Can The Supersymmetric Flavor Problem Decouple?

Hitoshi Murayama (UC Berkeley; LBNL); Nima Arkani-Hamed

REVIEW

Can The Supersymmetric Flavor Problem Decouple?

Nima Arkani-Hamed, Hitoshi Murayama (UC Berkeley, LBNL)

High Energy Physics - Phenomenology · Submitted 7 Mar 1997 · 20 references

Pith's verdict: A clean, checkable no-go for split sfermion spectra: the two-loop gauge running really does drive m^2_{Q3} negative, and the numbers are order-of-magnitude but honest.

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CitationHitoshi Murayama (UC Berkeley, LBNL), Nima Arkani-Hamed. "Can The Supersymmetric Flavor Problem Decouple?." arXiv:hep-ph/9703259 (1997). https://pith.science/paper/YSEXXI2K

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Editor's note

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The thing worth knowing is that this is not another fine-tuning argument. Dimopoulos-Giudice and Pomarol-Tommasini both leaned on how much tuning you tolerate, and the authors say so themselves. What's new here is a sign: the two-loop gauge contribution proportional to the heavy first- and second-generation scalar mass squared is negative for every third-generation species, so pushing the first two generations up drives m^2_{Q3} toward negative at the weak scale. That's a hard statement, independent of naturalness, and Eq. (3) plus Fig. 2 make it checkable in a few lines. The approximations are argued in the conservative direction — Yukawa couplings dropped because they lower masses further, heavy scalars decoupled at 10 TeV rather than at their actual mass — and the paper is explicit that it only constrains high-scale mediation, with a fair caveat about the more minimal scenario. The anomalous U(1) discussion is honest too: ref [13] scenario D is not excluded, just not better than the generic cases, and they say that rather than overclaiming an exclusion. That's the right instinct and it's rare enough to note. On soft spots, I'd push back on where the reader put the weight. Footnote 15's decoupling scale is a real unknown, but the running is logarithmic, so moving mu' over its allowed range shifts the 4 TeV bound by a few percent, not by a factor. The stress-test note has this right. The more genuine imprecision is that the abstract's 22 TeV reads as a universal number when Fig. 1 shows it running from 100 TeV down to multi-TeV depending on the gluino mass; 22 TeV is case (II) at a particular M_g. Minor, but it's the sentence people will quote. The SU(5)-multiplet degeneracy of footnote 12 does narrow the allowed spectra by assumption, though the authors flag it and it's a natural GUT consequence. None of this touches the load-bearing claim. Who should read it: anyone building split-spectrum or anomalous U(1) models, and anyone who still thinks heavy first two generations is a free lunch. It deserves referees.

Referee report

Significance

If correct, the result is a clean, model-independent negative answer to a widely discussed question, and it is derived analytically rather than numerically, with the approximations stated and argued in the conservative direction (Yukawa couplings dropped because they drive masses lower; heavy scalars decoupled at 10 TeV rather than at their physical mass; mass-insertion loop integrals replaced by ~m_{1,2} in a way that minimizes the contribution, footnote 11). The paper also makes falsifiable statements about specific published models: the Dvali-Pomarol spectrum is excluded by Fig. 2, the Mohapatra-Riotto ǫ_K constraint is shown to be too weak, and the Nelson-Wright scenario D is pushed to m_{Q3}(0) > 1.0 TeV. The caveat that the conclusions do not apply to low-scale mediation scenarios such as the 'more minimal' framework is stated explicitly and appropriately. The paper is a short letter, but the argument is self-contained and the conclusion has held up as a standard reference in the subsequent literature.

