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Implications of Supersymmetry Breaking with a Little Hierarchy between Gauginos and Scalars

High Energy Physics - Phenomenology · Submitted 13 Jun 2003 · 24 references

Pith's verdict: An early, honest sketch of the heavy-scalar/light-gaugino program: the synthesis is useful, but the two claims that make the spectrum viable are asserted, not computed.

T0 · AI review

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arXiv IDhep-ph/0306127 (version 3)
Pith ID4ZKGMDTK, Pith's permanent record of this paper and its review
CitationJames D. Wells (MCTP). "Implications of Supersymmetry Breaking with a Little Hierarchy between Gauginos and Scalars." arXiv:hep-ph/0306127 (2003). https://pith.science/paper/4ZKGMDTK
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Referee report
The paper

The paper claims

If the supersymmetry-breaking sector carries a charge, gauginos end up a loop factor lighter than the scalars, and most of the theory's phenomenological headaches go away with the scalars.

The reading

The paper asks what supersymmetry looks like if the sector that breaks it carries Standard Model charges, so that no gauge-invariant coupling of the form $S W W / M_{Pl}$ can be written. Gaugino masses then have to come from their anomaly-mediated values, $M_2 = m_{3/2}/360$, while scalar masses stay at the gravitino scale, $m_{3/2}$. Taking the gaugino lower bounds at face value puts the gauginos near the W mass and the scalars in the tens of TeV, so the only superpartners in reach are the electroweak gauginos and the gluino. The author argues this little hierarchy buys a great deal: flavor and CP violation are suppressed, dimension-five proton decay operators are suppressed, gauge and third-generation Yukawa unification fit better, and the lightest Higgs clears the 114 GeV bound for every value of $m_{3/2}$-consistent $m_{3/2}$ and every $m_{3/2}$-consistent $m_{3/2}$ parameter choice. What it costs is stated plainly: the electroweak hierarchy is no longer natural. The paper is a case that the cost is worth paying because naturalness is the least quantifiable of supersymmetry's successes.

What carries the argument

The load-bearing mechanism is anomaly mediation of gaugino masses: when the supersymmetry-breaking spurion is charged, the gaugino mass is generated by the superconformal anomaly, $M_λ = β(g_λ) g_λ m_{3/2}$, where $β(g_λ)$ is the gauge beta function. Because the beta function is itself a one-loop quantity, the gaugino masses arrive suppressed by roughly a loop factor relative to the scalar masses $m_{3/2}$ that come from the Kähler potential, producing the fixed ratios $M_1 ≃ m_{3/2}/120$, $M_2 ≃ m_{3/2}/360$, $M_3 ≃ m_{3/2}/45$. That single suppression is what converts a heavy-scalar spectrum from a fine-tuning problem into a package of phenomenological gains, and it fixes the entire gaugino spectrum up to one mass parameter.

Extended reading notes

Core claim

The central claim is that a spectrum with weak-scale gauginos and trans-TeV scalars is a coherent and predictive package rather than an arbitrary corner of parameter space. Its origin is dynamical: if the chiral superfield $S$ whose $F$-term breaks supersymmetry is charged under the Standard Model gauge group, the operator that would give gauginos tree-level masses is forbidden, and the leading contribution becomes the anomaly-mediated one, $M_2 = m_{3/2}/360$ for the Wino and $M_3 = m_{3/2}/45$ for the gluino, one loop down from the scalar masses $m_{3/2}$. The lightest superpartner is then the Wino, nearly degenerate with the charged Wino to within 165 MeV, and it annihilates efficiently enough through ordinary gauge bosons that the thermal relic abundance is negligible at weak-scale masses. From this single assumption the author derives a chain of consequences: heavy squarks suppress electric dipole moments and Kaon and B physics anomalies, suppress the dimension-five proton decay operators that trouble grand unification, and lift the lightest Higgs above the experimental bound across the whole viable range of $m_{3/2}$; the gluino, the heaviest gaugino, decays only through three-body modes into virtual squarks and gives four-jet-plus-missing-energy events at the LHC with a reach near 2 TeV; and the Wino, being nearly pure, scatters off nucleons far too weakly for table-top detectors but annihilates into monochromatic photons at a rate near $3$ to $5$ times $10^{-27}$ cm$^3$ s$^{-1}$, which next-generation gamma-ray instruments might resolve.

