REVIEW
More Visible Effects of the Hidden Sector
High Energy Physics - Phenomenology · Submitted 6 Sep 2007 · 26 references
Pith's verdict: A clean correction to a published claim about conformal sequestering, with honest caveats about what cannot be computed.
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Referee report
The paper
The paper claims
Strong conformal dynamics in a hidden sector suppresses gaugino masses relative to the gravitino mass, and the authors argue this reshapes how supersymmetry breaking reaches the visible world.
The reading
What carries the argument
The load-bearing object is the wavefunction renormalization factor $Z_S$ of the singlet, fixed in the superconformal limit by the $R$ charge: $Z_S(μ_R) = (Λ_*/μ_R)^{3R(S)-2}$. Two ingredients make it bite. First, the absence of 1PI renormalization of operators linear in $S$, which is what reduces their running to $Z_S^{-1/2}$ and makes the suppression exact and universal across $O_λ$, $O_A$, and $O_μ$. Second, the unitarity bound $R(S) > 2/3$ for gauge-singlet chiral superfields, which pins the sign of the exponent so the factor always grows toward the infrared. Operators quadratic in $S$, by contrast, do receive 1PI corrections and mix with each other; their suppression is governed by the smallest eigenvalue of $2γ_iδ_{ij} + α_{ij}$, an exponent the authors stress is incalculable in strong coupling. That calculable-versus-incalculable split is what lets the paper say the relative strengths among linear operators are fixed while the linear-versus-quadratic competition is not, producing the three cases.
Extended reading notes
Core claim
The paper's central claim is that operators linear in a hidden-sector singlet $S$ are sequestered relative to the gravitino mass, contrary to what the authors of Ref. [11] stated. Since no 1PI diagrams renormalize $O_λ$, $O_A$, or $O_μ$, these operators pick up only the wavefunction factor $Z_S^{-1/2}(μ_R)$. The superconformal algebra requires an $R$ charge $R(S) > 2/3$ for a gauge singlet, so $Z_S(μ_R) = (Λ_*/μ_R)^{3R(S)-2} > 1$, and the suppression is automatic in the infrared. The singlet's $F$ term is suppressed by the same factor, so the gravitino mass $m_{3/2} ≈ Z_S^{-1/2}|f|^2/M_{Pl}$ carries one factor while the gaugino mass $|M_a| ≈ Z_S^{-1}|c_{Sλ} f^2|/M$ carries two, giving $M_a/m_{3/2} ∼ Z_S^{-1/2}$. The same reasoning applies to $μ$ and the $A$ terms. The authors then sort the outcomes into three cases: linear-operator dominance, in which scalars are driven to cancel against the linear contributions leaving $m^2_I = 0$, $m^2_{H_u,d} = -μ^2$, $B = 0$ and $M_a ≈ μ ≈ A_I$; quadratic-operator dominance, in which scalars and $B_μ$ sit far above gauginos and $μ$; and anomaly-mediation dominance when both are suppressed enough.
Load-bearing premise
The whole result rests on taking the wavefunction factor to be the superconformal R-charge expression $Z_S = (Λ_*/μ)^{3R-2}$, which assumes the hidden sector sits at an infrared-attractive fixed point and that the relevant operators breaking supersymmetry do not anomalously enhance that factor — a caveat the authors themselves raise in section 7.
Editorial extensions
If this is right
- Anomaly mediation no longer needs the hidden sector to be singlet-free: the gaugino and $A$-term operators built from singlets are sequestered, so the anomaly-mediated piece can dominate even when singlets with $F$-term vacuum expectation values are present.
- In gauge mediation, if the linear operators dominate, the spectrum at the conformal exit scale has vanishing scalar masses, $m^2_{H_u,d} = -μ^2$, $B = 0$ and $M_a ≈ μ ≈ A$, which after standard-model running solves the $μ$($Bμ$) problem while keeping gauge coupling unification perturbative.
- If the quadratic operators dominate instead, the spectrum looks like gauge mediation with a fractional number of messengers $N_{mess} < 1$, with gaugino masses suppressed relative to scalars but their relative ratios unchanged.
