Pith. sign in

REVIEW 3 major objections 3 minor 63 references

A 10 TeV muon collider can determine the trilinear Higgs self-coupling to about ±5% (0.96<κ3<1.05 at 68% CL), using Higgs-pair production via vector boson fusion in the four-b-jet final state.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-04 18:44 UTC pith:3IZJNWWR

load-bearing objection A careful, transparent sensitivity projection that brings the 10 TeV muon collider's kappa3 reach to a few percent, conditional on beam-induced background mitigation working as assumed. the 3 major comments →

arxiv 2608.01888 v1 pith:3IZJNWWR submitted 2026-08-03 hep-ph

Measuring the trilinear Higgs self-coupling in Higgs boson pair production at multi-TeV muon colliders

Kingman Cheung , Jae Sik Lee , Soojin Lee , Chen Wang This is my paper
classification hep-ph
keywords Higgs self-couplingmuon colliderHiggs pair productionvector boson fusionb-quark final statemachine learning classifierstopological data analysiskappa3 measurement
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to show that a multi-TeV muon collider can measure the trilinear Higgs self-coupling, κ3, far more precisely than the HL-LHC, by using Higgs boson pair production through vector-boson fusion with both Higgses decaying to b-quark pairs. At 10 TeV with 10 ab−1, the combined resolved and boosted analysis projects 0.96<κ3<1.05 at 68% confidence, a few-percent determination; at 3 TeV with 1 ab−1 it projects 0.80<κ3<1.29. The analysis separates signal from backgrounds several orders of magnitude larger using a jet-to-Higgs pairing network, topological data analysis of energy flow, and two dedicated classifiers whose outputs feed a two-dimensional likelihood fit. A sympathetic reader would care because κ3 fixes the curvature of the Higgs potential, and a precision measurement would directly probe the shape of the electroweak vacuum and distinguish the Standard Model from extended Higgs sectors.

Core claim

On its own terms, the paper's central claim is that κ3 can be extracted from the (D_HH, D_κ3) score plane in VBF HH→bbbb at muon colliders, and that the combination of a resolved four-jet region and a boosted two-fat-jet region yields 68% confidence intervals of 0.80<κ3<1.29 at 3 TeV with 1 ab−1 and 0.96<κ3<1.05 at 10 TeV with 10 ab−1, with the SM signal observable at 5.4σ and 36σ respectively. The κ3 information comes from the shape of the m_HH spectrum near threshold, which the trilinear amplitude enhances or suppresses depending on the sign and magnitude of κ3−1; the D_κ3 classifier captures this shape variation, while D_HH handles signal-background separation. The authors emphasize that

What carries the argument

Two separately trained classifiers per kinematic region, D_HH (signal vs background) and D_κ3 (shape discriminator between κ3=0.4 and 1.6), whose outputs define a two-dimensional binned likelihood. In the resolved region a symmetry-preserving attention network (SPANet) assigns the four jets to two Higgs candidates before classification, and five topological data analysis (TDA) descriptors from persistent homology of the event's (η,ϕ) energy flow are included as global features. The workhorse is the orthogonality of the two scores: D_κ3 carries κ3 shape information that is essentially independent of the signal/background axis, so removing it widens the 68% interval by roughly 30%.

Load-bearing premise

The paper's own Sec. 4.6 states that beam-induced background is not overlaid on the simulated events, its mitigation being assumed achievable by future detector and reconstruction improvements; if that mitigation falls short, or if unmodeled systematics shift b-tagging or background normalizations, the few-percent 10 TeV interval and even the 5σ observability could degrade substantially.

