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REVIEW 3 major objections 4 minor 31 references

This paper constructs the complete low-energy effective field theory for baryon-number-violating nucleon decays into an invisible dark photon and uses existing two-body search data to set new lifetime limits.

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 →

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2026-08-01 04:40 UTC pith:4AEZPNM3

load-bearing objection Solid EFT+ChPT toolkit for BNV nucleon decays into a dark photon, but case-A limits depend on an ad hoc m_X normalization that the authors should flag more loudly. the 3 major comments →

arxiv 2607.22452 v1 pith:4AEZPNM3 submitted 2026-07-24 hep-ph

Baryon-number-violating nucleon decays into a dark photon particle

Jin-Han Liang , Yi Liao , Xiao-Dong Ma , Xiang Zhao This is my paper
classification hep-ph
keywords baryon number violationnucleon decaydark photonXLEFTchiral perturbation theoryeffective field theoryinvisible particle decaylifetime bounds
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 aims to give a complete, model-independent low-energy description of baryon-number-violating nucleon decays that emit a dark photon, and to turn existing null searches for ordinary two-body nucleon decays into constraints on these new modes. It builds the full leading-order operator basis—20 operators for a dark-photon potential and 26 for a field-strength tensor—matches them onto chiral perturbation theory, and derives decay widths for two- and three-body final states. Because the dark photon is assumed invisible and escapes the detector, the paper shows that searches for N→lepton+meson can be reinterpreted as limits on N→lepton+meson+X. The result is a set of partial-lifetime bounds and effective-scale limits for 55 operators across a broad range of dark-photon masses. A sympathetic reader would take this as a toolkit that connects concrete experimental signatures to underlying new-physics models.

Core claim

The central claim is that baryon-number-violating nucleon decays into an invisible dark photon are systematically tractable and already experimentally constrained. Treating the dark photon either as a four-potential (dimension-7 operators) or as a field-strength tensor (dimension-8 operators), the paper constructs the complete leading-order XLEFT operator basis, organizes the quark currents into chiral SU(3) irreps, and matches them onto a baryon-number-violating chiral Lagrangian. The resulting two- and three-body decay widths depend only on Wilson coefficients and hadronic low-energy constants, and the accompanying momentum distributions differ between operator structures and shift with th

What carries the argument

The load-bearing object is the complete XLEFT operator basis together with its chiral-spurion matching. Operators are classified by irreducible representations of the QCD chiral group SU(3)L⊗SU(3)R—8⊗1, ̄3⊗3, 6⊗3, and 10⊗1—so that quark currents can be traded for octet baryons and pseudoscalar mesons through spurion fields, while Fierz identities reduce the basis to independent structures. The matching produces baryon-lepton-dark-photon and baryon-lepton-meson-dark-photon vertices controlled by low-energy constants c1–c4, from which two- and three-body widths are computed. The same machinery generates normalized momentum spectra that can discriminate operator structures and probe the dark-ph

Load-bearing premise

The bounds rest on the assumption that the dark photon is invisible and escapes the detector, so that a three-body decay N→lMX has nearly the same visible signature as the conventional two-body decay N→lM—and that the two-body selection efficiencies transfer unchanged; if X decays or interacts inside the detector, the signal regions and lifetime limits must be recomputed.

What would settle it

Search for visible dark-photon decay products, such as e+e− pairs or displaced photon vertices, in nucleon-decay candidate events. If a dark photon produced in a bound nucleon decays inside the detector, the event would carry extra electromagnetic energy and the present recast bounds—which assume only a lepton and meson are visible—would not apply. Conversely, a dedicated three-body search binning the lepton-meson missing-mass spectrum would either confirm the predicted signal region or set limits that can be compared directly with the recast bounds.

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

If this is right

  • Null results from conventional two-body nucleon-decay searches already constrain dark-photon baryon-number-violating operators to effective scales near 10^6–10^7 GeV over most of the allowed mass range.
  • Three-body modes such as p→e+K0X, n→μ−π+X, n→νπ0X, and p→νK+X acquire lower partial-lifetime bounds of order 10^32–10^34 years for light dark photons, making them accessible to next-generation large detectors.
  • The momentum distributions of the charged lepton and meson differ measurably between operator classes and depend on the dark-photon mass, so spectral shapes can help identify the underlying operator and estimate mX.
  • Operators that feed several channels (the Xℓuud, Xν̄udd, and Xν̄uds classes) imply correlated lifetime limits: a bound on one decay mode translates into projected limits on partner modes ranging from about 10^30 to 10^40 years.
  • Field-strength operators in the 10⊗1 chiral irrep necessarily involve a meson and receive the weakest constraints, reflecting their higher chiral order and giving a clear target for dedicated three-body searches.

