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Measurements of Masses in SUGRA Models at LHC

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Henri Bachacou, Ian Hinchliffe, Frank E. Paige

High Energy Physics - Phenomenology · Submitted 27 Jul 1999 · 19 references

Pith's verdict: The kinematic core is sound and the upper-plus-lower-edge combination is a genuine methodological step, but the linchpin of the model-independent claim is the paper's own weakest measurement, and the numbers in Sections 4 and 7 don't match.

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arXiv IDhep-ph/9907518 (version 1)
Pith ID7VLCFVVP, Pith's permanent record of this paper and its review
CitationFrank E. Paige, Henri Bachacou, Ian Hinchliffe. "Measurements of Masses in SUGRA Models at LHC." arXiv:hep-ph/9907518 (1999). https://pith.science/paper/7VLCFVVP
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The paper

The paper claims

The LHC can extract four supersymmetric particle masses from cascade-decay edges without fitting a model.

The reading

The paper asks whether the LHC can measure superpartner masses without first assuming a particular model of supersymmetry breaking. It studies a benchmark minimal SUGRA point and shows that the three-step chain $%s$ produces upper kinematic edges in the $%s$, $%s$, and $%s$ distributions, plus a lower edge in $%s$, and that these edges can be inverted for the four masses. The same chain gives a very sharp dilepton endpoint whose statistical error is small enough, about $0.1%$, to test whether selectrons and smuons have equal masses. Extending the scalar-mass pattern produces extra edges or changes in lepton-pair rates, which the paper uses to argue that LHC data can constrain non-universal SUGRA parameters.

What carries the argument

The load-bearing device is the kinematic edge in a multistep cascade. For the chain $%s$, the upper endpoint of the $%s$ mass is fixed by $M_{%s}$, $M_{%s}$, and $M_{%s}$; the $%s$ and $%s$ endpoints involve different combinations of masses, and their ratio $%s$ is independent of the squark mass. The lower edge of $%s$ comes from the backward configuration of the two-body decay in the $%s$ rest frame and supplies the extra equation needed to close the system. Flavour weighting ($e^+e^-+%s - e^%s%s$) cancels uncorrelated lepton pairs and makes the edges visible above combinatorial background.

Extended reading notes

Core claim

At the benchmark point $m_0=100$ GeV and $m_{1/2}=300$ GeV, the paper finds that the four-body decay chain $%s$ yields enough independent kinematic features to determine $M_{%s}$, $M_{%s}$, $M_{%s}$, and $M_{%s}$ without a model fit. The measured features are the upper endpoints of the $%s$, $%s$, and $%s$ distributions and the lower edge of the $%s$ distribution. The resulting errors are about $%s$ for the squark, $%s$ for the second neutralino, $%s$ for the right-handed slepton, and $%s$ for the lightest neutralino, with strong correlations among them. A separate fit to the $%s$ endpoint gives $108.7$ GeV with a statistical uncertainty near $0.1%$, which the paper presents as a possible test of slepton universality. The paper also shows that changing the SU(5) scalar masses or the third-generation masses produces new dilepton or trilepton structures and changes in same-flavour and opposite-flavour lepton ratios.

Load-bearing premise

The model-independent mass errors rest on the assumption that the roughly $10%$ downward bias in the fitted jet-based endpoints, attributed to energy lost outside the $R=0.4$ jet cone, can be calibrated away with real data; if that calibration is not controlled, the extracted masses move by more than the quoted errors.

Editorial extensions

If this is right

  • At the LHC, the $%s$ chain can give a first measurement of four superpartner masses that does not assume minimal SUGRA.
  • The dilepton endpoint can be measured with a statistical error near $0.1%$, so a difference between the $e^+e^-$ and $%s$ endpoints would be direct evidence for non-universal slepton masses.
  • A second low-mass dilepton edge, or a trilepton edge in jet-vetoed events, would reveal left-handed sleptons or a heavier left-handed slepton sector and constrain $m_5$.
  • Ratios of same-flavour to opposite-flavour and same-charge lepton pairs can constrain the third-generation scalar mass $m_{3rd}$ and test $e/%s$ universality.
  • The improved global fit sharpens the minimal SUGRA parameters to $m_0=100.0%spm3.63$ GeV and $m_{1/2}=300.0%spm4.99$ GeV.