What would settle it

Overlay the beam-induced background on the Delphes-simulated signal and background at 10 TeV and rerun the two-dimensional likelihood; if the 68% interval widens beyond roughly ±10%, the central projection fails. Alternatively, a 5% shift in b-tagging efficiency or a 10% change in the dominant HZνν background normalization that moves the 10 TeV interval by more than its quoted width would falsify the claim.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • At 10 TeV, the combined analysis constrains κ3 to 0.96–1.05 at 68% CL and 0.92–1.10 at 95% CL, a direct few-percent measurement of the Higgs self-coupling.
  • The SM HH signal is observable above background at 5.4σ at 3 TeV and 36σ at 10 TeV, so the κ3 measurement is built on a detected signal.
  • The 3 TeV projection of 0.80–1.29 already beats the projected HL-LHC reach of about 0.5–1.6 at 68% CL.
  • Combining resolved and boosted regions narrows the interval beyond either channel alone, and the boosted channel becomes more important as the collision energy rises.
  • The extracted κ3 interval is asymmetric, with the lower edge tighter than the upper, reflecting the cross-section minimum near κ3≈1.7.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the projection holds, a 10 TeV muon collider would make κ3 one of the best-measured Higgs couplings, comparable to the HVV couplings, sharpening model discrimination in extended Higgs sectors.
  • The same two-classifier plus TDA architecture could be transferred to other lepton colliders or to the quartic HHVV coupling, where VBF also dominates.
  • Because the paper treats the 10 TeV result as statistics-limited, detector improvements such as higher b-tagging efficiency or stronger beam-background rejection would translate almost linearly into tighter κ3 bounds; conversely, unmitigated beam-induced background is the main threat to the projection.
  • A dedicated program to calibrate b-tagging and jet-mass scale at the muon collider would be a prerequisite for realizing the quoted precision, since the classifiers lean heavily on those inputs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. This paper presents a Monte Carlo sensitivity projection for measuring the trilinear Higgs self-coupling modifier κ3 in VBF HH production at 3 and 10 TeV muon colliders, using the HH→bbbb final state and combining a resolved four-jet region with a boosted two-fat-jet region. The analysis uses SPANet jet pairing, TDA descriptors, and two classifiers (D_HH for signal/background separation and D_κ3 for κ3 shape information) in a two-dimensional binned maximum likelihood fit. With Asimov data at κ3=1, the quoted combined 68% intervals are 0.80<κ3<1.29 at 3 TeV (1 ab^-1) and 0.96<κ3<1.05 at 10 TeV (10 ab^-1), with expected HH observability of 5.4σ and 36σ, respectively. The paper explicitly labels the result as a statistics-only projection: beam-induced background is not overlaid on the simulated events and systematic uncertainties are not included.

Significance. If the projection survives closer scrutiny, the paper demonstrates a qualitatively new level of precision for the Higgs self-coupling at a future multi-TeV muon collider, substantially surpassing the projected HL-LHC sensitivity. The analysis is carefully executed within its stated scope: independent MC samples are used for classifier training, template construction, and Asimov data; all performance figures are based on held-out test partitions; the training code is publicly available; and SHAP-based interpretability is used to validate the two-network design. The central methodological contribution is the combination of SPANet pairing, TDA descriptors, and a two-classifier likelihood, which is shown to improve the extracted κ3 interval by roughly 20–30% relative to using D_HH alone. The main caveat is that the quoted few-percent intervals are conditional on the assumption that beam-induced background can be fully mitigated and that no systematic uncertainties degrade the measurement; the paper is transparent about this, but the headline should be read with that condition.