Load-bearing premise

The spectrum is only viable if the assumed high-scale ordering of Higgs and stop soft masses, $m_{H_u}^2 < m_{H_d}^2 < m_{t}^2$, actually drives radiative electroweak symmetry breaking to the measured $Z$ mass; the paper concedes that the closest minimal-supergravity analogue fails and then asserts that the non-universal ordering will normally develop breaking without showing a renormalization-group calculation.

Editorial extensions

If this is right

  • The lightest superpartner is the neutral Wino, with the charged Wino split from it by between the pion mass and 165 MeV, so the signature is a soft pion from a short, unobservable track rather than a spectacular long-lived charged track.
  • Gluino pair production dominates LHC searches: every event yields at least four jets plus missing energy, and 100 fb$^{-1}$ at 14 TeV would probe gluino masses up to about 2 TeV, corresponding to scalar masses near 100 TeV.
  • Direct detection of dark matter is hopeless because the Wino has no Higgsino component and the spin-dependent channel vanishes for heavy sfermions and a heavy $μ$ term, but indirect searches for monochromatic photons from galactic annihilation are the natural place to look.
  • If the scalars are above about 5 TeV, the lightest Higgs mass exceeds 114 GeV for all viable parameter choices, so the low-$m_{3/2}$ quasi-infrared-fixed-point region near $m_{3/2}$ is revived without a Higgs mass conflict.
  • Gauge coupling unification and $b$-$τ$-$t$ Yukawa unification both improve in the multi-TeV scalar regime, though the author notes that unification compatibility fades once scalar masses reach hundreds of TeV.

Reading between the lines

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

  • Because the whole gaugino spectrum is fixed by the single parameter $m_{3/2}$, a gluino mass measurement at the LHC plus a monochromatic photon line at the Wino mass would over-determine the scenario; a mismatch between the two would rule out the anomaly-mediated assignment rather than merely tune it.
  • The LHC reach quoted here ($m_{\tilde{g}} \approx 2$ TeV, scalars near 100 TeV) sits close to where the author says gauge coupling unification compatibility begins to degrade, so the scenario occupies a finite window that a null gluino search at high luminosity could close from above and a light-squark discovery could close from below.
  • The same heavy gravitino that makes the scalars heavy also decays gravitationally after freeze-out and before big bang nucleosynthesis, so the cosmology of the scenario is testable independently of colliders through the non-thermal Wino relic abundance it injects.
  • The paper's concession that minimal supergravity with $m_0 \gg m_{1/2}$ fails radiative electroweak symmetry breaking means the scenario's viability rests on non-universal high-scale scalar masses; a dedicated renormalization-group study of the ordering in Eq. 9 would be the decisive follow-up the paper does not supply.
Original abstract

From a theoretical point of view it is not hard to imagine gaugino masses being much lighter than scalar masses. The dominant contributions to gaugino masses are then their anomaly-mediated values. Given current lower bounds on gauginos, which are near the W-mass scale, considering a little hierarchy between weak-scale gauginos and much heavier scalars requires suspending normal intuition on finetuning and naturalness of the Higgs potential. Nevertheless, tantalizing perks come from the hypothesis: lessened flavor and CP violation problems, more compatibility with gauge coupling unification and third generation Yukawa unification, suppressed dimension-five proton decay operators, and no problems satisfying the current Higgs mass constraint for any value of tan(beta) consistent with the top and bottom Yukawa couplings remaining finite up to the grand unified scale. The Tevatron has little chance of finding any evidence of this theory given current constraints. The LHC does well looking for pair production of gluinos which three-body decay into potentially spectacular final states. Dark matter relic abundance can be cosmologically interesting, but table-top experiments will not see LSPs scattering off nucleons. On the other hand, experiments looking for monochromatic photons from LSP annihilations in the galactic halo may find them.

