REVIEW
Predictive Neutrino Spectrum in Minimal $SO(10)$ Grand Unification
High Energy Physics - Phenomenology · Submitted 4 Sep 1992 · 20 references
Pith's verdict: The induced-126-vev mechanism is a real idea and the prediction structure is honest, but one of the four headline numbers contradicts the paper's own printed mixing matrix.
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Referee report
The paper
The paper claims
In a minimal SO(10) grand unified model, an induced Higgs vacuum expectation value ties the heavy neutrino mass matrix to charged-fermion observables, so the light neutrino spectrum becomes a prediction rather than a fit.
The reading
What carries the argument
The load-bearing object is the induced vacuum expectation value of the $126$'s $(2,2,15)$ doublet, $v_{u,d} ~ lambda (v_R^2 / M_Sigma^2) kappa_{u,d}$, generated by the $Delta_R Delta_R Sigma Phi$ contraction of the cubic term $lambda Delta Delta Delta H$. It does double duty: it shifts the charged-lepton and down-quark matrices apart by an amount of the right size to fix $m_d = m_e$ and $m_s = m_mu$, and because the same $f$ matrix sets the Majorana mass $f v_R$, it converts the see-saw formula into a statement about quark masses and the CKM matrix. The paper rewrites the three lepton mass matrices directly in terms of $M_u$, $M_d$ and two vev ratios, so that the leptonic mixing matrix follows from the CKM matrix plus two parameters.
Extended reading notes
Core claim
The paper claims that in minimal $SO(10)$ with a single complex $10$ and a single $126$ of Higgs scalars, the light neutrino spectrum is computable from charged-fermion observables. The mechanism is the induced vacuum expectation value of the $126$'s Standard Model doublet, generated at tree level by the cubic Higgs coupling, which enters the mass matrices as $M_u = h kappa_u + f v_u$, $M_d = h kappa_d + f v_d$, $M_{D nu} = h kappa_u - 3 f v_u$, $M_l = h kappa_d - 3 f v_d$ and $M_{M nu} = f v_R$. The relative factor of $-3$ between the neutrino and charged-lepton channels is what makes the two sectors distinguishable while keeping them tied to the same coupling matrix $f$. Solving the charged-fermion sector first — using the trace relation to fix $r_1 = kappa_d/kappa_u$ and fitting $r_2 = v_d/v_u$ — the authors obtain three acceptable numerical solutions and read off $sin theta_{e tau} = 3|V_{td}| = 0.05$, $sin theta_{mu tau} = 3|V_{cb}| = 0.12$–$0.16$, $sin theta_{e mu} = 0$–$0.3$, and $m_{nu_tau}/m_{nu_mu} >= 10^3$. They note explicitly that no solution gives large enough $nu_e$–$nu_mu$ mixing for vacuum oscillation, and that the atmospheric neutrino anomaly cannot be explained this way.
Load-bearing premise
The whole prediction rests on the induced doublet vacuum expectation value landing near 100 MeV, which the authors obtain by assuming the survival hypothesis with $M_U ~ 10^{15}$ GeV, $M_I ~ 3 times 10^{12}$ GeV and $M_Sigma ~ 10^{14}$ GeV; they acknowledge this as an assumption rather than deriving those scales from the breaking chain.
Editorial extensions
If this is right
- The $nu_mu$–$nu_tau$ mixing angle is fixed near three times $|V_{cb}|$, roughly $0.12$–$0.16$, so $nu_mu$–$nu_tau$ oscillations should appear in forthcoming experiments.
- The mass ratio $m_{nu_tau}/m_{nu_mu} >= 10^3$ forces $m_{nu_mu} <= 1.6 times 10^{-3}$ eV, which places the small-angle non-adiabatic MSW solution within reach and predicts a gallium capture rate near 50 SNU.
- The $nu_e$–$nu_tau$ mixing angle is predicted at about $3|V_{td}| = 0.05$, opening a second, subdominant channel for solar neutrino depletion.