major comments (3)
  1. [Sec. 4.6; Eq. (4.3)–(4.4); abstract] The headline combined intervals of Sec. 5.2.3 are statistical-only Asimov projections under the explicit assumption that beam-induced background (BIB) can be fully mitigated and that no systematic uncertainties exist. The text states: 'the beam-induced background is not overlaid on the simulated events, its mitigation being assumed to be achievable...' and 'Systematic uncertainties ... are not included.' This assumption is load-bearing: the TDA descriptors in Eq. (4.2) are computed from all EFlow constituents with E_T>0, and the classifiers use low-level particle clouds, b-tags, fat-jet masses, and lepton vetoes, all of which BIB directly degrades. From Tables 2 and 4, d ln N_signal/dκ3 is about 0.6–0.7 near κ3=1, so a few-percent shift in signal rate, b-tag efficiency, or background normalization changes κ3 by O(0.03–0.05), comparable to the 10 TeV interval half-width. I recommend eithe
  2. [Sec. 5.2.3; Fig. 16] The combined result is defined by adding the -ΔlnL profiles, but the input profiles are not fit over a common range: at 10 TeV the resolved profile uses only κ3∈[0.8,1.2] (Sec. 5.2.1), while the combined figure is said to be fit to the full grid. The quoted combined interval is therefore not tied to a single, reproducible likelihood fit. Please specify explicitly whether the quoted interval is obtained from (a) a single binned fit to the concatenated (D_HH,D_κ3) planes of both regions, (b) the sum of two polynomial fits with different ranges, or (c) something else. A combined fit over a common κ3 range would remove the ambiguity and let the reader verify the 0.96<κ3<1.05 interval.
  3. [Sec. 5.2.2; Eq. (5.3)] At 3 TeV the boosted channel contributes to the combined interval using only a single-bin D_HH>0.95 selection with about six signal events after pre-selection (Table 3) and only of order three expected signal events after the cut. The authors note that the asymptotic conversion is approximate, but with such low yields the Poisson likelihood is discrete and the fourth-order polynomial fit through the coarse κ3 grid may introduce spurious curvature. This channel is not essential to the 10 TeV claim, but it does affect the quoted 3 TeV combined interval. Please check the result with an exact Poisson (or profile-likelihood) treatment, or state how much the 3 TeV interval changes if the boosted channel is removed.
minor comments (3)
  1. [Sec. 4.6] The fourth-order polynomial fit to -ΔlnL is used without showing residuals or goodness-of-fit. Please include a validation plot or quantify the fit quality, especially in the narrow 10 TeV trough where the quoted interval is read off.
  2. [Sec. 5.2.3; Table 5] The comparison with Refs. [45,46] should state explicitly whether the cited intervals are also statistical-only Asimov projections and whether they use the same detector and BIB assumptions. Otherwise the claim of being 'about 20% narrower' is difficult to interpret.
  3. [Sec. 3.2] The upper pT cuts in the boosted region (800 GeV and 600 GeV) are motivated by MC generation efficiency. Please clarify whether these cuts are optimized for sensitivity or are fixed by the generation choices, and whether the quoted intervals are stable under reasonable variations of these thresholds.

Circularity Check

0 steps flagged

No significant circularity: the kappa3 interval is a likelihood projection from independently generated MC templates, not an input-output equivalence.

full rationale

The central claim (Sec. 5.2.3, Eq. 5.6) is obtained from a binned maximum-likelihood fit, Eq. (4.3), whose signal templates s_i(kappa3) are generated at discrete, independently simulated kappa3 points (Eqs. 2.4 and 2.5), with the Asimov dataset taken at kappa3=1 from a statistically independent sample. The resulting -Delta lnL profile is the standard way a sensitivity projection is computed in high-energy physics: the 'prediction' (0.96<kappa3<1.05 at 10 TeV) is the expected confidence interval under the SM hypothesis, not a parameter that has been fitted to the data and then renamed a prediction. D_kappa3 is trained on the two bracketing hypotheses kappa3=0.4 and 1.6, but it is then applied as a shape discriminant to all kappa3 hypotheses; the final likelihood fit does not reduce to those two training points by construction. The paper explicitly states in Sec. 4.6 that the quoted sensitivities are statistical-only Asimov projections and that systematic uncertainties and beam-induced background are not included; this is a clearly stated limitation that makes the result conditional, but it is not a circular step. The comparisons with Refs. [45,46,47,48] are external benchmarks, not self-citations. The few self-citations (e.g., Refs. [28,73]) are contextual and not load-bearing for the projection. No derivation-equals-input pattern, fitted-input-called-prediction pattern, or self-citation chain is present. The analysis is therefore self-contained as a sensitivity study and receives a circularity score of 0.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The projection is built entirely on a simulation chain with no real data: MadGraph/Pythia/Delphes, a simplified detector card, hand-chosen kinematic cuts, and ML hyperparameters. The free parameters listed are the most consequential analysis choices. The axioms are the physics and simulation assumptions required for the MC templates to represent a real experiment. No invented physical entities are introduced.