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, 6,287 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.59 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.26 · compares with prior results 0.19 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

From a theoretical point of view it is not hard to imagine gaugino masses being much lighter than scalar masses. The dominant contributions to gaugino masses are then their anomaly-mediated values. Given current lower bounds on gauginos, which are near the W-mass scale, considering a little hierarchy between weak-scale gauginos and much heavier scalars requires suspending normal intuition on finetuning and naturalness of the Higgs potential. Nevertheless, tantalizing perks come from the hypothesis: lessened flavor and CP violation problems, more compatibility with gauge coupling unification and third generation Yukawa unification, suppressed dimension-five proton decay operators, and no problems satisfying the current Higgs mass constraint for any value of tan(beta) consistent with the top and bottom Yukawa couplings remaining finite up to the grand unified scale. The Tevatron has little chance of finding any evidence of this theory given current constraints. The LHC does well looking for pair production of gluinos which three-body decay into potentially spectacular final states. Dark matter relic abundance can be cosmologically interesting, but table-top experiments will not see LSPs scattering off nucleons. On the other hand, experiments looking for monochromatic photons from LSP annihilations in the galactic halo may find them.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 From a theoretical point of view it is not hard to imagine gaugino masses being much lighter than scalar masses. background 0.99 0.05 0.04 hedged possibility 0.49
s1 The dominant contributions to gaugino masses are then their anomaly-mediated values. background 0.53 0.12 0.06 asserted 0.97
s2 Given current lower bounds on gauginos, which are near the W-mass scale, considering a little hierarchy between weak-scale gauginos and much heavier scalars requires suspending normal intuition on finetuning and naturalness of the Higgs potential. interpretation 0.51 0.07 0.21 asserted 0.95
s3 Nevertheless, tantalizing perks come from the hypothesis: lessened flavor and CP violation problems, more compatibility with gauge coupling unification and third generation Yukawa unification, suppressed dimension-five proton decay operators, and no problems satisfying the current Higgs mass constraint for any value of tan(beta) consistent with the top and bottom Yukawa couplings remaining finite up to the grand unified scale. interpretation 0.68 0.25 0.40 asserted 0.70
s4 The Tevatron has little chance of finding any evidence of this theory given current constraints. interpretation 0.62 0.16 0.09 asserted 0.74
s5 The LHC does well looking for pair production of gluinos which three-body decay into potentially spectacular final states. interpretation 0.56 0.14 0.07 asserted 0.93
s6 Dark matter relic abundance can be cosmologically interesting, but table-top experiments will not see LSPs scattering off nucleons. interpretation 0.56 0.21 0.05 hedged possibility 0.58
s7 On the other hand, experiments looking for monochromatic photons from LSP annihilations in the galactic halo may find them. interpretation 0.67 0.12 0.06 hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 0.52 · evidence from argument 0.99.

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

Figures
Figure 1. Production cross-section of gluino pairs at the

Figures reproduced from arXiv:hep-ph/0306127 by the authors.

References
How the literature uses it

93 arXiv papers cite this in 109 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 · 78 sentences without a confident label

Compares with it 2 papers
  • While this is similar to split-SUSY models [ref] , the $A$-terms are not necessarily loop suppressed, and may allow for a lower sfermion mass scale.

    Naturalizing Supersymmetry with a Two-Field Relaxion Mechanism · Introduction · 0.88

  • The required range of the scalar mass is in remarkable agreement with scenarios without supersymmetry breaking singlet fields in the hidden sector, which we call the “without-singlet" scenario [ref] .

    R-Parity Violation Axiogenesis · Introduction · 0.81

Cites it as background 28 papers

Discussion

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