Major objections (2)

[Abstract; Figs. 1 and 3] The abstract states 'the first two generation scalars must be heavier than 22 TeV' and 'm_{Q3} > 4 TeV' as if these were universal bounds, but Fig. 1 shows that min(~m_{1,2}) ranges from 100 TeV to the multi-TeV range as a function of the gluino mass and of the mixing pattern (I)-(IV), and Fig. 3 likewise shows min(m_{Q3}(0)) varying with M_g. The 22 TeV and 4 TeV numbers correspond to case (II) at a particular point in the (M_g, ~m_{1,2}) plane. The abstract should either state the parameter point at which these numbers apply or quote the range, so that the headline quantitative claim is not read as a universal bound. The qualitative conclusion is unaffected, but the abstract currently overstates the precision of the numbers.
[Footnote 15; Eq. (2)] The decoupling scale mu' ~ 10 TeV at which the heavy-scalar two-loop contribution is switched off is acknowledged in footnote 15 as uncertain, and the authors correctly note that an explicit threshold study is needed. The negative two-loop term is proportional to ln(M_GUT/mu'), so the sensitivity is logarithmic: for ~m_{1,2} in the 10-100 TeV range, moving mu' from 10 TeV to the physical threshold changes the bound by only a few percent, and the choice mu' = 10 TeV over-estimates the negative contribution when ~m_{1,2} > 10 TeV, i.e. it is conservative in the direction the authors claim. A sentence in the text quantifying this sensitivity, and stating explicitly that the sign of the effect is independent of mu', would preempt the natural objection and strengthen the paper without changing any conclusion.

Minor objections (7)

[First paragraph] 'embarassment' should be 'embarrassment'.
[Third paragraph] 'Fayet-Illiopoulos' should be 'Fayet-Iliopoulos'.
[Acknowledgements] 'NSE RC' should be 'NSERC'.
[Eq. (2) and the text following it] The notation t(') and mu(') is compressed; a sentence immediately after Eq. (2) stating that t' corresponds to mu' (the heavy-scalar decoupling scale) and t to mu (the gaugino decoupling scale) would make the analytic solution easier to follow.
[Fig. 2 caption] The caption should state explicitly which direction of the vertical axis is excluded and confirm that the curves are for N5 = N10 = 2, since the figure is the basis for the exclusion of the Dvali-Pomarol spectrum.
[Footnote 12; Conclusions] The requirement that scalars within each 5* and 10 of SU(5) be degenerate is an assumption that restricts the model space; it is justified in footnote 12 but should be restated in the concluding paragraph so that the scope of the bound is clear.
[Title block] The preprint number 'LBNL-4-0077' looks unusual and should be checked against the laboratory's numbering convention.

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The paper

The paper claims

Pushing the first two generations of squarks and sleptons to multi-TeV masses to suppress flavor-changing processes drives the third-generation scalar mass squared negative through two-loop running, so the supersymmetric flavor problem does

The reading

Low-energy supersymmetry has a flavor problem: squarks and sleptons of the first two generations, sitting near the weak scale with arbitrary mixing, generate kaon mixing, $mu$ to $e gamma$ and electric dipole moments far larger than observed. A popular escape is to push those first- and second-generation scalars up to multi-TeV masses, where their flavor-changing effects are suppressed, while keeping the third generation, gauginos and higgsinos light enough to stabilize the weak scale. The paper asks whether that split spectrum survives its own quantum corrections and answers no: the heavy scalars enter the two-loop renormalization group equations with a negative sign, dragging the third-generation scalar mass squared toward negative values, which would break color and charge. Requiring the kaon-mixing contribution to stay below the measured value forces the first two generations above 22 TeV even with order-$lambda$ alignment, and that in turn forces the boundary value of the left-handed stop mass above 4 TeV, far outside any natural range. The authors conclude that raising the first two generations does not solve the flavor problem, and that a real flavor symmetry or a dynamical mechanism for degenerate scalar masses is needed instead.

