REVIEW
Novel Supersymmetric SO(10) Seesaw Mechanism
High Energy Physics - Phenomenology · Submitted 28 Jun 2005 · 22 references
Pith's verdict: A clean structural result — the B-L scale cancels from the light neutrino mass — with one load-bearing gap: μ = 0 is asserted rather than bounded.
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Referee report
The paper
The paper claims
In a supersymmetric SO(10) model with broken D-parity, the B-L breaking scale cancels out of the light neutrino mass formula, so that scale can sit at a few TeV while neutrinos stay as light as observed.
The reading
What carries the argument
The load-bearing object is the induced vacuum expectation value $⟨χ_L⟩ ≡ v_L ≃ ρ v_R v / M_{16}$, read off from the $F$-term condition of the $(1,2,1,∓1)$ component of $16_H$ in the superpotential $W_H$. It converts the $S$ to $ν_L$ entry of the neutrino mass matrix from an independent parameter into a quantity strictly proportional to $v_R$, which is exactly what cancels the $ν^c$ to $S$ entry in the determinant and yields a mass depending only on $v^2/M_G$. The second piece of machinery is the two-step breaking chain with broken D-parity, in which a light admixture of $(1,1,3,0)$ from $45_H$ and $210_H$ breaks $SU(2)_R$ at $V_R$ well above $10^{14}$ GeV while a light component of $16_H$ plus its conjugate breaks $U(1)_R ⊗ U(1)_{B-L}$ at $v_R$, keeping the unification prediction for $α_1^{-1}(M_Z)$ insensitive to $v_R$.
Extended reading notes
Core claim
The central claim is that in a supersymmetric $SO(10)$ theory with broken D-parity, the light neutrino mass is suppressed by the unification scale rather than by the $B-L$ breaking scale. The mechanism is a cancellation. In the basis $(ν_L, ν^c_L, S_L)$ the mass matrix has a $ν^c$ to $S$ entry $F v_R$ generated by $⟨χ_R⟩$, and an $S$ to $ν_L$ entry $F v_L$ generated by the left-handed partner $χ_L$. Supersymmetry ties the two: the $F$-term for the $(1,2,1,∓1)$ component of $16_H$ forces $v_L ≃ ρ v_R v / M_{16}$ once $χ_R$ and the electroweak doublets take vacuum expectation values. Substituting this into the mass matrix gives $M_ν ≃ (v^2/M_G) ρ [Y (F F_{inv})^T + (F F_{inv}) Y^T]$, in which $v_R$ no longer appears. Two features distinguish this from the ordinary and inverse seesaw: the result is linear, not quadratic, in the Dirac Yukawa couplings $Y$, and the overall scale can be tuned by the cubic Higgs coupling $ρ$ and by the ratio of $F$ to its partner coupling, which tends to one when there is a single $16_H$ plus its conjugate. The authors also show that gauge coupling unification tolerates this, provided the breaking is staged as $SU(2)_R ⊗ U(1)_{B-L}$ to $U(1)_R ⊗ U(1)_{B-L}$ to $U(1)_Y$ with $V_R$ much greater than $v_R$, so that the $v_R$ scale drops out of the prediction for $α_1^{-1}(M_Z)$ at one loop.
Load-bearing premise
The cancellation depends on the induced vacuum expectation value relation $v_L ≃ ρ v_R v / M_{16}$ holding exactly at leading order, with no extra contribution to the $ν$ to $S$ entry from additional Higgs copies, from the singlet mass $μ$ the paper sets to zero, or from higher-order superpotential terms.
Editorial extensions
If this is right
- The $B-L$ breaking scale can be as low as a few TeV, so a new neutral gauge boson with $B-L$ couplings may be light enough to be produced at the LHC through the Drell-Yan process.
- The heavy neutrinos of the mass matrix get their masses at $v_R$ and can be relatively light quasi-Dirac states at the TeV scale rather than superheavy.
- Exchange of those TeV-scale states can induce lepton flavour and CP violating processes, such as $μ$ to $e γ$, at rates comparable to the inverse seesaw.
- Gauge coupling unification survives because the two-stage breaking makes the prediction for $α_1^{-1}(M_Z)$ independent of $v_R$ at one loop, leaving $V_R$ above about $10^{14}$ GeV as the only constrained intermediate scale.
Reading between the lines
- The cancellation is a structural statement about one superpotential, not a symmetry: if the $ν$ to $S$ entry ever received a contribution not proportional to $v_R$, the suppression by $M_G$ would degrade to suppression by that new scale, so the mechanism's reach is set by how well the proportionality can be protected.
- Because the mass formula is linear in $Y$ rather than quadratic, the model's neutrino mass ratios trace the Dirac Yukawa matrix more directly than in the ordinary seesaw, which in principle makes the pattern of mixing angles a sharper discriminant between this scheme and its relatives.
- A TeV-scale $B-L$ boson with these couplings would also mediate rare decays and matter effects; the same parameter space that makes $μ$ to $e γ$ large tends to make the $Z'$ width and Drell-Yan cross section large, so a null LHC search and a null flavour-violation search constrain the scenario from two sides at once.
- The paper sets the singlet mass $μ$ to zero by invoking an unbroken $U(1)$ factor from an $E_6$ embedding; if that factor is broken at any scale, a nonzero $μ$ re-enters the mass matrix and the question becomes whether the resulting contribution stays subleading to the $v^2/M_G$ term.