Reading between the lines

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

  • The same edge-inversion strategy should apply to any cascade with two visible steps and one invisible particle, so the method is not tied to this benchmark point; what travels is the bookkeeping of independent endpoints, not the particular masses.
  • Because the quoted $0.1%$ dilepton precision is below the expected lepton energy-scale systematic, a real universality test will need an in-situ calibration of the lepton scale, not just more events.
  • The non-observation of extra dilepton structure already turns the $m_5$ scan into a bound; with more luminosity the rate ratios could become a discovery channel for the tau sector rather than only a constraint.
  • The paper's own unsuccessful attempt at full event reconstruction suggests that the endpoint method, not event-by-event reconstruction, is the realistic route at a hadron collider with jet-dominated final states.
Original abstract

This paper presents new measurements in a case study of the minimal SUGRA model with m_0=100 GeV, mhalf=300 GeV, A_0=0, tan(beta)=2.1, and mu=+1 based on four-body distributions from three-step decays and on minimum masses in such decays. These measurements allow masses of supersymmetric particles to be determined without relying on a model. The feasibility of testing slepton universality at the ~0.1% level at high luminosity is discussed. In addition, the effect of enlarging the parameter space of the minimal SUGRA model is discussed. The direct production of left handed sleptons and the non-observation of additional structure in the dilepton invariant mass distributions is shown to provide additional constraints.

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, 4,320 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.70 · compares with prior results 0.14 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

This paper presents new measurements in a case study of the minimal SUGRA model with m_0=100 GeV, mhalf=300 GeV, A_0=0, tan(beta)=2.1, and mu=+1 based on four-body distributions from three-step decays and on minimum masses in such decays. These measurements allow masses of supersymmetric particles to be determined without relying on a model. The feasibility of testing slepton universality at the ~0.1% level at high luminosity is discussed. In addition, the effect of enlarging the parameter space of the minimal SUGRA model is discussed. The direct production of left handed sleptons and the non-observation of additional structure in the dilepton invariant mass distributions is shown to provide additional constraints.

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 This paper presents new measurements in a case study of the minimal SUGRA model with m_0=100 GeV, mhalf=300 GeV, A_0=0, tan(beta)=2.1, and mu=+1 based on four-body distributions from three-step decays and on minimum masses in such decays. contribution 0.94 0.95 0.11 asserted 1.00
s1 These measurements allow masses of supersymmetric particles to be determined without relying on a model. interpretation 0.75 0.79 0.65 asserted 0.85
s2 The feasibility of testing slepton universality at the ~0.1% level at high luminosity is discussed. future work 0.35 0.37 0.06 hedged possibility 0.71
s3 In addition, the effect of enlarging the parameter space of the minimal SUGRA model is discussed. contribution 0.83 0.50 0.03 unclear 0.66
s4 The direct production of left handed sleptons and the non-observation of additional structure in the dilepton invariant mass distributions is shown to provide additional constraints. result 0.85 0.84 0.08 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.41 · evidence from observation or experiment 0.63.