free parameters (5)
  • Mass-window reference masses M1, M2 for XHH pairing = Resolved: 120/110 GeV; boosted: 124/115 GeV
    Hand-chosen below mH to account for detector, neutrino, and out-of-cone mass shifts; used in pre-selection and as classifier input. Different choices would shift which events enter the selection.
  • Kinematic region thresholds and pre-selection cuts = pT(H)<200 GeV resolved; 200<pT(J1)<800 GeV, 200<pT(J2)<600 GeV, 65<M(J)<150 GeV boosted; lepton veto pT>10 GeV
    Chosen from physics motivation and visual inspection of MC distributions; these boundaries define the two analyses and materially affect signal and background yields in Tables 1-4.
  • D_kappa3 training endpoints = kappa3 = 0.4 and 1.6
    Chosen symmetric about the SM point and far enough apart for a clear shape difference; this choice determines the shape discriminant and hence the information gained from the two-dimensional fit.
  • 3 TeV boosted D_HH score cut = 0.95
    Fixed because the expected significance rises monotonically with the cut value and tighter cuts leave fewer than three expected signal events; this working point is an analysis choice, not derived from first principles.
  • Fourth-order polynomial fit to -delta lnL(kappa3) = Quartic polynomial over the scanned kappa3 grid
    Interpolates the likelihood profile to read 68% and 95% intervals; interval boundaries therefore inherit the polynomial shape assumption, partially checked with dedicated endpoint samples.
axioms (5)
  • domain assumption SM Higgs sector with mH=125 GeV, v=246 GeV, and kappaV=kappa2V=1; only kappa3 is varied.
    Sets the signal model and fixes all other Higgs couplings to SM values, so deviations in kappaW, kappaZ, or kappa2V cannot contaminate the projection.
  • domain assumption The MadGraph5_aMC@NLO + Pythia8 + Delphes3 simulation chain with the MuonColliderDet card accurately represents signal, backgrounds, and detector response.
    All yields, shapes, and efficiencies come from this simulation chain; no real-data validation is provided.
  • ad hoc to paper Beam-induced background is absent from the simulation because its mitigation is assumed achievable.
    Explicitly stated at the end of Sec. 4.6; muon colliders have large beam-induced backgrounds, so this is a strong assumption that could invalidate the quoted precision if false.
  • domain assumption Classifiers trained on Monte Carlo generalize to the Asimov dataset, with statistically independent training, template, and Asimov samples.
    The kappa3 extraction uses classifier outputs and template binning from MC; if classifier performance differs in a real detector, the intervals change.
  • domain assumption Asymptotic binned Poisson likelihood and single-parameter confidence-level conventions apply, including the low-statistics 3 TeV boosted channel.
    The paper itself notes the asymptotic conversion is approximate at 3 TeV boosted, where fewer than ten signal events survive pre-selection.

pith-pipeline@v1.3.0-daily-deepseek · 28176 in / 13386 out tokens · 143060 ms · 2026-08-04T18:44:28.532344+00:00 · methodology

0 comments
read the original abstract

The trilinear Higgs self-coupling determines the shape of the Higgs potential, and its measurement is a central goal of future colliders. We assess the sensitivity of multi-TeV muon colliders to the coupling modifier $\kappa_3$ in Higgs boson pair production via vector boson fusion, using the $b\bar{b}b\bar{b}$ final state at $\sqrt{s}=3$ TeV with $1$ ab$^{-1}$ and at $10$ TeV with $10$ ab$^{-1}$. Events are analyzed in two complementary regions, a resolved region with four jets and a boosted region with two large-radius jets. To extract the signal from backgrounds a few orders of magnitude larger, we combine a supervised jet-to-Higgs pairing network based on the SPANet approach, topological data analysis of the event energy flow, and two dedicated classifiers, $D_{\rm HH}$ for the signal-to-background separation and $D_{\kappa_3}$ for the $\kappa_3$ shape information. The coupling is extracted from a two-dimensional likelihood fit to the distribution of the two classifier outputs. Combining the two regions, we obtain $0.80<\kappa_3<1.29$ at $3$ TeV and $0.96<\kappa_3<1.05$ at $10$ TeV at $68\%$ confidence level. The $10$ TeV determination reaches the few-percent level in this statistics-limited projection, which surpasses by a large amount the precision projected for the HL-LHC.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

63 extracted references · 43 linked inside Pith

  1. [1]

    Higgs,Broken Symmetries and the Masses of Gauge Bosons,Phys

    P.W. Higgs,Broken Symmetries and the Masses of Gauge Bosons,Phys. Rev. Lett.13 (1964) 508

    1964

  2. [2]

    Englert and R

    F. Englert and R. Brout,Broken Symmetry and the Mass of Gauge Vector Mesons,Phys. Rev. Lett.13(1964) 321

    1964

  3. [3]

    Guralnik, C.R

    G.S. Guralnik, C.R. Hagen and T.W.B. Kibble,Global Conservation Laws and Massless Particles,Phys. Rev. Lett.13(1964) 585. [4]ATLAScollaboration,Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,Phys. Lett. B716(2012) 1 [1207.7214]. [5]CMScollaboration,Observation of a New Boson at a Mass of 1...