What carries the argument

The engine is the two-loop renormalization group equation for a third-generation scalar mass, Eq. (1) of the paper, which retains only the one-loop gaugino term and the two-loop term proportional to the heavy scalar mass squared $m^2_{1,2}$. The coefficient of the heavy-scalar term is fixed by the Standard Model quantum numbers of the heavy fields and by how many heavy $5^*$ and $10$ multiplets of $SU(5)$ are present, counted as $N_5$ and $N_{10}$; the hypercharge piece also depends on the $D$-term cancellation requirement that scalars within a single $SU(5)$ multiplet be degenerate. Solving the equation analytically gives Eq. (3), an explicit expression for $m^2_{tilde f}(t)$ at the weak scale in terms of the boundary stop mass, the universal gaugino mass $M_0$, and $m^2_{1,2}$, with the heavy-scalar contribution switched off at a decoupling scale taken as 10 TeV. Setting the result to zero yields the exclusion curves of Fig. 2, which are then intersected with the kaon-mixing bounds of Fig. 1 to produce the stop-mass bounds of Fig. 3.

Extended reading notes

Core claim

The claim is that a split scalar spectrum, with the first two generations heavy and the third light, is radiatively unstable in any theory where the soft supersymmetry-breaking parameters are generated at a high scale. The heavy scalars contribute at two loops to the running of the third-generation scalar masses, and the contribution is negative and proportional to the heavy mass squared $m^2_{1,2}$. Combining the two steps, the authors first bound $m_{1,2}$ from the requirement that the squark-gluino contribution to $K^0$-$bar K^0$ mixing not exceed the observed value, obtaining bounds from the multi-TeV range up to about 100 TeV depending on the assumed squark mixing pattern, and stronger by a factor of 13 if order-one CP-violating phases are allowed. They then solve the two-loop renormalization group equations analytically and find that the third-generation mass squared vanishes along curves in the plane of $m_{tilde f}(0)/m_{1,2}$ versus $M_0/m_{1,2}$, with everything below those curves excluded. For the two most favorable mixing patterns the two constraints together require $m_{tilde Q_3}(0) > 4$ TeV, which corresponds to electroweak fine-tuning worse than the $10^{-3}$ level, and only a scenario with an extra factor of about five in degeneracy marginally allows a stop near 1 TeV, still at the percent fine-tuning level.

Load-bearing premise

The size of the negative two-loop contribution depends on the scale at which the heavy first- and second-generation scalars are removed from the running, which the authors take to be 10 TeV and which they explicitly state is not known without a dedicated study of threshold corrections; the sign of the effect survives any choice, but the quoted 22 TeV and 4 TeV numbers scale with that logarithm.

Editorial extensions

If this is right

In high-scale mediation schemes, suppressing flavor-changing neutral currents by making the first two generations heavy requires a boundary stop mass above 4 TeV for order-$lambda$ alignment, which corresponds to electroweak fine-tuning worse than one part in a thousand.
The anomalous $U(1)$ string models that predict $m_{tilde f}(0)/m_{1,2} = 0.1$ and $M_0/m_{1,2} = 0.01$ are excluded, because their third-generation mass squared is driven negative.
Models with $m_{1,2}$ in the few-TeV range and order-$10^{-2}$ squark mixing, previously claimed to solve the flavor problem including CP violation, actually require $m_{1,2} > 13$ TeV and $m_{tilde Q_3}(0) > 2.5$ TeV.
Any concrete realization of a split spectrum with a low mediation scale must be checked explicitly, since the negative two-loop contribution is smaller there but not absent.

Reading between the lines

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

The same negative two-loop effect should appear for any heavy matter charged under the Standard Model gauge group, so GUT-scale threshold multiplets introduced for unification reasons could destabilize the stop even when no flavor problem is being addressed.
Because the sign of the effect is robust while its magnitude scales with the logarithm between the decoupling scale and the weak scale, a low-scale mediation model is the sharpest surviving version of the split-spectrum idea, and the paper's own numbers suggest it is the place to look next.
A discovery of a first-generation squark in the multi-TeV range would be a direct test: the spectrum would have to come with either a heavier stop or a mediation scale low enough that the running length is short.
The argument reframes the flavor problem as a radiative-stability problem, which suggests that any solution should be judged by whether it keeps the third-generation scalar mass squared positive, not only by whether it suppresses the flavor-changing operators.

