Proposal for a Supersymmetric Standard Model

C. Munoz; D.E. Lopez-Fogliani

REVIEW

Proposal for a Supersymmetric Standard Model

D.E. Lopez-Fogliani, C. Munoz

High Energy Physics - Phenomenology · Submitted 29 Aug 2005 · 16 references

Pith's verdict: A clean, genuinely new identification of the NMSSM singlet with the right-handed neutrino superfield, but the μ problem is relocated rather than solved and the numerical claims are unbacked.

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arXiv IDhep-ph/0508297 (version 3)

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CitationC. Munoz, D.E. Lopez-Fogliani. "Proposal for a Supersymmetric Standard Model." arXiv:hep-ph/0508297 (2005). https://pith.science/paper/SIY5CQZY

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Worth your time, but read it as a model-building proposal, not a solution to the μ problem. The idea is clean and, as far as I can tell, new: once you accept neutrino masses the MSSM already wants gauge-singlet superfields, so use ν^c in place of the NMSSM singlet S. The λ ν^c H1 H2 term then gives μ = λ⟨ν̃^c⟩, and the cubic κ(ν^c)^3 kills the axion and feeds an electroweak-scale see-saw. Same trick, no extra field. The algebra holds up — I checked the scalar potential (4) against (1) plus (2), the minimization conditions (5), and the 6×6 neutralino matrix (7)–(9); it all follows, and the see-saw structure is standard. They are also upfront about the price: explicit lepton-number and R-parity violation, no neutralino dark matter, a Z3 domain-wall problem. Where I would push back is the framing. The paper says outright that Eq. (6) is the NMSSM minimization condition with ν^c ↔ s, and cites [12] for the existence of solutions. That is honest, but it means the μ problem is relocated, not solved: you still need m²_{ν̃^c} at the weak scale, and nothing here derives that. The abstract's 'without having to introduce an extra singlet' is true in field content and misleading in substance. Second, the 10^-2 eV eigenvalue is quoted with no parameter point; the back-of-envelope m_D²/M with m_D = 10^-4 GeV and M ~ 100 GeV gives ~0.1 eV, so the number is not reproducible from what is printed. The real analysis is deferred to [16], listed as in preparation. None of this sinks the paper — the construction is consistent and it is a legitimate variant of the NMSSM program — but it is a sketch, and the interesting phenomenology (neutralino–neutrino mixing, R-parity-violating collider signals) is asserted rather than worked out. Send it out. It is short, the claims are checkable, and the model deserves to be in the literature with a referee's eye on the naturalness claim.

Referee report

Major objections (3)

[Abstract and paragraph following Eq. (6)] The abstract states that the model 'solve[s] the μ problem of the MSSM without having to introduce an extra singlet superfield' [abstract:s1]. The manuscript itself shows, in the paragraph following Eq. (6), that the minimization conditions are 'the same as the ones defining the minimization conditions for the NMSSM, with the substitution ν^c ↔ s', and it refers to [12] for the existence of solutions. That establishes that ⟨ν̃^c⟩ can be of order the electroweak scale in some region of parameter space; it does not address why m^2_{ν̃^c} should be at the electroweak scale rather than at some higher scale. The naturalness question is therefore relocated, not resolved, and the abstract's wording is stronger than what is demonstrated. The manuscript should state explicitly what is gained (no additional singlet; ν^c is already required by neutrino masses) and what is not (the hierarchy/naturalness question of the singlet sector remains as in the NMSSM).
[Eq. (1) and the Z_3 paragraph] The paragraph following Eq. (1) invokes a Z_3 symmetry 'as is usually done in the NMSSM' to forbid the bare μ term, but the Z_3 charges are never specified. For any Z_3 assignment that leaves the five terms of Eq. (1) invariant, the standard trilinear R-parity-violating operators L L e^c and L Q d^c are also invariant: writing the charges as a(H1), b(H2), c(L), d(e^c), e(Q), f(u^c), g(d^c), h(ν^c), the constraints from Eq. (1) imply c = d = a and g = −a − e, hence 2c + d = 3a = 0 and c + e + g = 0. Since R-parity is explicitly broken in this model, these operators cannot be removed by hand, and with O(1) couplings they would generate unacceptable neutrino masses and lepton-flavor violation. The manuscript should state the Z_3 charges explicitly, show that Eq. (1) is the most general renormalizable superpotential consistent with them, and identify the additional symmetry or suppression mechanism that removes L L e^c and L Q d^c.
[Numerical claims in the paragraph after Eq. (9), the sneutrino-antisneutrino paragraph, and the Higgs paragraph] The paper reports three numerical checks — that the lightest eigenvalue of Eq. (7) is of order 10^-2 eV for a Dirac mass of order 10^-4 GeV, that the sneutrino-antisneutrino loop correction is negligible, and that one CP-odd Higgs can be light — but gives no parameter point for any of them, and defers the detailed analysis to [16], listed as 'in preparation'. A simple see-saw estimate m_D^2/M with m_D = 10^-4 GeV and M of order the electroweak scale gives about 0.1 eV, an order of magnitude above the quoted 10^-2 eV; the quoted value requires either M of order 10^3 GeV or a smaller m_D. At least one benchmark point (λ, κ, tan β, A_λ, A_κ, m^2_{ν̃^c}, m_D) should be given so that the eigenvalue can be reproduced, and the claims that rest on [16] should either be supported in this manuscript or explicitly labelled as preliminary.