    Pith/arXiv arXiv 1964

  4. [6]

    Gunion, H.E

    J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson,The Higgs Hunter’s Guide, vol. 80 (2000), 10.1201/9780429496448

    doi:10.1201/9780429496448 2000

  5. [7]

    Ivanov,Building and testing models with extended Higgs sectors,Prog

    I.P. Ivanov,Building and testing models with extended Higgs sectors,Prog. Part. Nucl. Phys. 95(2017) 160 [1702.03776]

    Pith/arXiv arXiv 2017

  6. [8]

    Nilles,Supersymmetry, Supergravity and Particle Physics,Phys

    H.P. Nilles,Supersymmetry, Supergravity and Particle Physics,Phys. Rept.110(1984) 1

    1984

  7. [9]

    Haber and G.L

    H.E. Haber and G.L. Kane,The Search for Supersymmetry: Probing Physics Beyond the Standard Model,Phys. Rept.117(1985) 75

    1985

  8. [10]

    Martin,A Supersymmetry primer,Adv

    S.P. Martin,A Supersymmetry primer,Adv. Ser. Direct. High Energy Phys.18(1998) 1 [hep-ph/9709356]

    Pith/arXiv arXiv 1998

  9. [11]

    Lee,A Theory of Spontaneous T Violation,Phys

    T.D. Lee,A Theory of Spontaneous T Violation,Phys. Rev. D8(1973) 1226

    1973

  10. [12]

    Branco, P.M

    G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva,Theory and phenomenology of two-Higgs-doublet models,Phys. Rept.516(2012) 1 [1106.0034]

    Pith/arXiv arXiv 2012

  11. [13]

    Djouadi,The Anatomy of electro-weak symmetry breaking

    A. Djouadi,The Anatomy of electro-weak symmetry breaking. II. The Higgs bosons in the minimal supersymmetric model,Phys. Rept.459(2008) 1 [hep-ph/0503173]. – 32 –

    Pith/arXiv arXiv 2008

  12. [14]

    Kaplan and H

    D.B. Kaplan and H. Georgi,SU(2) x U(1) Breaking by Vacuum Misalignment,Phys. Lett. B 136(1984) 183

    1984

  13. [15]

    Georgi and D.B

    H. Georgi and D.B. Kaplan,Composite Higgs and Custodial SU(2),Phys. Lett. B145(1984) 216

    1984

  14. [16]

    Panico and A

    G. Panico and A. Wulzer,The Composite Nambu-Goldstone Higgs, vol. 913, Springer (2016), 10.1007/978-3-319-22617-0, [1506.01961]

    Pith/arXiv arXiv 2016

  15. [17]

    Glover and J.J

    E.W.N. Glover and J.J. van der Bij,HIGGS BOSON PAIR PRODUCTION VIA GLUON FUSION,Nucl. Phys. B309(1988) 282

    1988

  16. [18]

    Dicus, C

    D.A. Dicus, C. Kao and S.S.D. Willenbrock,Higgs Boson Pair Production From Gluon Fusion,Phys. Lett. B203(1988) 457

    1988

  17. [19]

    Plehn, M

    T. Plehn, M. Spira and P.M. Zerwas,Pair production of neutral Higgs particles in gluon-gluon collisions,Nucl. Phys. B479(1996) 46 [hep-ph/9603205]

    Pith/arXiv arXiv 1996

  18. [20]

    Djouadi, W

    A. Djouadi, W. Kilian, M. Muhlleitner and P.M. Zerwas,Production of neutral Higgs boson pairs at LHC,Eur. Phys. J. C10(1999) 45 [hep-ph/9904287]

    Pith/arXiv arXiv 1999

  19. [21]

    Dawson, S

    S. Dawson, S. Dittmaier and M. Spira,Neutral Higgs boson pair production at hadron colliders: QCD corrections,Phys. Rev. D58(1998) 115012 [hep-ph/9805244]

    Pith/arXiv arXiv 1998

  20. [22]

    U. Baur, T. Plehn and D.L. Rainwater,Determining the Higgs Boson Selfcoupling at Hadron Colliders,Phys. Rev. D67(2003) 033003 [hep-ph/0211224]

    Pith/arXiv arXiv 2003

  21. [23]