Original abstract

It has been argued that the squarks and sleptons of the first and second generations can be relatively heavy without destabilizing the weak scale, thereby improving the situation with too-large flavor-changing neutral current (FCNC) and CP violating processes. In theories where the soft supersymmetry breaking parameters are generated at a high scale (such as the Planck scale), we show that such a mass spectrum tends to drive the scalar top mass squared $m_{\tilde{Q}_3}^2$ negative from two-loop renormalization group evolution. Even ignoring CP violation and allowing $O(\lambda) \sim .22$ alignment, the first two generation scalars must be heavier than 22 TeV to suppress FCNC. This in turn requires the boundary condition on $m_{\tilde{Q}_3} > 4 TeV$ to avoid negative $m_{\tilde{Q}_3}^2$ at the weak scale. Some of the models in the literature employing the anomalous U(1) in string theory are excluded by our analysis.

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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, 4,477 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.41 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.59 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

It has been argued that the squarks and sleptons of the first and second generations can be relatively heavy without destabilizing the weak scale, thereby improving the situation with too-large flavor-changing neutral current (FCNC) and CP violating processes. In theories where the soft supersymmetry breaking parameters are generated at a high scale (such as the Planck scale), we show that such a mass spectrum tends to drive the scalar top mass squared $m_{\tilde{Q}_3}^2$ negative from two-loop renormalization group evolution. Even ignoring CP violation and allowing $O(\lambda) \sim .22$ alignment, the first two generation scalars must be heavier than 22 TeV to suppress FCNC. This in turn requires the boundary condition on $m_{\tilde{Q}_3} > 4 TeV$ to avoid negative $m_{\tilde{Q}_3}^2$ at the weak scale. Some of the models in the literature employing the anomalous U(1) in string theory are excluded by our analysis.

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	It has been argued that the squarks and sleptons of the first and second generations can be relatively heavy without destabilizing the weak scale, thereby improving the situation with too-large flavor-changing neutral current (FCNC) and CP violating processes.	background 1.00	0.04	0.06	hedged possibility 0.87
s1	In theories where the soft supersymmetry breaking parameters are generated at a high scale (such as the Planck scale), we show that such a mass spectrum tends to drive the scalar top mass squared $m_{\tilde{Q}_3}^2$ negative from two-loop renormalization group evolution.	result 0.89	0.91	0.27	asserted 0.94
s2	Even ignoring CP violation and allowing $O(\lambda) \sim .22$ alignment, the first two generation scalars must be heavier than 22 TeV to suppress FCNC.	result 1.00	0.73	0.22	asserted 0.99
s3	This in turn requires the boundary condition on $m_{\tilde{Q}_3} > 4 TeV$ to avoid negative $m_{\tilde{Q}_3}^2$ at the weak scale.	result 0.98	0.81	0.26	asserted 1.00
s4	Some of the models in the literature employing the anomalous U(1) in string theory are excluded by our analysis.	interpretation 0.60	0.77	0.13	asserted 0.95

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.81.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

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

levels run

P abstract

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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

Figures

**Figure 1.** The minimum mass of the first- and second-generation sca

**Figure 2.** Constraint on the mass ratio between the first- and seco

**Figure 3.** The minimum boundary mass of the left-handed scalar top

Figures reproduced from arXiv:hep-ph/9703259 by the authors.