Minor objections (8)

[Eq. (4)] The term written as 'kYν* v*2 ν* νc^2' should read 'κYν* v2* ν* νc^2'; the symbol k is not defined anywhere in the paper.
[Eqs. (3)-(10)] The symbols ν and νc are used both for the sneutrino fields and for their VEVs (Eq. (3) and below). A notation such as v_L, v_R or ⟨ν̃⟩, ⟨ν̃^c⟩ would make Eqs. (4)-(10) much easier to read.
[Paragraph following Eq. (1)] 'Obviosly' should be 'Obviously'; the version I read also contains numerous broken words (e.g., 'minima l', 'in clude', 's upersymmetric'), which should be checked at proof stage.
[Paragraph following Eq. (1)] The sentence 'this is actually what happens in the low energy limit of string constructions: only trilinear couplings are present in the superpotential' needs a citation; as written it is a strong claim about string model building.
[Eq. (6)] The text should state explicitly which terms are neglected in passing from Eq. (5) to Eq. (6) and give the size of the neglected Yν contributions, since the whole neutrino-mass discussion rests on Yν being small but nonzero.
[Reference [16]] Since [16] is 'in preparation', the reader cannot check the numerical claims; either include the essential results here or soften the sentences that depend on them.
[Abstract] 'eigenvalues reproducing the correct scale of neutrino masses' should specify the scale (10^-2 eV) and the assumed M, so that the statement can be compared with the see-saw estimate.
[Higgs paragraph] Even a sentence on the LEP and b-physics constraints on a light CP-odd Higgs in NMSSM-like models would help the reader judge whether the 'in principle light' CP-odd state is viable.

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The paper

The paper claims

The MSSM's missing Higgs-mixing term can come from the neutrino superfields that neutrino masses already require, with no extra singlet added.

The reading

The Minimal Supersymmetric Standard Model needs a Higgs-mixing parameter $mu$ of order the electroweak scale, but nothing in the theory explains why it should sit there rather than at the Planck scale. This paper observes that once massive neutrinos force you to add the three gauge-singlet neutrino superfields $hat nu^c_i$, those same fields can do the $mu$ job: a superpotential coupling $lambda_i hat nu^c_i hat H_1 hat H_2$ becomes an effective $mu = lambda_i langle tilde nu^c_i rangle$ as soon as a right-handed sneutrino takes an electroweak-scale vacuum expectation value. The same singlets carry a cubic coupling $kappa_{ijk} hat nu^c_i hat nu^c_j hat nu^c_k$, which removes the axion that a pure global symmetry would leave behind and, through a see-saw built into the neutralino mass matrix, generates Majorana neutrino masses at the electroweak scale instead of at a grand-unified scale. The price is explicit breaking of lepton number and R-parity, so the lightest R-odd particle is unstable and the neutralino is no longer a dark-matter candidate; the authors present this as a rich and distinctive phenomenology rather than a defect. The paper is a proposal: it sets out the superpotential, the soft terms, the minimization conditions and the leading mass matrices, and defers detailed collider, renormalization-group and neutrino-mass analyses to later work.