    Binoth, S

    T. Binoth, S. Karg, N. Kauer and R. Ruckl,Multi-Higgs boson production in the Standard Model and beyond,Phys. Rev. D74(2006) 113008 [hep-ph/0608057]

    Pith/arXiv arXiv 2006

  22. [24]

    U. Baur, T. Plehn and D.L. Rainwater,Examining the Higgs boson potential at lepton and hadron colliders: A Comparative analysis,Phys. Rev. D68(2003) 033001 [hep-ph/0304015]

    Pith/arXiv arXiv 2003

  23. [25]

    Baglio, A

    J. Baglio, A. Djouadi, R. Gr¨ ober, M.M. M¨ uhlleitner, J. Quevillon and M. Spira,The measurement of the Higgs self-coupling at the LHC: theoretical status,JHEP04(2013) 151 [1212.5581]

    Pith/arXiv arXiv 2013

  24. [26]

    Grigo, J

    J. Grigo, J. Hoff, K. Melnikov and M. Steinhauser,On the Higgs boson pair production at the LHC,Nucl. Phys. B875(2013) 1 [1305.7340]

    Pith/arXiv arXiv 2013

  25. [27]

    Barger, L.L

    V. Barger, L.L. Everett, C.B. Jackson and G. Shaughnessy,Higgs-Pair Production and Measurement of the Triscalar Coupling at LHC(8,14),Phys. Lett. B728(2014) 433 [1311.2931]

    Pith/arXiv arXiv 2014

  26. [28]

    C.-T. Lu, J. Chang, K. Cheung and J.S. Lee,An exploratory study of Higgs-boson pair production,JHEP08(2015) 133 [1505.00957]. [29]CMS, ATLAScollaboration,Combination of ATLAS and CMS searches for Higgs boson pair production at √s= 13TeV,2602.23991. [30]ATLAScollaboration,HL-LHC prospects for the measurement of Higgs boson pair production in theb ¯bb¯bfina...

    Pith/arXiv arXiv 2015

  27. [31]

    Palmer et al.,Muon collider design,Nucl

    R. Palmer et al.,Muon collider design,Nucl. Phys. B Proc. Suppl.51(1996) 61 [acc-phys/9604001]

    Pith/arXiv arXiv 1996

  28. [32]

    Ankenbrandt et al.,Status of muon collider research and development and future plans, Phys

    C.M. Ankenbrandt et al.,Status of muon collider research and development and future plans, Phys. Rev. ST Accel. Beams2(1999) 081001 [physics/9901022]. – 33 –

    Pith/arXiv arXiv 1999

  29. [33]

    Delahaye, M

    J.P. Delahaye, M. Diemoz, K. Long, B. Mansouli´ e, N. Pastrone, L. Rivkin et al.,Muon Colliders,1901.06150

    Pith/arXiv arXiv 1901

  30. [34]

    Al Ali et al.,The muon Smasher’s guide,Rept

    H. Al Ali et al.,The muon Smasher’s guide,Rept. Prog. Phys.85(2022) 084201 [2103.14043]. [35]Muon Collidercollaboration,The International Muon Collider Collaboration,JACoW IP AC2021(2021) 3792

    Pith/arXiv arXiv 2022

  31. [36]

    Black et al.,Muon Collider Forum report,JINST19(2024) T02015 [2209.01318]

    K.M. Black et al.,Muon Collider Forum report,JINST19(2024) T02015 [2209.01318]

    Pith/arXiv arXiv 2024

  32. [37]

    Accettura et al.,Towards a muon collider,Eur

    C. Accettura et al.,Towards a muon collider,Eur. Phys. J. C83(2023) 864 [2303.08533]

    Pith/arXiv arXiv 2023

  33. [38]

    Costantini, F

    A. Costantini, F. De Lillo, F. Maltoni, L. Mantani, O. Mattelaer, R. Ruiz et al.,Vector boson fusion at multi-TeV muon colliders,JHEP09(2020) 080 [2005.10289]

    Pith/arXiv arXiv 2020

  34. [39]

    T. Han, D. Liu, I. Low and X. Wang,Electroweak couplings of the Higgs boson at a multi-TeV muon collider,Phys. Rev. D103(2021) 013002 [2008.12204]

    Pith/arXiv arXiv 2021

  35. [40]

    Edelsbrunner, D

    H. Edelsbrunner, D. Letscher and A. Zomorodian,Topological persistence and simplification, Discrete & Computational Geometry28(2002) 511

