REVIEW
Electroweak Precision Observables in the Minimal Supersymmetric Standard Model
High Energy Physics - Phenomenology · Submitted 15 Dec 2004 · 265 references
Pith's verdict: A careful, quantitative review of MSSM electroweak precision physics; the only real soft spot is that the abstract states the mSUGRA light-scale preference more flatly than the body's own caveats support.
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Referee report
The paper
The paper claims
Precision electroweak data can already feel the effects of supersymmetric particles, and the fits prefer a light SUSY scale.
The reading
What carries the argument
The load-bearing quantity is the $rho$ parameter, $Delta rho = Sigma_Z(0)/M_Z^2 - Sigma_W(0)/M_W^2$, which isolates the leading universal corrections induced by mass splitting inside an isospin doublet — in the Standard Model the top-bottom splitting, in the MSSM the stop-sbottom splitting. Because $Delta rho$ shifts both $M_W$ and $sin^2 theta_{eff}$ in a fixed proportion, $delta M_W approx M_W c_W^2/(c_W^2 - s_W^2) Delta rho$ and $delta sin^2 theta_{eff} approx -c_W^2 s_W^2/(c_W^2 - s_W^2) Delta rho$, a single calculable number carries most of the supersymmetric sensitivity. The $W$ mass prediction itself follows from the muon-decay relation $M_W^2(1 - M_W^2/M_Z^2) = pi alpha/(sqrt{2} G_mu)(1 + Delta r)$, with $Delta r = Delta alpha - (c_W^2/s_W^2) Delta rho + (Delta r)_{rem}$, so the same $Delta rho$ reappears there. The paper's recurring technical check is that the $Delta rho$ approximation reproduces the full two-loop gluonic corrections to $Delta r$ to better than ten percent, which justifies using it to propagate supersymmetric effects into the observables. The numerical results are delivered through the public codes FeynHiggs and POMSSM, which package the resummed Higgs-sector and precision-observable calculations.
Extended reading notes
Core claim
The paper's central claim is that the electroweak precision observables have reached a level of experimental and theoretical control where they constrain the Minimal Supersymmetric Standard Model rather than merely accommodating it. On the theory side, the authors assemble the state of the art: complete one-loop corrections to $M_W$, $sin^2 theta_{eff}$ and $m_h$; the leading two-loop corrections of $O(alpha alpha_s)$ to the $rho$ parameter and to $Delta r$; the two-loop $O(alpha_t^2)$, $O(alpha_t alpha_b)$ and $O(alpha_b^2)$ corrections in the large-$M_{SUSY}$ limit; the resummation of $tan beta$-enhanced bottom-Yukawa effects; and the two-loop supersymmetric contributions to $(g-2)_mu$. They then quantify the residual uncertainty from unknown higher orders and from the experimental errors on $m_t$ and the hadronic contribution to $alpha$, arriving at estimated intrinsic uncertainties of roughly $10$ MeV in $M_W$, $12 times 10^{-5}$ in $sin^2 theta_{eff}$, and $3$ GeV in $m_h$. Confronting these predictions with LEP, SLC, Tevatron and Brookhaven data, the authors report that the mSUGRA scenario with cosmological constraints describes the data very well and shows a clear preference for a relatively light supersymmetric mass scale, while the Standard Model fit is also acceptable but slightly less favoured by the current central values.
Load-bearing premise
The fits assume that the precision observables extracted from the data using Standard Model subtraction terms can be reused unchanged as inputs for the MSSM, because the shifts from the full supersymmetric particle content are taken to be negligible at current experimental precision.
Editorial extensions
If this is right
- If the mSUGRA preference for a light superpartner scale holds, the LHC and a future linear collider should discover supersymmetric particles within their kinematic reach rather than only setting limits.
- The projected GigaZ accuracy on $sin^2 theta_{eff}$ of about $1.3 times 10^{-5}$ and the ILC accuracy on $M_W$ of about $7$ MeV would turn these observables into sharp discriminators between the Standard Model and the MSSM, provided the intrinsic theory errors fall to the estimated future levels of $2 times 10^{-5}$ and $2$ MeV.
- A measured Higgs mass near the MSSM upper bound of roughly $136$ GeV for $m_t = 178$ GeV and $M_{SUSY} leq 1$ TeV would point to large stop mixing, while a much lighter value would point to small mixing or a heavier superpartner scale.
- Non-minimal flavour violation in the second and third squark generations can shift $M_W$ by up to about $0.14$ GeV and $sin^2 theta_{eff}$ by up to about $7 times 10^{-4}$ in extreme regions, so improved precision would probe flavour mixing in the squark sector even without direct production.