- Because the model relates the Majorana matrix to charged-fermion observables, a measured deviation in the down-quark to electron mass ratio at the unification scale would feed directly into a shift in the predicted neutrino mixings.
- The overall neutrino mass scale is not predicted, only the ratios; it is set separately by $v_R$, which differs between the non-supersymmetric chain and the supersymmetric version.
Reading between the lines
- The prediction $sin theta_{mu tau} = 3|V_{cb}|$ is a genuinely sharp number rather than a range, so the model would be cleanly distinguished by any oscillation result showing near-maximal $nu_mu$–$nu_tau$ mixing.
- The same induced-vev mechanism could be transplanted to other unified embeddings where a heavy scalar supplies both the see-saw scale and a correction to the down-quark mass relations, which suggests the predictivity is a property of the double duty, not of $SO(10)$ specifically.
- Since the paper finds no solution with large $nu_e$–$nu_mu$ mixing, the model's viability depends on the solar solution being the small-angle MSW one; a confirmed large-mixing-angle solar solution would remove the model's most natural home.
- The authors treat the CP-violating phases as small perturbations and report finding no consistent fit for large phases, which hints that the parameter counting that yields eight predictions may be tighter than the stated thirteen-to-thirteen match suggests.
Original abstract
We show that minimal SO(10) Grand Unification models where the fermions have Yukawa couplings to only one (complex) {\bf 10} and one {\bf 126} of Higgs scalars lead to a very predictive neutrino spectrum. This comes about since the standard model doublet contained in the {\bf 126} of Higgs (needed for the see--saw mechanism) receives an induced vacuum expectation value at tree--level, which, in addition to correcting the bad asymptotic mass relations $m_d=m_e$ and $m_s=m_\mu$, also relates the Majorana neutrino mass matrix to observables in the charged fermion sectors. We find that (i) the $\nu_e-\nu_{\mu}$ mixing angle relevant for the solar neutrinos can be considerably smaller than the Cabibbo angle and lies in the range ${\rm sin}\theta_{e \mu}= 0-0.3$, (ii) $\nu_e-\nu_\tau$ mixing is sin$\theta_{e \tau} \simeq 3|V_{td}| \simeq 0.05$, (iii) the $\nu_\mu-\nu_\tau$ mixing angle is large, ${\rm sin}\theta_{\mu \tau} \simeq 3|V_{cb}|=0.12-0.16$, and (iv) $m_{\nu_\tau}/m_{\nu_\mu} \ge 10^3$, implying that $\nu_{\mu}-\nu_\tau$ oscillations should be accessible to forthcoming experiments.
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 show that minimal SO(10) Grand Unification models where the fermions have Yukawa couplings to only one (complex) {\bf 10} and one {\bf 126} of Higgs scalars lead to a very predictive neutrino spectrum. This comes about since the standard model doublet contained in the {\bf 126} of Higgs (needed for the see--saw mechanism) receives an induced vacuum expectation value at tree--level, which, in addition to correcting the bad asymptotic mass relations $m_d=m_e$ and $m_s=m_\mu$, also relates the Majorana neutrino mass matrix to observables in the charged fermion sectors. We find that (i) the $\nu_e-\nu_{\mu}$ mixing angle relevant for the solar neutrinos can be considerably smaller than the Cabibbo angle and lies in the range ${\rm sin}\theta_{e \mu}= 0-0.3$, (ii) $\nu_e-\nu_\tau$ mixing is sin$\theta_{e \tau} \simeq 3|V_{td}| \simeq 0.05$, (iii) the $\nu_\mu-\nu_\tau$ mixing angle is large, ${\rm sin}\theta_{\mu \tau} \simeq 3|V_{cb}|=0.12-0.16$, and (iv) $m_{\nu_\tau}/m_{\nu_\mu} \ge 10^3$, implying that $\nu_{\mu}-\nu_\tau$ oscillations should be accessible to forthcoming experiments.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that minimal SO(10) Grand Unification models where the fermions have Yukawa couplings to only one (complex) {\bf 10} and one {\bf 126} of Higgs scalars lead to a very predictive neutrino spectrum. | contribution 0.63 | 0.91 | 0.78 | asserted 1.00 |