    2002

  36. [41]

    L. Li, T. Liu and S.-J. Xu,Jet Topology,2006.12446

    Pith/arXiv arXiv 2006

  37. [42]

    Beuria,Persistent homology of collider observations: When (w)hole matters,Phys

    J. Beuria,Persistent homology of collider observations: When (w)hole matters,Phys. Lett. B 846(2023) 138188 [2308.10588]

    Pith/arXiv arXiv 2023

  38. [43]

    Beuria,Probing Invisible Decay ofZ ′ at Muon Collider with Topological Data Analysis and Machine Learning,2509.19756

    J. Beuria,Probing Invisible Decay ofZ ′ at Muon Collider with Topological Data Analysis and Machine Learning,2509.19756

    arXiv

  39. [44]

    Mittal,Topology-Informed Jet Tagging using Persistent Homology,2601.01450

    S. Mittal,Topology-Informed Jet Tagging using Persistent Homology,2601.01450

    arXiv

  40. [45]

    Andreetto et al.,Aspects of Higgs Physics at a √s= 3TeV Muon Collider with detailed detector simulation,Eur

    P. Andreetto et al.,Aspects of Higgs Physics at a √s= 3TeV Muon Collider with detailed detector simulation,Eur. Phys. J. C85(2025) 221 [2405.19314]

    Pith/arXiv arXiv 2025

  41. [46]

    Andreetto, M

    P. Andreetto, M. Casarsa, A. Gianelle, C. Giraldin, D. Lucchesi, L. Palombini et al., (Aspects of ) Higgs physics at a √s= 10TeV Muon Collider,Nuovo Cim. C49(2026) 43. [47]International Muon Collidercollaboration,Higgs physics at a 10 TeV muon collider with the MUSIC detector,PoSEPS-HEP2025(2026) 385

    2026

  42. [48]

    Andreetto, M

    P. Andreetto, M. Casarsa, A. Gianelle, C. Giraldin, D. Lucchesi, L. Palombini et al.,Higgs Physics at a √s= 10TeV Muon Collider, in32nd International Symposium on Lepton Photon Interactions at High Energies: Lepton-Photon 2025, 4, 2026 [2604.17514]

    Pith/arXiv arXiv 2025

  43. [49]

    Shmakov, M.J

    A. Shmakov, M.J. Fenton, T.-W. Ho, S.-C. Hsu, D. Whiteson and P. Baldi,SPANet: Generalized permutationless set assignment for particle physics using symmetry preserving attention,SciPost Phys.12(2022) 178 [2106.03898]

    Pith/arXiv arXiv 2022

  44. [50]

    Glashow,Partial Symmetries of Weak Interactions,Nucl

    S.L. Glashow,Partial Symmetries of Weak Interactions,Nucl. Phys.22(1961) 579

    1961

  45. [51]

    Weinberg,A Model of Leptons,Phys

    S. Weinberg,A Model of Leptons,Phys. Rev. Lett.19(1967) 1264

    1967

  46. [52]

    Salam,Weak and Electromagnetic Interactions,Conf

    A. Salam,Weak and Electromagnetic Interactions,Conf. Proc. C680519(1968) 367. [53]CMScollaboration,A portrait of the Higgs boson by the CMS experiment ten years after the discovery,Nature607(2022) 60 [2207.00043]

    Pith/arXiv arXiv 1968

  47. [54]

    Alwall, R

    J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer et al.,The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations,JHEP07(2014) 079 [1405.0301]. – 34 –

    Pith/arXiv arXiv 2014

  48. [55]

    Artoisenet, R

    P. Artoisenet, R. Frederix, O. Mattelaer and R. Rietkerk,Automatic spin-entangled decays of heavy resonances in Monte Carlo simulations,JHEP03(2013) 015 [1212.3460]

    Pith/arXiv arXiv 2013

  49. [56]

    Sj¨ ostrand, S

    T. Sj¨ ostrand, S. Ask, J.R. Christiansen, R. Corke, N. Desai, P. Ilten et al.,An introduction to PYTHIA 8.2,Comput. Phys. Commun.191(2015) 159 [1410.3012]. [57]DELPHES 3collaboration,DELPHES 3, A modular framework for fast simulation of a generic collider experiment,JHEP02(2014) 057 [1307.6346]