What carries the argument

The machinery is the superpotential $W = epsilon_{ab}(Y^u_{ij} hat H^b_2 hat Q^a_i hat u^c_j + Y^d_{ij} hat H^a_1 hat Q^b_i hat d^c_j + Y^e_{ij} hat H^a_1 hat L^b_i hat e^c_j + Y^nu_{ij} hat H^b_2 hat L^a_i hat nu^c_j) - epsilon_{ab} lambda_i hat nu^c_i hat H^a_1 hat H^b_2 + frac{1}{3} kappa_{ijk} hat nu^c_i hat nu^c_j hat nu^c_k$, together with its soft-breaking counterpart. The $lambda$ term supplies the effective $mu$ once $langle tilde nu^c rangle neq 0$; the $kappa$ term supplies the explicit lepton-number breaking that keeps the pseudoscalar spectrum free of an unacceptable axion and feeds the see-saw. The see-saw itself is carried by the block matrix $M_n = begin{pmatrix} M & m m^T & 0 end{pmatrix}$, where $M$ is the NMSSM-like neutralino matrix with $tilde nu^c$ playing the role of $S$, and $m^T = (-g_1 nu/sqrt{2}, g_2 nu/sqrt{2}, 0, Y_nu nu^c, Y_nu v_2)$ holds the small entries that make one eigenvalue tiny. The same structure repeats in the charged sector, where charginos mix with charged leptons and a light eigenvalue equal to $Y_e v_1$ survives automatically.

Extended reading notes

Core claim

The claim is that the $mu$ problem of the MSSM can be solved without the extra singlet superfield of the NMSSM, by reusing the gauge-singlet neutrino superfields that neutrino masses already motivate. The superpotential contains no bare $mu$ term, only trilinear couplings: the MSSM Yukawas plus $Y^{ij}_nu hat H_2 hat L_i hat nu^c_j$, the $mu$-generating $lambda_i hat nu^c_i hat H_1 hat H_2$, and $frac{1}{3} kappa_{ijk} hat nu^c_i hat nu^c_j hat nu^c_k$. When the scalar partner of the right-handed neutrino takes a vacuum expectation value, an effective $mu = lambda_i langle tilde nu^c_i rangle$ appears at the electroweak scale. Because the left-handed sneutrino vacuum expectation value is suppressed by the tiny Dirac Yukawa, the minimization conditions collapse to exactly the NMSSM ones with $tilde nu^c$ replacing the singlet $S$, so the parameter-space solutions already known for the NMSSM carry over. The neutralino mass matrix becomes $6 times 6$ (or $10 times 10$ with three generations), mixing gauginos and Higgsinos with the $tilde nu^c$ and $tilde nu$ fermions; for a Dirac neutrino mass of order $10^{-4}$ GeV the lightest eigenvalue lands near $10^{-2}$ eV, the observed neutrino scale.

Load-bearing premise

The whole mechanism rests on the right-handed sneutrino vacuum expectation value sitting naturally at the electroweak scale, an assumption the paper supports only by noting that its minimization conditions are the NMSSM's with the singlet renamed, so that known NMSSM solutions exist.

Editorial extensions

If this is right

An effective $mu$ term of electroweak size arises with no fundamental $mu$ parameter and no additional singlet superfield beyond the three right-handed neutrino singlets already needed for neutrino mass.
Majorana neutrino masses are generated at the electroweak scale through a dynamical see-saw that is always present in the neutralino mass matrix, so Yukawa couplings of order the electron's are enough and no grand-unified scale is required.
R-parity and lepton number are explicitly broken, so the lightest R-odd particle decays, the neutralino cannot be the dark matter, and alternative candidates such as the gravitino must be considered.
The neutralino, chargino and Higgs mass matrices all mix with neutrino and sneutrino states, giving light CP-odd Higgs bosons, Higgs–sneutrino mixing and charged-Higgs–slepton mixing that distinguish the model from the MSSM and the NMSSM.
The superpotential retains a $Z_3$ symmetry and therefore inherits the NMSSM's cosmological domain-wall problem, which the authors argue can be cured by small non-renormalizable operators that lift the vacuum degeneracy without introducing hierarchies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the $mu$ term is now a dynamical variable fixed by the sneutrino vacuum expectation value, the model ties the Higgsino mass to the same sector that fixes neutrino masses; a measurement of both would over-determine the $lambda$ and $Y_nu$ couplings and give a sharp consistency check.
The explicit R-parity breaking makes the lightest neutralino decay, typically with displaced vertices or missing-energy signatures that differ from the MSSM; existing collider limits on R-parity-violating couplings therefore already constrain the parameter space, even though the paper does not attempt that comparison.
The mapping onto the NMSSM with $tilde nu^c leftrightarrow S$ means the model inherits the NMSSM's fine-tuning questions about the singlet soft mass; whether an electroweak-scale sneutrino vacuum expectation value survives renormalization-group running to the weak scale without tuning is the calculation that would decide how natural the solution really is.
If the cubic $kappa$ coupling is small, the see-saw scale is effectively the electroweak scale and the light neutrino mass scales quadratically in the Dirac mass; this predicts a correlated pattern between the neutrino mass hierarchy and the neutralino mixing angles that future precision measurements could probe.