Original abstract
We propose a new seesaw mechanism for neutrino masses within a class of supersymmetric SO(10) models with broken D-parity. It is shown that in such scenarios the B-L scale can be as low as TeV without generating inconsistencies with gauge coupling unification nor with the required magnitude of the light neutrino masses. This leads to a possibly light new neutral gauge boson as well as relatively light quasi-Dirac heavy leptons. These particles could be at the TeV scale and mediate lepton flavour and CP violating processes at appreciable levels.
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 propose a new seesaw mechanism for neutrino masses within a class of supersymmetric SO(10) models with broken D-parity. It is shown that in such scenarios the B-L scale can be as low as TeV without generating inconsistencies with gauge coupling unification nor with the required magnitude of the light neutrino masses. This leads to a possibly light new neutral gauge boson as well as relatively light quasi-Dirac heavy leptons. These particles could be at the TeV scale and mediate lepton flavour and CP violating processes at appreciable levels.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose a new seesaw mechanism for neutrino masses within a class of supersymmetric SO(10) models with broken D-parity. | contribution 1.00 | 0.87 | 0.21 | asserted 0.82 |
| s1 | It is shown that in such scenarios the B-L scale can be as low as TeV without generating inconsistencies with gauge coupling unification nor with the required magnitude of the light neutrino masses. | result 0.99 | 0.82 | 0.46 | asserted 0.77 |
| s2 | This leads to a possibly light new neutral gauge boson as well as relatively light quasi-Dirac heavy leptons. | interpretation 0.60 | 0.67 | 0.17 | hedged possibility 0.87 |
| s3 | These particles could be at the TeV scale and mediate lepton flavour and CP violating processes at appreciable levels. | interpretation 0.87 | 0.49 | 0.19 | hedged possibility 1.00 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:hep-ph/0506296 by the authors.
References
How the literature uses it
184 arXiv papers cite this in 258 sentences
Papers citing it · 141 sentences without a confident label
Contests it 1 paper
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This result shows that current data clearly favours the NP hypothesis, exclude conventional models with right-handed neutrinos leading to necessary destructive interference [ref] and promote the search for NP models as the ones presented in Refs. [ref] .
Modified lepton couplings and the Cabibbo-angle anomaly · Results and Conclusions · contest 0.73
Builds on it 4 papers
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This latter possibility is the case we have studied in a previous paper [ref] using the minimal $U(1)_B-L×U(1)_R$ models of [ref] .
Phenomenology of the minimal supersymmetric $U(1)_{B-L}\times U(1)_R$ extension of the standard model · Introduction · 0.81
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We will construct variants of the models proposed in [ref] and will also consider a completely new model, in which $v_R$ can be brought down to the electro-weak scale with the help of an intermediate Pati-Salam scale [ref] .
Soft masses in SUSY SO(10) GUTs with low intermediate scales · Introduction · 1.00
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We have discussed that one can not only construct sliding models in which an inverse or linear seesaw is consistent with GCU, as done in earlier work [ref] , but also all other known types of seesaws can, in principle, be found.
Supersymmetric SO(10) GUTs with sliding scales · Summary and conclusions · 0.94
Compares with it 5 papers
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The form of the mass matrix is same as in reference [ref] but the mechanism and the elements are different.
Type I and $new$ seesaw in left-right symmetric theories · $new$ seesaw in left-right symmetric theories · 1.00
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At this point we also stress that, in contrast to low-scale inverse [ref] or linear seesaw schemes [ref] , the presence of TeV-scale neutrino-mass-mediators does not require the addition of extra gauge singlets beyond the “right-handed neutrinos”.
Dynamical scoto-seesaw mechanism with gauged $B-L$ · Dynamical scoto-seesaw mechanism · 0.88
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In contrast to most previous formulations [ref] , here we assume just the minimal gauge structure.
Large lepton number violation at colliders: predictions from the minimal linear seesaw mechanism · Introduction · 0.85
Cites it as background 94 papers
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In [ref] , an extended supersymmetric model based on $SU(3)_c ×SU(2)_L ×U(1)_R ×U(1)_B-L$ was proposed.
Exploring the supersymmetric U(1)$_{B-L} \times$ U(1)$_{R}$ model with dark matter, muon $g-2$ and $Z^\prime$ mass limits · Introduction · 0.89
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Two popular models in this scenario are the ones obtained by setting $ϵm_S=μ'=0$, dubbed as Inverse Seesaw (ISS) [ref] or by imposing $μ=μ'=0$, dubbed as Linear Seesaw (LSS) [ref] , that predict the following active neutrino masses respectively m_ν^ISS≃- μ m_N m_N^TΛ_NS^2 , m_ν^LSS≃- ϵ m_S m_N^T + m_N m_S^TΛ_NS .
The Minimal Massive Majoron Seesaw Model · The Low-Scale Seesaw models · 0.87
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Instead, if the small parameter is the block $[M^(ν)]_13 ≡ε$, the model is called linear Seesaw [ref] , because the light neutrino masses are linear in $m_D$, of order $m_ν∼ε m_D/M_R$.
Neutrinos with a linear seesaw mechanism in a scenario of gauged B-L symmetry · Introduction · 0.82
Discussion
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