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
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. Mass distribution for the smaller of the two
Figure 2. Distribution of the larger of the two ℓ ±q masses for ℓ +ℓ −q events in which Mℓℓq < 600 GeV and a fit described in the text. 0 500 1000 1500 2000 2500 0 200 400 600 800 1000 117.1 / 25 P1 0.1991 P2 -0.7660E-03 P3 498.0 P4 121.7 P5 -0.1236 Mllq (GeV) Events/20 GeV/100 fb-1
Figure 3. Distribution for the smaller of the two ℓ +ℓ −q masses from
Figure 4. Distribution of the larger of the two ℓℓq masses after cuts described in the text, showing the lower edge. • Transverse sphericity ST > 0.2. In addition, events were selected to have exactly two b jets with pT,b > 25 GeV, 70 < Mbb < 110 GeV, and the larger of the two masses formed by combining this pair with either of the two hardest jets was selected, since at least one of the two should be greater than the minimum mass. This distribution is shown in
Figure 5. Larger of the two b ¯bq jet masses, showing the hq mass threshold. • Mmax ℓq = " (M2 q˜L −M2 χ˜ 0 2 )(M2 χ˜ 0 2 −M2 ℓ˜R ) M2 χ˜ 0 2 #1/2 = 479.3 ± 5.5 GeV • Mmin ℓℓq (Equation 2) = 271.8 ± 5.4 GeV There are also two measurements related to ˜χ 0 2 → χ˜ 0 1h: • The maximum hq mass (see Reference 2) (Mmax hq ) 2 = M2 h +  M2 q˜ − M2 χ˜ 0 2    M2 χ˜ 0 2 + M2 h − M2 χ˜ 0 1 + q (M2 χ˜ 0 2 − M2 h − M2 χ˜ 0 1 ) 2 − 4M2 hM2 χ˜ 0 1 2M2 χ˜ 0 2   . which has the value Mmax hq = 522.6 ± 5.2 GeV. • The minimum hq mass Mmin hq (Equation 3) = 346.5 ± 17.3 GeV A large error is assigned to the…
Figure 6. Distribution of the ˜χ 0 1 , ˜ℓR, ˜χ 0 2 , and ˜qL masses satisfying all constraints discussed in the text. The fitted widths are about ±12%, ±9%, ±6%, and ±3% respectively. mass of ˜qL. If the error on Mmin ℓℓq were reduced to ±1%, as might be possible with a more careful understanding of the systematics, the error on Mχ˜ 0 1 would be reduced to ±7.5%. The errors are highly correlated as can be seen from Figures 7–8 which show the scatter plots of Mχ˜ 0 2 vs. Mχ˜ 0 1 and M˜ℓR vs. Mχ˜ 0 1 . Of course, the errors on the masses are much poorer than those that arise from
Figure 7. Scatter plot of Mχ˜ 0 2 vs. Mχ˜ 0 1 solutions satisfying all constraints discussed in the text. -0.5 -0.25 0 0.25 0.5 -0.5 -0.25 0 0.25 0.5 ∆M1 /M1 ∆ Me/Me
Figure 8. Scatter plot of M˜ℓR vs. Mχ˜ 0 1 solutions satisfying all constraints discussed in the text. so are only measured with an accuracy of several percent. An important exception is the decay χ˜ 0 2 → ˜ℓ ± R ℓ ∓ → χ˜ 0 1 ℓ +ℓ −, which has an end point at Mmax ℓℓ = Mχ˜ 0 2 vuuut1 − M2 ˜ℓR M2 χ˜ 0 2 vuuut1 − M2 χ˜ 0 1 M2 ℓ˜R . (4) 13
Figure 9. ℓ +ℓ − mass distribution showing the χ 2 MINUIT fit using PAW. A difference in the end points for e +e − and µ +µ − would directly indicate a difference in the ˜eR and µ˜R masses, which obviously an important issue for testing models that purport to understand flavor physics. This decay is generally allowed in SUGRA models which give cosmologically interesting cold dark matter [13], such as the one discussed here. It is also common in GMSB models since the ˜ℓR has only U(1) couplings and tends to be light. The derivative of the end-point with respect to M˜ℓR vanishes at the…
Figure 10. ℓ +ℓ − mass distribution showing the maximum likelihood MINUIT fit using PAW. 0 200 400 600 800 1000 0 0.5 1 1.5 2 2.5 ηmax Events/0.05/100 fb-1
Figure 11. Maximum |ηℓ | for dilepton events. Clearly a lot more work is needed to understand how to calibrate the detector and to extract information at this level of accuracy. In particular, the discrepancy between the fitted and calculated end points even in this highly idealized simulation needs to be understood, presumably by studying many different samples of SUSY events. It seems clear, however, that statistical errors below about 0.1% may be achievable, especially if the masses were a bit lower so that the ˜χ 0 2 → χ˜ 0 1h decay were absent. 15
Figure 12. Mℓℓ distribution after the cuts at the m5 = m10 = 100 GeV point (dashed line) and modified point with m5 = 75 GeV (solid line). 0 25 50 75 100 0 50 100 150 200 Mµµ (GeV) Events/4 GeV/10 fb-1
Figure 13. Mµµ distribution after the cuts at the m5 = m10 = 100 GeV point (dashed line) and modified point with m5 = 75 GeV (solid line). Figures 12 and 14 show the lepton pair invariant mass for the benchmark case and the modified cases with m5 = 75 GeV and m5 = 50 GeV. Figures 13 and 15 show the muon pair invariant mass for the same cases. The edge at low Mℓℓ for m5 = 75 GeV is clearer in the muon case due to the increased acceptance at low pT . The presence of two structures with comparable rates enables one to deduce the presence of two decay chains and to measure the two end points.…
Figure 14. Mℓℓ distribution after the cuts at the m5 = m10 = 100 GeV point (dashed line) and modified point with m5 = 50 GeV (solid line). 0 25 50 75 100 0 50 100 150 200 Mµµ (GeV) Events/4 GeV/10 fb-1
Figure 15. Mµµ distribution after the cuts at the m5 = m10 = 100 GeV point (dashed line) and modified point with m5 = 50 GeV (solid line). is reduced to 50 GeV, the higher mass structure is becoming weaker because the ˜χ 0 2 ℓ ˜ℓL coupling is larger than the ˜χ 0 2 ℓ ˜ℓR one. As m5 increases, M˜ℓL increases, and the branching ratio for ˜χ 0 2 → ℓ ˜ℓL vanishes quickly around m5 = 80 GeV. Hence, m5 = 75 GeV is about the upper limit where one can distinguish from the benchmark case using this channel. 18
Figure 16. Mℓℓℓ distribution after the cuts for the m5 = m10 = 100 GeV point. Note that the number of events is very small. 0 2.5 5 7.5 10 0 100 200 300 Mlll (GeV) Events/10 GeV/300 fb-1
Figure 17. Mℓℓℓ distribution after the cuts for the modified point with m5 = 115 GeV. that for masses larger than this, the position of the edge can be measured with a precision of 3 GeV and is very sensitive to m5. As m5 increases further, the production rate falls off and the signal disappears for m5 above 250 GeV. 6.2 Variations of masses for the third generation Here we investigate the possibility that m0 for the third generation squarks and sleptons is different from that for the first two generations. As in the m5 cases, the greatest sensitivity to this change is in the slepton sector,…
Figure 18. Mℓℓℓ distribution after the cuts for the modified point with m5 = 125 GeV. In another study [16], the use of hadronic tau decays was illustrated. It was shown how the τ τ invariant mass distribution could be inferred from the observed decay products and the kinematic end point extracted. This method enables mτ˜R to be constrained. If this method could be exploited in the case of interest here, slepton universality could be tested with great accuracy. The method fails for several reasons all of which are related to the observable event rate and background. • The signal is less clear…
Figure 19. Mτ+τ− distribution at point 5 after the cuts and after subtraction of same sign pairs. -50 0 50 100 0 100 200 300 Mττ (GeV) Events/20 GeV/10 fb-1
Figure 20. Mτ+τ− distribution at modified point with tanβ = 5 (other parameters at their nominal point 5 value) after the cuts and after subtraction of same sign pairs. luminosity would not be enough to reduce them to a satisfying level. LHC high luminosity would give enough statistics, but the Mττ reconstruction method used here is based on full simulation [17] and has not been proven to be viable at high luminosity; additional pile-up events could compromise it. To emphasize the deterioration of the signal due to the ˜χ 0 2 → h 0χ˜ 0 1 channel, a model with tan β shifted from 2.1 to 5 (th
Figure 21. rOC and rSC for various m3 rd values (see text). The error bars correspond to an integrated luminosity of 10 fb−1 . To summarize: for m3 rd < 100 GeV, rOC is very sensitive to m3 rd . If 10 GeV < m3 rd < 75 GeV, one should be able to constrain it with an accuracy of a few GeV. For m3 rd > 100 GeV, things are not so easy: for (m3 rd < 200 GeV), rOC increases slightly, giving some sensitivity to its value. As a result, models with m3 rd above 200 GeV can hardly be distinguished from each other. 7 Determination of parameters In previous studies [2, 6] we needed to rely on a global
Figure 22. difference ∆p/p between the generated and the best reconstructed |~p|. (pχ˜ 0 1 + pℓ,1 + pℓ,2) 2 = M2 χ˜ 0 2 (pχ˜ 0 1 + pℓ,1 + pℓ,2 + pq) 2 = M2 q˜ There are also two constraints from /ET . Since the measurement errors on the jets are comparable to those on /ET , the jet energies were smeared by factors λi distributed in Gaussian manner, and the best solution was taken to be the one which minimizes χ 2 = ( /Ex − p1x − p2x) 2 σ 2( /Ex) + ( /Ey − p1y − p2y) 2 σ 2( /Ey) + λ 2 1 σ 2(λ1) + λ 2 2 σ 2(λ2) , where both the missing energy resolutions σ( /Ex,y) and the jet energy scale…