Original abstract

The fact that neutrinos are massive suggests that the minimal supersymmetric standard model (MSSM) might be extended in order to include three gauge-singlet neutrino superfields with Yukawa couplings of the type $H_2 L \nu^c$. We propose to use these superfields to solve the $\mu$ problem of the MSSM without having to introduce an extra singlet superfield as in the case of the next-to-MSSM (NMSSM). In particular, terms of the type $\nu^c H_1 H_2$ in the superpotential may carry out this task spontaneously through sneutrino vacuum expectation values. In addition, terms of the type $(\nu^c)^3$ avoid the presence of axions and generate effective Majorana masses for neutrinos at the electroweak scale. On the other hand, these terms break lepton number and R-parity explicitly implying that the phenomenology of this model is very different from the one of the MSSM or NMSSM. For example, the usual neutralinos are now mixed with the neutrinos. For Dirac masses of the latter of order $10^{-4}$ GeV, eigenvalues reproducing the correct scale of neutrino masses are obtained.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,779 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.88 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.84 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

The fact that neutrinos are massive suggests that the minimal supersymmetric standard model (MSSM) might be extended in order to include three gauge-singlet neutrino superfields with Yukawa couplings of the type $H_2 L \nu^c$. We propose to use these superfields to solve the $\mu$ problem of the MSSM without having to introduce an extra singlet superfield as in the case of the next-to-MSSM (NMSSM). In particular, terms of the type $\nu^c H_1 H_2$ in the superpotential may carry out this task spontaneously through sneutrino vacuum expectation values. In addition, terms of the type $(\nu^c)^3$ avoid the presence of axions and generate effective Majorana masses for neutrinos at the electroweak scale. On the other hand, these terms break lepton number and R-parity explicitly implying that the phenomenology of this model is very different from the one of the MSSM or NMSSM. For example, the usual neutralinos are now mixed with the neutrinos. For Dirac masses of the latter of order $10^{-4}$ GeV, eigenvalues reproducing the correct scale of neutrino masses are obtained.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The fact that neutrinos are massive suggests that the minimal supersymmetric standard model (MSSM) might be extended in order to include three gauge-singlet neutrino superfields with Yukawa couplings of the type $H_2 L \nu^c$.	background 0.98	0.08	0.11	hedged possibility 0.85
s1	We propose to use these superfields to solve the $\mu$ problem of the MSSM without having to introduce an extra singlet superfield as in the case of the next-to-MSSM (NMSSM).	contribution 0.97	0.71	0.48	asserted 0.54
s2	In particular, terms of the type $\nu^c H_1 H_2$ in the superpotential may carry out this task spontaneously through sneutrino vacuum expectation values.	method 0.70	0.37	0.13	hedged possibility 1.00
s3	In addition, terms of the type $(\nu^c)^3$ avoid the presence of axions and generate effective Majorana masses for neutrinos at the electroweak scale.	contribution 0.62	0.46	0.12	asserted 0.90
s4	On the other hand, these terms break lepton number and R-parity explicitly implying that the phenomenology of this model is very different from the one of the MSSM or NMSSM.	interpretation 0.64	0.49	0.15	asserted 1.00
s5	For example, the usual neutralinos are now mixed with the neutrinos.	result 0.55	0.54	0.06	asserted 1.00
s6	For Dirac masses of the latter of order $10^{-4}$ GeV, eigenvalues reproducing the correct scale of neutrino masses are obtained.	result 1.00	0.79	0.13	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from argument 0.81.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (16)

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Simulated five-year Fermi-LAT observations of the Virgo cluster show that a mu-nuSSM gravitino of 0.6 to 2 GeV and lifetime 3e27 to 2e28 s would be detectable at signal-to-noise above 3.
LHC Phenomenology of an Extended Standard Model with a Real Scalar Singlet
hep-ph 2007-06 conditional novelty 4.0 of 10