- The residual $2.7sigma$ discrepancy in $(g-2)_mu$ can be accounted for by supersymmetric loops with a mass scale between roughly $100$ and $600$ GeV for positive $mu$, which is compatible with the light-scale preference from the $W$ and $Z$ observables.
Reading between the lines
- The paper's light-scale preference and the $(g-2)_mu$ preferred region overlap, so a combined fit treating both as constraints on one spectrum would be a sharper test than the separate discussions given here.
- Because the $Delta rho$ approximation carries most of the supersymmetric sensitivity and is accurate to about ten percent at two loops, the dominant near-term gain may come less from new loop calculations than from reducing the experimental error on $m_t$, which currently induces about $26$ MeV of uncertainty in $M_W$ alone.
- The acknowledged model dependence of the pseudo-observables — extracted using Standard Model subtraction terms — becomes a real liability precisely in the light-supersymmetry region the fit prefers, so a self-consistent MSSM extraction of $M_W$ and $sin^2 theta_{eff}$ would be the natural next step.
- If the LHC finds a superpartner spectrum heavier than a few TeV, the precision-observable route to supersymmetry loses most of its discriminating power, since the loop effects decouple; that outcome would redirect the same machinery toward other weakly coupled new physics rather than toward the MSSM.
Original abstract
The current status of electroweak precision observables in the Minimal Supersymmetric Standard Model (MSSM) is reviewed. We focus in particular on the $W$ boson mass, M_W, the effective leptonic weak mixing angle, sin^2 theta_eff, the anomalous magnetic moment of the muon, (g-2)_\mu, and the lightest CP-even MSSM Higgs boson mass, m_h. We summarize the current experimental situation and the status of the theoretical evaluations. An estimate of the current theoretical uncertainties from unknown higher-order corrections and from the experimental errors of the input parameters is given. We discuss future prospects for both the experimental accuracies and the precision of the theoretical predictions. Confronting the precision data with the theory predictions within the unconstrained MSSM and within specific SUSY-breaking scenarios, we analyse how well the data are described by the theory. The mSUGRA scenario with cosmological constraints yields a very good fit to the data, showing a clear preference for a relatively light mass scale of the SUSY particles. The constraints on the parameter space from the precision data is discussed, and it is shown that the prospective accuracy at the next generation of colliders will enhance the sensitivity of the precision tests very significantly.
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
The current status of electroweak precision observables in the Minimal Supersymmetric Standard Model (MSSM) is reviewed. We focus in particular on the $W$ boson mass, M_W, the effective leptonic weak mixing angle, sin^2 theta_eff, the anomalous magnetic moment of the muon, (g-2)_\mu, and the lightest CP-even MSSM Higgs boson mass, m_h. We summarize the current experimental situation and the status of the theoretical evaluations. An estimate of the current theoretical uncertainties from unknown higher-order corrections and from the experimental errors of the input parameters is given. We discuss future prospects for both the experimental accuracies and the precision of the theoretical predictions. Confronting the precision data with the theory predictions within the unconstrained MSSM and within specific SUSY-breaking scenarios, we analyse how well the data are described by the theory. The mSUGRA scenario with cosmological constraints yields a very good fit to the data, showing a clear preference for a relatively light mass scale of the SUSY particles. The constraints on the parameter space from the precision data is discussed, and it is shown that the prospective accuracy at the next generation of colliders will enhance the sensitivity of the precision tests very significantly.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The current status of electroweak precision observables in the Minimal Supersymmetric Standard Model (MSSM) is reviewed. | contribution 0.71 | 0.29 | 0.04 | asserted 0.68 |
| s1 | We focus in particular on the $W$ boson mass, M_W, the effective leptonic weak mixing angle, sin^2 theta_eff, the anomalous magnetic moment of the muon, (g-2)_\mu, and the lightest CP-even MSSM Higgs boson mass, m_h. | contribution 0.96 | 0.35 | 0.04 | asserted 0.63 |
| s2 | We summarize the current experimental situation and the status of the theoretical evaluations. | contribution 0.79 | 0.60 | 0.02 | asserted 0.79 |
| s3 | An estimate of the current theoretical uncertainties from unknown higher-order corrections and from the experimental errors of the input parameters is given. | contribution 0.54 | 0.71 | 0.03 | asserted 0.97 |
| s4 | We discuss future prospects for both the experimental accuracies and the precision of the theoretical predictions. | future work 0.90 | 0.60 | 0.03 | unclear 0.62 |
| s5 | Confronting the precision data with the theory predictions within the unconstrained MSSM and within specific SUSY-breaking scenarios, we analyse how well the data are described by the theory. | method 0.56 | 0.85 | 0.10 | asserted 0.82 |
| s6 | The mSUGRA scenario with cosmological constraints yields a very good fit to the data, showing a clear preference for a relatively light mass scale of the SUSY particles. | result 0.96 | 0.76 | 0.47 | asserted 1.00 |
| s7 | The constraints on the parameter space from the precision data is discussed, and it is shown that the prospective accuracy at the next generation of colliders will enhance the sensitivity of the precision tests very significantly. | result 0.43 | 0.76 | 0.18 | asserted 0.98 |
What was examined, and what was not
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- P abstract
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Figures
Showing 3 of the paper's 4 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0412214 by the authors.