    Pith/arXiv arXiv 2015

  50. [58]

    Boronat, J

    M. Boronat, J. Fuster, I. Garcia, E. Ros and M. Vos,A robust jet reconstruction algorithm for high-energy lepton colliders,Phys. Lett. B750(2015) 95 [1404.4294]

    Pith/arXiv arXiv 2015

  51. [59]

    Boronat, J

    M. Boronat, J. Fuster, I. Garcia, P. Roloff, R. Simoniello and M. Vos,Jet reconstruction at high-energy electron–positron colliders,Eur. Phys. J. C78(2018) 144 [1607.05039]. [60]ATLAScollaboration,Search for resonant pair production of Higgs bosons in theb ¯bb¯bfinal state usingppcollisions at √s= 13 TeV with the ATLAS detector,Phys. Rev. D105(2022) 09200...

    Pith/arXiv arXiv 2018

  52. [61]

    Bauer,Ripser: efficient computation of vietoris–rips persistence barcodes,Journal of Applied and Computational Topology5(2021) 391–423

    U. Bauer,Ripser: efficient computation of vietoris–rips persistence barcodes,Journal of Applied and Computational Topology5(2021) 391–423

    2021

  53. [62]

    Vaswani, N

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A.N. Gomez et al.,Attention is all you need,CoRRabs/1706.03762(2017) [1706.03762]

    Pith/arXiv arXiv 2017

  54. [63]

    Paszke, S

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan et al.,PyTorch: An Imperative Style, High-Performance Deep Learning Library, inAdvances in Neural Information Processing Systems, H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alch´ e-Buc, E. Fox and R. Garnett, eds., vol. 32, Curran Associates, Inc., 2019

    2019

  55. [64]

    Chollet et al., “Keras.”https://keras.io, 2015

    F. Chollet et al., “Keras.”https://keras.io, 2015

    2015

  56. [65]

    Akiba, S

    T. Akiba, S. Sano, T. Yanase, T. Ohta and M. Koyama,Optuna: A next-generation hyperparameter optimization framework, inThe 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 2623–2631, 2019

    2019

  57. [66]

    Chen and C

    T. Chen and C. Guestrin,XGBoost: A Scalable Tree Boosting System,1603.02754

    Pith/arXiv arXiv

  58. [67]

    Lundberg and S.-I

    S.M. Lundberg and S.-I. Lee,A Unified Approach to Interpreting Model Predictions, 1705.07874. [68]ATLAScollaboration,Observation ofH→b ¯bdecays andV Hproduction with the ATLAS detector,Phys. Lett. B786(2018) 59 [1808.08238]. [69]Particle Data Groupcollaboration,Review of particle physics,Phys. Rev. D110(2024) 030001

    Pith/arXiv arXiv 2018

  59. [70]

    Cowan, K

    G. Cowan, K. Cranmer, E. Gross and O. Vitells,Asymptotic formulae for likelihood-based tests of new physics,Eur. Phys. J. C71(2011) 1554 [1007.1727]. [71]Muon Collidercollaboration,The physics case of a 3 TeV muon collider stage, 2203.07261

    Pith/arXiv arXiv 2011

  60. [72]

    Maura, B.A

    V. Maura, B.A. Stefanek and T. You,The Higgs Self-Coupling at FCC-ee,Phys. Rev. Lett. 135(2025) 141802 [2503.13719]

    Pith/arXiv arXiv 2025

  61. [73]

    J. Park, J. Chang, K. Cheung and J.S. Lee,Measuring the trilinear Higgs boson self-coupling at the 100 TeV hadron collider via multivariate analysis,Phys. Rev. D102(2020) 073002 [2003.12281]. – 35 –

    Pith/arXiv arXiv 2020

  62. [74]

    Mangano, G

    M.L. Mangano, G. Ortona and M. Selvaggi,Measuring the Higgs self-coupling via Higgs-pair production at a 100 TeV p-p collider,Eur. Phys. J. C80(2020) 1030 [2004.03505]

    Pith/arXiv arXiv 2020

  63. [75]

    Stapf, A

    B. Stapf, A. Taliercio, E. Gallo, K. Tackmann and P. Mastrapasqua,Higgs self-coupling measurements at the FCC-hh,PoSEPS-HEP2023(2024) 413 [2312.03513]. – 36 –

    Pith/arXiv arXiv 2024