A single real scalar singlet added to the Standard Model either dilutes LHC Higgs signals through mixing or hides the Higgs behind invisible decays, and precision electroweak data plus the relic density pin down which.
Collider aspects of flavour physics at high Q
hep-ph 2008-01 conditional novelty 3.0 of 10

A community review compiling the theoretical and experimental status of flavour physics in LHC production and decays of heavy states, from top quarks through supersymmetry to extra dimensions, plus the public software...
Higgs-mass predictions in the MSSM and beyond
hep-ph 2020-12 accept novelty 2.0 of 10

A comprehensive review of Higgs-mass calculations in supersymmetric models, documenting fixed-order, effective-field-theory, and hybrid approaches and their theory uncertainties.

How later papers used it

63 later papers cite it

Evidence: some. 30 of the citing papers share no author with it, and 2 of those carry a confident label from Pith's citation classifier.

Pith read 12 of the 210 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 paper by the same authors is listed below: 1 used its method or tool.

Uses its method or tool 1 paper · 1 by the same authors

By the same authors

Determined the neutrino Yukawa couplings through the 10x10 neutral fermion mass matrix written as in this paper, with a 7x7 matrix of the MSSM neutralino mass matrix and its mixing with the neutrino superfields and a 7x3 mixing matrix.

Analysis of the parameter space and spectrum of the $\mu \nu$SSM (2008) (same authors) · 0.82 · paraphrased: the licence does not allow quoting

How the literature uses it

63 arXiv papers cite this in 210 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 131 sentences without a confident label

Builds on it 2 papers

[ref] , where the characteristics of the $μν$SSM were introduced, and only some points concerning its phenomenology were sketched.

Analysis of the parameter space and spectrum of the $\mu \nu$SSM · Introduction · 1.00
In the present paper, we study the phenomenology of the $μν$SSM, extending previous work [ref] .

LHC phenomenology of the $\mu\nu$SSM · Introduction · 1.00

Uses its method or tool 1 paper

At this point we determine the neutrino Yukawa couplings through the $10×10$ neutral fermion mass matrix which can be written as [ref] [equation] where $M$ is a $7×7$ matrix composed by the MSSM neutralino mass matrix and its mixing with the $ν^c_i$, while $m$ is a $7×3$ matrix containing the mixing of the $ν_i$ with MSSM neutralinos and the $ν^c_i$.

Analysis of the parameter space and spectrum of the $\mu \nu$SSM · Strategy for the analysis · 0.82

Compares with it 1 paper

The nature of neutrino mass generation mechanism in this framework appears similar to the one in $μν$SSM model [ref] .

Weak scale right-handed neutrino as pseudo-Goldstone fermion of spontaneously broken $U(1)_{L_\mu-L_\tau}$ · Summary and Discussions · 0.98

Cites it as support 3 papers

In fact, the couplings $λ_ijk$ and $λ'_ijk$ can be naturally added to $W_$μν$SSM$ [ref] .

Right-handed neutrinos, domain walls and tadpoles in the superstring inspired $\mu\nu$SSM · The $$ and renormalizable terms · 0.97
Moreover, as shown in [ref] , taking the limit $h_ν→0$ and, consequently, $v_i →0$, one recovers the tadpole equations of the NMSSM, ensuring the existence of solutions to this set of equations.

LHC phenomenology of the $\mu\nu$SSM · Scalar potential and its minimization · 0.99
The smallness of the left sneutrino VEVs for a correct description of the neutrino sector, compatible with current data, has been shown in Refs. [ref] .

$U(1)'$ extensions of the $\mu \nu$SSM · The scalar potential · 0.99

Cites it as background 44 papers

As explained in the Introduction, this model was proposed [ref] as a SUSY standard model for solving the crucial $μ$ problem of SUSY constructions, generating at the same time the small neutrino masses through a dynamical see-saw at the electroweak scale.

Analysis of the parameter space and spectrum of the $\mu \nu$SSM · Conclusions and outlook · 0.84
Since it was proposed [ref] , the $μν$SSM has been studied in Ref. MuNuSSM2

The seesaw mechanism in the $\mu \nu$SSM · Introduction · 0.98
The superpotential of the $μν$SSM is given by [ref] [Although we assume three families of right-handed neutrinos motivated by the Standard Model generation replication pattern, a different number of right-handed neutrinos can be used.]: [equation]

The Higgs sector of the munuSSM and collider physics · The $μν$SSM · 0.80

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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