theta_{13}\simeq0.026$ with $\theta_{23}\simeq44.3^\circ$ and $\theta_{13}\simeq0.198$ with $\theta_{23}\simeq41.2^\circ$, while most scan points have $\sin^2\theta_{13}\le0.05$. The paper concludes that a viable supersymmetric SU(5) model with $\mu$-$\tau$ symmetry, type-II seesaw, and no extra matter fermions exists.
Load-bearing premise
The charged-fermion fit assumes that quantum corrections from superpartner loops change the down-quark mass matrix significantly only in its (1,1) entry; if those corrections also affect other entries or the charged-lepton matrix, the fitted $U_l$, and hence the predicted $\theta_{13}$, could change.
Editorial extensions
If this is right
- A measurement of $\theta_{13}$ at the level typical of the model's fits, with most scan points having $\sin^2\theta_{13}\le0.05$, would support the $\mu$-$\tau$ GUT picture, while a high-precision null result would disfavor this class of models.
- The fitted $U_l$ ties the departure of $\theta_{23}$ from $\pi/4$ to $\theta_{13}$, so long-baseline measurements of both angles provide a direct test of the correlation.
- The type-II seesaw scale near $10^{14}$ GeV is compatible with gauge-coupling unification at $M_{\rm GUT}\simeq2.36\times10^{16}$ GeV, so the neutrino-mass mechanism does not spoil the unification the model is built on.
- Replacing the 45-dimensional Higgs with a Planck-suppressed operator yields $\sin^2\theta_{23}\sim0.76$\,–\,0.8, which is already excluded by data, so the 45 representation is the viable embedding.
- The model adds no new fermion families beyond the three SU(5) generations, so the matter content needed for this unification is minimal.
Reading between the lines
- The paper does not compute charged-lepton flavor-violating rates; a direct extension would be to derive $\mu\to e\gamma$ and $\tau\to\mu\gamma$ branching ratios from the same $U_l$, turning the fitted mixings into collateral predictions.
- A further test would be to check whether the (1,1)-only threshold correction survives a complete treatment of non-universal soft supersymmetry breaking; if it does not, the scan's allowed $\theta_{13}$ range would shift.
- The S3-symmetric version of the neutrino mass matrix, which the paper discusses, reproduces tribimaximal mixing in the symmetric limit; if future data require $\theta_{13}$ near the upper end of the SU(5) model's range, that would point to the GUT corrections rather than the S3 limit.
Original abstract
Near maximal neutrino mixing needed to understand atmospheric neutrino data can be interpreted to be a consequence of an interchange symmetry between the muon and tau neutrinos in the neutrino mass matrix in the flavor basis. This idea can be tested by a measurement of the neutrino mixing parameter $\theta_{13}$ and looking for its correlation with $\theta_{23}-\pi/4$. We present a supersymmetric SU(5) grand unified model for quarks and leptons which obeys this exchange symmetry and is a realistic model that can fit all observations. GUT embedding shifts $\theta_{13}$ from its zero $\mu-\tau$ symmetric value to a nonzero value keeping it under an upper limit.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. 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.
The abstract, sentence by sentence
Near maximal neutrino mixing needed to understand atmospheric neutrino data can be interpreted to be a consequence of an interchange symmetry between the muon and tau neutrinos in the neutrino mass matrix in the flavor basis. This idea can be tested by a measurement of the neutrino mixing parameter $\theta_{13}$ and looking for its correlation with $\theta_{23}-\pi/4$. We present a supersymmetric SU(5) grand unified model for quarks and leptons which obeys this exchange symmetry and is a realistic model that can fit all observations. GUT embedding shifts $\theta_{13}$ from its zero $\mu-\tau$ symmetric value to a nonzero value keeping it under an upper limit.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Near maximal neutrino mixing needed to understand atmospheric neutrino data can be interpreted to be a consequence of an interchange symmetry between the muon and tau neutrinos in the neutrino mass matrix in the flavor basis. | background 0.68 | 0.13 | 0.26 | hedged possibility 0.75 |
| s1 | This idea can be tested by a measurement of the neutrino mixing parameter $\theta_{13}$ and looking for its correlation with $\theta_{23}-\pi/4$. | future work 0.74 | 0.09 | 0.08 | asserted 0.53 |
| s2 | We present a supersymmetric SU(5) grand unified model for quarks and leptons which obeys this exchange symmetry and is a realistic model that can fit all observations. | contribution 0.96 | 0.89 | 0.46 | asserted 1.00 |
| s3 | GUT embedding shifts $\theta_{13}$ from its zero $\mu-\tau$ symmetric value to a nonzero value keeping it under an upper limit. | result 0.95 | 0.72 | 0.26 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- 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
Figures
Figures reproduced from arXiv:hep-ph/0603020 by the authors.
References
How the literature uses it
4 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 2 papers
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The subindex $μ-τ$ in Eq. ([ref]) refers to the so-called $μ-τ$ symmetry [ref] since it satisfies the relations $|U_μi| = |U_τi|$.
Deviations to Tri-Bi-Maximal mixing in the limit of $\mu-\tau$ symmetry · Introduction · 0.91
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Such a specific form of the mixing matrix has inspired a large number of theoretical works based on this symmetry pattern [ref] .
Restricting Majorana phases in the Tri-Bi-Maximal limit · Introduction · 0.90
Discussion
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