| s1 | This comes about since the standard model doublet contained in the {\bf 126} of Higgs (needed for the see--saw mechanism) receives an induced vacuum expectation value at tree--level, which, in addition to correcting the bad asymptotic mass relations $m_d=m_e$ and $m_s=m_\mu$, also relates the Majorana neutrino mass matrix to observables in the charged fermion sectors. | interpretation 0.60 | 0.63 | 0.13 | asserted 1.00 |
| s2 | We find that (i) the $\nu_e-\nu_{\mu}$ mixing angle relevant for the solar neutrinos can be considerably smaller than the Cabibbo angle and lies in the range ${\rm sin}\theta_{e \mu}= 0-0.3$, (ii) $\nu_e-\nu_\tau$ mixing is sin$\theta_{e \tau} \simeq 3|V_{td}| \simeq 0.05$, (iii) the $\nu_\mu-\nu_\tau$ mixing angle is large, ${\rm sin}\theta_{\mu \tau} \simeq 3|V_{cb}|=0.12-0.16$, and (iv) $m_{\nu_\tau}/m_{\nu_\mu} \ge 10^3$, implying that $\nu_{\mu}-\nu_\tau$ oscillations should be accessible to forthcoming experiments. | result 1.00 | 0.95 | 0.64 | asserted 0.99 |
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References
How the literature uses it
79 arXiv papers cite this in 126 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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In this talk, I report some recent work with K.S.Babu, where we discovered that the minimal SO(10) model, both with and without SUSY, has in it a built-in mechanism that not only corrects the bad mass relations between the charged fermions but at the same time allows a complete prediction for the masses and mixings in the neutrino sector.
Minimal SO(10) Grand Unification: Predictions for Proton Decay and Neutrino Masses and Mixings: · 0.84
Papers citing it · 81 sentences without a confident label
Compares with it 1 paper
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The Yukawa sum rules obtained in Eq. ([ref]) are identical to the one obtained in the minimal suspersymmetric $SO(10)$ model [ref] with an important difference that the effective theory below the GUT scale is two-Higgs-doublet model (2HDM) of type II in the present case.
Leptogenesis and fermion mass fit in a renormalizable $SO(10)$ model · Yukawa sector of minimal $SO(10)$ and Right-Handed neutrino mass spectrum · 0.95
Cites it as support 2 papers
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These vevs are unavoidably induced when $SU(2)_L×U(1)_Y$ is broken by the $_H$ [ref] .
Dark Matter from the vector of SO(10) · The SO(10) framework · 0.96
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The Yukawa Lagrangian of the model is given by: [equation] The first two terms of Eq. ([ref]) with symmetric Yukawa matrices $Y_10$ and $Y_126$ lead to realistic and predictive neutrino spectrum which is compatible with current observations [ref] .
Hybrid SO(10) Axion Model Without Quality Problem · Introduction · 0.97
Cites it as background 36 papers
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The minimal supersymmetric version, coined renormalizable, suggested already in 1982 [ref] and rediscussed ten years later [ref] , has been under scrutiny in recent years [ref] .
Supersymmetry and Unification: Heavy Top Was the Key · SO(10) · 0.81
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The super heavy gauge bosons and scalars carrying fractional charges as well as nontrivial color quantum numbers can mediate various proton decay modes [ref] .
CDF II W-mass anomaly and SO(10) GUT · CDF W boson mass anomaly and non-SUSY $SO(10)$ GUT · 0.92
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The minimal $SO(10)$ model containing $10,126, 126$ and $210$ representations has been extensively studied [ref] .
Fermion Masses and Mixings in a $\mu$-$\tau$ symmetric SO(10) · Introduction · 0.97
Discussion
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