Figures reproduced from arXiv:hep-ph/9907518 by the authors.

References
How later papers used it

50 later papers cite it

Evidence: substantial. 50 of the citing papers share no author with it, and 5 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 80 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

Uses its method or tool 2 of 5 papers with this label
How the literature uses it

46 arXiv papers cite this in 76 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 · 50 sentences without a confident label

Uses its method or tool 5 papers
  • The figure shows several mass differences (left) and the edge variables (right) stemming from the decay chain $q̃ →q χ^0_2$ with the subsequent decay $χ^0_2 →l^± l̃^∓ →l^±l^∓χ^0_1$ [ref] .

    Supersymmetric mass spectra and the seesaw scale · Mass spectra and LHC and ILC observables · 0.91

  • We use a Gaussian smeared fitting function in Ref. [ref] for that. $χ^2$/n.d.f is not good for both fits, therefore our fits should be regarded as crude estimates.

    Inclusive transverse mass analysis for squark and gluino mass determination · Monte Carlo analysis: Point A (MMAM) · 0.99

  • The kinematic endpoint of the dilepton invariant mass distribution from [ref] is a well-known tool for extracting superpartner masses [ref] .

    Flavor and LHC Searches for New Physics · Interpreting the new physics in the presence of generation-dependence · 0.91

Cites it as background 21 papers

Discussion

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