References

Works cited (20)

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This is of course a natural consequence of a ﬁeld-theoretical grand uni- ﬁcation. Our analysis does not depend on the mechanism to make the scalars within the SU(5)-multiplets degenerate. DY may cancel in other ways as well, see [13] for examples

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Forward citations

Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Simply Unnatural Supersymmetry
hep-ph 2012-12 conditional novelty 6.0 of 10

Split supersymmetry with scalars at 100-1000 TeV and TeV-scale gauginos fits the 125 GeV Higgs mass, gauge coupling unification, and wino dark matter, and predicts distinctive displaced gluino decays.
(De)Constructing a Natural and Flavorful Supersymmetric Standard Model
hep-ph 2011-03 conditional novelty 6.0 of 10

Splitting Standard Model generations across two gauge sites in a deconstructed supersymmetric model reproduces the quark hierarchy, solves the mu/Bmu problem, and yields a natural spectrum with light third-generation ...
Hierarchical Soft Terms and Flavor Physics
hep-ph 2008-12 conditional novelty 6.0 of 10

Making the first two squark generations heavy produces a specific, testable pattern of flavor violation in which the d-to-s transition is fixed by the product of d-to-b and b-to-s transitions, allowing a B_s mixing ph...
A Gravity Dual and LHC Study of Single-Sector Supersymmetry Breaking
hep-ph 2007-04 conditional novelty 6.0 of 10

A five-dimensional warped-gravity dual of single-sector supersymmetry breaking yields a calculable sparticle spectrum whose two-photon plus missing-energy signal should be visible at the LHC within 1 to 10 inverse femtobarns.
Supersymmetry Breaking through Transparent Extra Dimensions
hep-ph 1999-11 conditional novelty 6.0 of 10

Supersymmetry breaking on a brane spatially separated from the Standard Model brane in an extra dimension gives gauginos mass directly while suppressing scalar masses to at least a loop factor, so scalar masses come f...

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QCD Corrections to Flavor-Changing Neutral Currents in the Supersymmetric Standard Model
hep-ph 1997-07 accept novelty 6.0 of 10

Leading QCD corrections to gluino-box K-Kbar mixing in the MSSM tighten limits on first-two-generation squark mass splittings by a factor of two to three.
Living dangerously with decoupled first/second generation scalars: SUSY prospects at the LHC
hep-ph 2024-11 conditional novelty 5.0 of 10

In the NUHM3 SUSY model, a landscape draw to heavy first and second generation scalars forces the surviving natural parameter space to have light top squarks but heavy gluinos, with low-mass regions excluded by charge...
The Constrained Minimal Dirac Gaugino Supersymmetric Standard Model
hep-ph 2014-03 conditional novelty 5.0 of 10

Adding a vector-like lepton pair and two right-handed electron pairs to a Dirac-gaugino supersymmetric model restores two-loop gauge coupling unification near 10^17 GeV, and the resulting constrained model predicts a ...
Anatomy of maximal stop mixing in the MSSM
hep-ph 2012-04 accept novelty 5.0 of 10

Maximal stop mixing in the MSSM, needed for a 125 GeV Higgs with sub-TeV stops, requires a large negative trilinear coupling at the GUT scale, which gaugino mediation can supply but gauge and radion mediation cannot.
Not Even Decoupling Can Save Minimal Supersymmetric SU(5)
hep-ph 2001-08 accept novelty 5.0 of 10

Minimal supersymmetric SU(5) is excluded by Super-Kamiokande proton decay limits, and making the first two generations of superpartners heavy does not rescue it.
String phenomenology from the landscape
hep-ph 2026-10 conditional novelty 4.0 of 10

Natural supersymmetry with a 125 GeV Higgs is presented as the emergent end point of a landscape draw to large A-terms halted by charge-and-color-breaking and no-EWSB vetoes.

How the literature uses it

37 arXiv papers cite this in 57 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 · 43 sentences without a confident label

Uses its method or tool 1 paper

In this simplified case, we can solve the RGE for the stop mass analytically to find [ref] [equation] where $t̃$ can refer to $t̃_L$ or $t̃_R$ with appropriate choice of Casimirs (the stronger bound is on $t̃_L$), $i = 1,2,3,$ $b_i$ and $C_i$ are the usual GUT-normalized $β$ function parameters and Casimirs respectively, $m̃_1,2^2$ are the mean squark masses, $μ$ is the low scale (taken to be 1 TeV), $μ'$ is the scale where the heavy squarks decouple (taken to be 10 TeV), and $Λ$ is the scale where supersymmetry is broken and RG flow commences (taken to be 100 TeV).

