REVIEW
Quark Mass Ratios and Mixing Angles from SU(3) Family Gauge Symmetry
High Energy Physics - Phenomenology · Submitted 14 Mar 2006 · 10 references
Pith's verdict: A genuinely predictive radiative flavor model that honestly reports its own theta13 failure, but the hidden-sector VEV hierarchy it leans on is assumed rather than derived.
T0 · AI review
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Referee report
The paper
The paper claims
A weak SU(3) family gauge force can radiatively generate the quark masses and CKM angles, except for θ13.
The reading
What carries the argument
The load-bearing object is the hidden-sector sextet vacuum $\langle H\rangle$ of Eq. (4)---a symmetric $3\times3$ matrix (the symmetric tensor representation of SU(3)) with order-one diagonal entries $a_i$ and small off-diagonal entries $b_i$ of order $b<1$, misaligned with the visible-sector sextet vacua $\langle S\rangle$ and $\langle\Sigma\rangle$. Through the family gauge boson mass matrix, this $b$ hierarchy propagates into the one-loop corrected visible vacua $\langle S\rangle'$ and $\langle\Sigma\rangle'$ (Eqs. (11)--(12)), whose first row and column carry powers of $b$. These corrected vacua produce the down-type mass matrix directly and, through the up-type seesaw formula of Eq. (16), generate the up-type masses and CKM angles; the Yukawa ratio $z=y_2/y_3$ controls the charm and up masses. The whole predictive structure is the way powers of $\alpha/\pi$ and $b$ assemble into the observed small numbers.
Extended reading notes
Core claim
The paper's central claim is that the pattern of up-type quark masses, down-type quark masses, and CKM mixing angles---with the exception of $\theta_{13}$---arises radiatively from a relatively weak SU(3) family gauge interaction with sequential symmetry breaking. At tree level the visible-sector vacuum makes only the $b$ and $t$ quarks massive and leaves mixing angles zero. One-loop exchange of the family gauge bosons corrects the effective scalar vacuum, producing entries of order $\alpha/\pi$ and $\alpha b/\pi$ in the down and up mass matrices. The resulting leading-order formulas are $m_d/m_b\sim(\alpha/\pi)b^2$, $m_s/m_b\sim\alpha/\pi$, $m_u/m_t\sim(\alpha^2/\pi^2) b z$, $m_c/m_t\sim(\alpha/\pi) z/b$, $\theta_{23}\sim\alpha/\pi$, and $\theta_{12}\sim b$, with $\theta_{13}\sim(\alpha^2/\pi^2)b$. Using $\alpha/\pi\approx0.04$, $b\approx0.2$, and $z\approx0.04$, these fit the measured six quantities up to order-one coefficients, while $\theta_{13}$ is too small by nearly an order of magnitude; the CP-violating phase is naturally $O(1)$.
Load-bearing premise
The entire derivation rests on the hidden-sector scalar $H$ developing the hierarchical, misaligned vacuum assumed in Eq. (4), with order-one diagonal entries and small off-diagonal entries $b\approx0.2$; the paper does not exhibit a potential that produces this vacuum, and if the $b$ hierarchy fails the predicted mass ratios and mixing angles collapse.
Editorial extensions
If this is right
- If the framework is correct, the light-generation quark masses and CKM angles are outputs of one loop of family gauge exchange, controlled by just two small parameters ($b$, $z$) plus the gauge coupling; they are not independent inputs.
- The very small up-quark mass is protected: $m_u/m_t$ is second order in $\alpha/\pi$, and the paper argues that two-loop corrections cannot change its leading-order value.
- The predicted $\theta_{13}\sim(\alpha/\pi)^2 b$ is about $4\times10^{-4}$, while the measured value is near $3.7\times10^{-3}$; within this model the observed $\theta_{13}$ therefore requires additional physics beyond the minimal field content.
- The $b$ and $t$ masses set $y_d\approx10^{-2}$ and $y_1\approx4$ at the family scale, so a precise low-energy comparison requires renormalization-group running from that scale down to $M_Z$, which the paper sets aside.
Reading between the lines
- Beyond the paper: the assumed $b$ hierarchy should be verified by constructing an explicit scalar potential for $S$, $\Sigma$, and $H$ whose global minimum realizes Eq. (4) with $b\approx0.2$; the paper asserts that such terms exist but does not exhibit them.
- Beyond the paper: the exact cancellation that leaves $\theta_{13}$ small follows only from the up-down universality of the one-loop corrections, so any repair of the $\theta_{13}$ deficit likely needs non-universal up/down couplings or additional tree-level flavor structure, not just higher-loop effects.
- Beyond the paper: if the same hidden-sector tilt also controls neutrinos, lepton mixing angles and the seesaw scale would be correlated with the same $b$ and $\alpha/\pi$ parameters, giving a checkable link between the quark and lepton sectors.
Original abstract
We explore a framework for the computation of quark mass ratios and CKM mixing angles based on an SU(3) family gauge symmetry. The four ratios md/mb, ms/mb, mu/mt, and mc/mt can be fit at one-loop in the family gauge interaction. The same is true of the quark mixing angles theta12 and theta23, although the result for theta13 is too small. The CP violating phase is naturally O(1).
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
We explore a framework for the computation of quark mass ratios and CKM mixing angles based on an SU(3) family gauge symmetry. The four ratios md/mb, ms/mb, mu/mt, and mc/mt can be fit at one-loop in the family gauge interaction. The same is true of the quark mixing angles theta12 and theta23, although the result for theta13 is too small. The CP violating phase is naturally O(1).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We explore a framework for the computation of quark mass ratios and CKM mixing angles based on an SU(3) family gauge symmetry. | contribution 0.96 | 0.78 | 0.09 | asserted 0.52 |
| s1 | The four ratios md/mb, ms/mb, mu/mt, and mc/mt can be fit at one-loop in the family gauge interaction. | result 0.98 | 0.84 | 0.22 | asserted 0.95 |
| s2 | The same is true of the quark mixing angles theta12 and theta23, although the result for theta13 is too small. | result 0.72 | 0.89 | 0.26 | asserted 1.00 |
| s3 | The CP violating phase is naturally O(1). | result 0.98 | 0.80 | 0.13 | 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
References
How the literature uses it
4 arXiv papers cite this in 6 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 4 papers
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Based on the dominant contribution, these models can generally be classified into two categories: * Spin-0 mediated models: These involve scalar particles in the fermion self-energy loops (see [ref] for examples), and require the extension of the SM Yukawa sector. * Spin-1 mediated models: These involve vector bosons in the self-energy loops [ref] .
Radiative Mass Generation in Gauged Theories of Flavour: A Path to Fermion Mass Hierarchies · Radiative mass generation · 0.85
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However, the model can be put into one of these categories depending on the most-dominant contribution considered.] (a) spin-0 (see [ref] for example) and (b) spin-1 [ref] .
Gauged $SU(3)_F$ and loop induced quark and lepton masses · Introduction · 0.97
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other types of flavor models including extra-dims [ref] and Froggatt Nielsen [ref] and family symmetries [ref] with funny charges [ref] a model without flavor symmetries [ref]
A Domino Theory of Flavor · Flavor Philosophy · 0.96
Discussion
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