- In gaugino mediation, the volume suppression that gives $B ≈ 16π^2 M_a$ can be undone by the same conformal mechanism, provided the conformal running distance $Λ_*/m_X$ is not too large.
- The gravity-mediated contribution can be either more harmless (when the quadratic exponent $\hat{α}_S > 0$) or more harmful (when $\hat{α}_S < 0$) than in a theory without the conformal dynamics, so the sequestering cuts both ways depending on incalculable signs.
Reading between the lines
- The same R-charge argument should apply to any gauge-singlet operator linear in a hidden field, not only the ones catalogued here, which suggests a general bookkeeping rule: an operator's suppression is set by how many powers of the singlet wavefunction it carries.
- Because $R(S) > 2/3$ is a unitarity bound rather than a dynamical accident, the sign of the effect is one of the few things in this class of models that a lattice or dual-description calculation could in principle confirm without resolving the full strong dynamics.
- If the linear-operator case is realized, the prediction $m^2_{H_u} = m^2_{H_d} = -μ^2$ with $B = 0$ at the conformal exit scale is sharp enough to be checked against the measured Higgs mass and stop spectrum once superpartners are seen.
- The paper's own caveat about higher-dimension operators being anomalously enhanced suggests a natural stress test: find a dual description where a cubic or quartic operator in the singlet grows enough to compete with the linear ones, which would erase the predicted gaugino suppression.
Original abstract
There is a growing appreciation that hidden sector dynamics may affect the supersymmetry breaking parameters in the visible sector (supersymmetric standard model), especially when the dynamics is strong and superconformal. We point out that there are effects that have not been previously discussed in the literature. For example, the gaugino masses are suppressed relative to the gravitino mass. We discuss their implications in the context of various mediation mechanisms. The issues discussed include anomaly mediation with singlets, the mu (B mu) problem in gauge and gaugino mediation, and distinct mass spectra for the superparticles that have not been previously considered.
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
There is a growing appreciation that hidden sector dynamics may affect the supersymmetry breaking parameters in the visible sector (supersymmetric standard model), especially when the dynamics is strong and superconformal. We point out that there are effects that have not been previously discussed in the literature. For example, the gaugino masses are suppressed relative to the gravitino mass. We discuss their implications in the context of various mediation mechanisms. The issues discussed include anomaly mediation with singlets, the mu (B mu) problem in gauge and gaugino mediation, and distinct mass spectra for the superparticles that have not been previously considered.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | There is a growing appreciation that hidden sector dynamics may affect the supersymmetry breaking parameters in the visible sector (supersymmetric standard model), especially when the dynamics is strong and superconformal. | background 1.00 | 0.05 | 0.10 | hedged possibility 0.98 |
| s1 | We point out that there are effects that have not been previously discussed in the literature. | gap 0.68 | 0.77 | 0.14 | asserted 1.00 |
| s2 | For example, the gaugino masses are suppressed relative to the gravitino mass. | result 0.96 | 0.66 | 0.37 | asserted 1.00 |
| s3 | We discuss their implications in the context of various mediation mechanisms. | contribution 0.92 | 0.81 | 0.06 | asserted 0.67 |
| s4 | The issues discussed include anomaly mediation with singlets, the mu (B mu) problem in gauge and gaugino mediation, and distinct mass spectra for the superparticles that have not been previously considered. | contribution 0.96 | 0.55 | 0.16 | asserted 0.89 |
What was examined, and what was not
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- P abstract
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References
How later papers used it
49 later papers cite it
1 later paper by other authors is listed below: 1 used its method or tool.
Uses its method or tool 1 paper
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Treated the dynamics of the gauge term by using this paper's anomalous dimensions.
Suppression of Supergravity Anomalies in Conformal Sequestering (2007) · 0.94 · paraphrased: the licence does not allow quoting
How the literature uses it
49 arXiv papers cite this in 87 sentences
Papers citing it · 64 sentences without a confident label
Contests it 2 papers
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As a result, we find that the idea suggested in [ref] has a tachyonic sector at low energy.