Dynamical Supersymmetry Breaking, with Flavor · Constraints from tachyonic stop mass · 0.81

Compares with it 4 papers

In Fig. [ref] (left) we report the analogous of Fig. 2 of [ref] for different values of $M$[The solid line is in agreement with [ref] , taking into account the fact that we keep only the gluino (while they keep all the gauginos with equal mass at $M_GUT$) and that our $M_g$ is the gluino mass at low energies.].

Can the Supersymmetric Flavour Problem decouple in case of a Non Standard Supersymmetric Spectrum? · Constraint from colour conservation · 0.84
Notice that, in the case of the MSSM, for $M=M_GUT$ we obtain basically the same bound as in Figure 2 of [ref] , with the proper translation of the parameters[Our colour conservation constraint is actually slightly stronger because we keep only the gluino mass, while [ref] keeps all the gauginos with equal mass at $M_GUT$.].

A Non Standard Supersymmetric Spectrum · Constraint from colour conservation · 1.00
Notice that, in the case of the MSSM, for $M=M_GUT$ we obtain basically the same bound as in Figure 2 of [ref] (to be compared with our Figure [ref], see also [ref] ), with the proper translation of the parameters[Our colour conservation constraint is actually slightly stronger because we keep only the gluino mass, while [ref] keeps all the gauginos with equal mass at $M_GUT$.].

A Motivated Non-Standard Supersymmetric Spectrum · Constraint from colour conservation · 0.99

Cites it as support 3 papers

For very heavy 1st/2nd generation squarks or too-high messenger scales, the stop squarks can even become tachyonic due to this effect [ref] .

Precision Corrections to Fine Tuning in SUSY · Transfer matrix RGEs: stop and gluino masses · 0.96
In RG scaling from high scales, 2-loop correction to the third generation soft masses from the first two generations give large negative soft masses that would lead to color breaking [ref] .

Simply Unnatural Supersymmetry · New Flavor Physics and Radiative Fermion Masses · 0.99
But they cannot get too heavy, as they induce a logarithmically enhanced negative mass for the (light) third-generation squarks [ref] , and so cannot be pushed higher than at most $∼30$ TeV.

Physics Opportunities of a 100 TeV Proton-Proton Collider · Natural Theories and the Tests at the 100 TeV $pp$ Collider · 0.96

Cites it as background 4 papers

Analyses with Radiatively Generated Inverted Mass Hierarchy Models (RIMH) were made in Ref. [ref] .

Higgs funnel region of SUSY dark matter for small $\tan\beta$ and renormalization group effects on pseudoscalar Higgs boson with scalar mass non-universality · Introduction · 0.91
It is interesting to consider fully solving the supersymmetric flavor problem by raising the masses of the first two generation sparticles a bit more - for discussions of whether this is possible or not, see also [ref] .

Single-Sector Supersymmetry Breaking in Supersymmetric QCD · Brief comments on phenomenology · 0.92
[ref] using the RG MSSM equations in the $DR$ scheme; they were revisited in ref.

Large, negative threshold contributions to light soft masses in models with Effective Supersymmetry · Tachyon bounds for squarks and gaugino masses · 0.85

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.

[1] [13]

A. E. Nelson and D. Wright, hep-ph/9702359

View on Pith Pith review arXiv

[2] [1]

M. Dine, W. Fischler, and M. Srednicki, Nucl. Phys. B189, 575 (1981); C. Nappi and B. Ovrut, Phys. Lett. B113, 175 (1982); M. Dine and W. Fischler, Nucl. Phys. B204, 346 (1982); L. Alvarez-Gaum´ e, M. Claudson and M. Wise, Nucl. Phys. B207 96 (1982)

View on Pith 1981

[3] [2]

V. S. Kaplunovsky and J. Louis, Phys. Lett. B306, 269 (1993)

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