References
How later papers used it
79 later papers cite it
1 later paper by other authors is listed below: 1 used its data or values. 1 more paper by the same authors is listed: 1 used its data or values.
Uses its data or values 2 of 7 papers with this label · 1 by the same authors
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Assumed an uncertainty of 10 MeV as discussed in the context of the theory error on Delta rho in this paper.
SpecBit, DecayBit and PrecisionBit: GAMBIT modules for computing mass spectra, particle decay rates and precision observables (2017) · 0.86 · paraphrased: the licence does not allow quoting
By the same authors
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Set a theoretical uncertainty of 3 GeV/c^2 on the prediction of this paper.
Prediction for the Lightest Higgs Boson Mass in the CMSSM using Indirect Experimental Constraints (2007) (same authors) · 0.86 · paraphrased: the licence does not allow quoting
How the literature uses it
77 arXiv papers cite this in 103 sentences
Papers citing it · 68 sentences without a confident label
Uses its method or tool 1 paper
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For the RGE running of the soft SUSY-breaking parameters, it uses SoftSUSY [ref] , which is combined consistently with the codes used for the various low-energy observables: FeynHiggs [ref] is used for the evaluation of the Higgs masses and $a_μ^SUSY$ (see also [ref] ), for the other electroweak precision data we have included a code based on [ref] , SuFla [ref] and SuperIso [ref] are used for flavour-related observables, and for dark-matter-related observables MicrOMEGAs [ref] and DarkSUSY [ref] are used.
Predictions for m_t and m_W in Minimal Supersymmetric Models · Introduction · 1.00
Uses its data or values 7 papers
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In the case where the constraint on $m_h$ is applied (Eq. [ref]), its experimental error is parameterized from the $χ^2$ distribution of the measurement [ref] , and a theoretical uncertainty of 3 GeV$/c^2$ is set on its prediction [ref] .
Prediction for the Lightest Higgs Boson Mass in the CMSSM using Indirect Experimental Constraints · Multi-parameter Fit to Experimental Observables · 0.86
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The current intrinsic error of $$ due to unknown higher-order corrections have been estimated to be [ref] ^intr,current = 3 .
Confronting Finite Unified Theories with Low-Energy Phenomenology · The lightest MSSM Higgs boson mass · 0.85
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The remaining theoretical uncertainty on the light $$-even Higgs boson mass has been estimated to be $^theory ≲3$ depending on the parameter region [ref] .
MSSM Higgs Boson Searches at the LHC: Benchmark Scenarios after the Discovery of a Higgs-like Particle · Higgs mass calculations and their scheme dependence · 0.84
Compares with it 1 paper
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Incidentally, let us point out that this is a different approach with respect to the MSSM (see e.g. [ref] ), in which case and owing to the supersymmetric invariance, less freedom is left over to settle independent renormalization conditions.
Neutral Higgs-pair production at Linear Colliders within the general 2HDM: quantum effects and triple Higgs boson self-interactions · Renormalization of the 2HDM Higgs sector · 0.83
Cites it as background 21 papers
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In the context of the Standard Model, the mass of the W-boson can be inferred by comparing the muon decay prediction with the Fermi model [ref] M_W^2 (1-M_W^2/M_Z^2)= πα_em/√(2) G_F (1+Δr) , where $α_em$ and $G_F$ are the fine structure and Fermi constants respectively, and $Δr$ stands for all possible radiative corrections [ref] .
Sterile neutrinos, $0\nu\beta\beta$ decay and the W-boson mass anomaly in a Flipped $SU(5)$ from F-theory · A possible interpretation of the CDF measurement of the W-mass · 0.88
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Corresponding calculations have been performed in [ref] and references therein for the MSSM, and for the NMSSM in [ref] .
$M_W$, Dark Matter and $a_\mu$ in the NMSSM · Introduction · 0.84
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A large amount of work has been invested into calculating higher-order corrections to the mass spectrum within the MSSM with real parameters [ref] as well as the MSSM with complex parameters [ref] .
Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters · Introduction · 0.93
Discussion
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