Constraints of the $B_{\mu}/\mu$ solution due to the hidden sector renormalization · Introduction · contest 0.81
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This also implies that the solution to the $μ/Bμ$-problem proposed in [ref] cannot easily work near $(Φ) ∼1$.
Carving Out the Space of 4D CFTs · Introduction · contest 0.71
Uses its method or tool 1 paper
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A dynamics of the gauge term $∫d^2θZ WW$ is treated by using the anomalous dimensions [ref] .
Suppression of Supergravity Anomalies in Conformal Sequestering · Discussion and Conclusions · 0.94
Compares with it 3 papers
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The squark and slepton mass spectrum of scalar sequestering resembles that of gaugino mediation [ref] [ref] , however as was pointed out in [ref] there are important differences for the Higgs sector.
Phenomenology of SUSY with scalar sequestering · Introduction · 0.80
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As reviewed in the introduction, this is in contrast to the generation of $μ$ by Giudice-Masiero type 1-loop Kähler potential couplings in gauge mediation, where the $16 π^2$ discrepancy to the $B μ$ term is generic [ref] and avoidable only with extra effort [ref] .
Retrofitting and the mu Problem · The general idea · 0.85
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Note added: During completion of the manuscript we learned that Murayama, Nomura and Poland are developing a similar solution to the $μ/B_μ$ problem [ref] .
A hidden solution to the mu/B_mu problem in gauge mediation · Introduction · 0.84
Cites it as support 1 paper
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[ref] , the dimension two parameters that undergo conformal scaling include the combined quantity $m^2_H_u + |μ|^2$ (and not the individual parameters $m^2_H_u$ or $|μ|^2$), just as called for in the preceding paragraph.
Quasi-fixed points from scalar sequestering and the little hierarchy problem in supersymmetry · Introduction · 0.96
Cites it as background 15 papers
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See Ref. [ref] for the detail.
A Realistic Extension of Gauge-Mediated SUSY-Breaking Model with Superconformal Hidden Sector · GMSB Models with SCHS and Minimal Messenger Model · 0.80
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Often using “locality" in set-ups with extra dimensions [ref] , or lattices of gauge groups connected by link fields [ref] , or even strong and nearly conformal dynamics of the hidden sector [ref] , these models sequester scalar masses at the input scale (say $$), thereby ensuring that flavor universal gaugino mediation remains the sole source of scaler masses at infrared (IR).
A radiatively generated source of flavor universal scalar soft masses · Introduction · 0.89
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The important remaining issue in this model is the $μ$ - $B_μ$ problem [ref] : if $μ$ and $B_μ$ terms are generated dynamically, it usually predicts $μ^2 ≪B_μ∼m_H_u,d^2$, where $m_H_u$ ($m_H_d$) is a soft SUSY breaking mass for the up-type (down-type) Higgs.
Light Higgsino and Gluino in $R$-invariant Direct Gauge Mediation · Introduction · 0.81
What it cites · 21 sentences without a confident label
Contests 2 papers
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Note that the authors of Ref. [ref] stated that these operators are not sequestered, which we do not agree with.
Visible Effects of the Hidden Sector · Introduction · contest 0.87
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They claim to obtain a spectrum identical to minimal gaugino mediation [ref] , while we find that finite $A$ terms and Higgs soft masses that cancel the $μ^2$ mass contribution are generic.
Minimal Gaugino Mediation · Note Added · contest 0.79
Cites as background 7 papers
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One of the most drastic examples of hidden sector dynamics is conformal sequestering [ref] , which occurs when the hidden sector exhibits strong superconformal dynamics.
Supersymmetry Breaking and Composite Extra Dimensions · Introduction · 0.95
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Anomaly mediation of supersymmetry breaking [ref] is a subtle quantum effect in which the soft supersymmetry breaking parameters are induced due to the superconformal anomaly.
Out Of This World Supersymmetry Breaking · Anomaly Mediation · 1.00
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Anomaly mediation of supersymmetry breaking [ref] is a subtle quantum effect in which the soft supersymmetry breaking parameters are induced due to the superconformal anomaly.
Gaugino Mass without Singlets · Anomaly Mediation · 1.00
Discussion
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