Where Pith is reading between the lines

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

  • The recast bounds depend critically on the dark photon being invisible and escaping the detector; if X decays visibly (for example, X→e+e− through kinetic mixing) or interacts before leaving the detector, the signal regions change and the quoted lifetime limits would need to be recomputed.
  • The same operator basis and chiral matching could be adapted to a long-lived or displaced dark photon, turning these bounds into a bridge to long-lived-particle searches at neutrino experiments.
  • The momentum-distribution analysis implies a practical search strategy: even without a dedicated three-body analysis, binning by lepton or meson momentum and total visible mass could separate a baryon-number-violating dark-photon signal from atmospheric-neutrino backgrounds.
  • Because the widths are expressed purely in terms of Wilson coefficients and hadronic low-energy constants, any ultraviolet completion that matches onto these operators can be tested directly against the bounds; the main uncertainty is the hadronic constants c3 and c4, currently estimated by naive dimensional analysis.

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 / 4 minor

Summary. The paper constructs a low-energy EFT (XLEFT) for baryon-number-violating nucleon decays into a dark photon. For a four-potential description (case A) it builds a basis of dimension-7 operators, and for a field-strength description (case B) a dimension-8 basis, and then matches the light-quark operators onto baryon chiral perturbation theory using the chiral framework of Refs. [11,20]. It derives general expressions for the two-body decays N→ℓX and the three-body decays N→ℓMX (M=π,η,K), including momentum distributions, and then recasts Super-K searches for N→ℓM to set partial-lifetime limits for the corresponding three-body modes with an invisible X. These bounds are translated into constraints on the effective scales of 55 lepton-flavor-blind operators, and further used to predict lifetime limits for correlated decay modes.

Significance. If the results are correct, this is the first systematic EFT treatment of BNV nucleon decays into a dark photon, and it provides a practical toolkit for future searches at JUNO, Hyper-K, DUNE, and water-Cherenkov detectors. The explicit operator tables, width formulas, and the cross-checks against the ALP framework in App. A.1 are valuable. The paper also correctly exploits existing Super-K data to obtain non-trivial bounds without dedicated searches. The main strength is the breadth and internal consistency of the technical derivation; however, the case-A constraints carry a convention-dependent normalization that limits the claimed model independence, and the numerical bounds depend on NDA estimates for the c3,c4 LECs and on approximate transfer of experimental efficiencies.

major comments (3)
  1. [Sec. 4 preamble; Eq. (4.1a); Sec. 5.2] The case-A width formalism is built on an ad hoc insertion of m_X into every operator. The text states that the longitudinal polarization would give inverse powers of m_X and that 'we introduce an operational factor of m_X for each operator' (Sec. 4.1). This changes the operator dimension from the claimed dimension 7 in Table 1 to dimension 8, changes the m_X dependence of every case-A width in eq. (4.3a) and App. A.1, and therefore changes the effective-scale bounds in Fig. 8 and all recast limits. For a generic massive dark photon coupled as X_μ J^μ, the m_X factor is not present; the derived Λ_eff constraints are thus not directly applicable to the standard normalization. The claim of a model-independent toolkit for 25 case-A operators is not supported unless this normalization is derived from a UV completion or the results are recast in a convention-independent manner (e.g., quoting
  2. [Sec. 5; Sec. 5.1.1; Eq. (5.3)] All recast bounds assume the dark photon is invisible and escapes the detector. Section 5.1 states: 'Given the invisible nature of the dark photon in our consideration, the experimental signatures for both processes are nearly identical...'. If X decays inside the detector to visible states (e.g., X→e+e− via kinetic mixing), the three-body events deposit additional energy and the two-body signal regions, such as the M_tot–P_tot box in eq. (5.3), no longer apply. The derived lifetime limits would need to be recomputed. The paper should state this assumption more prominently in the abstract or conclusions, and clarify that the constraints apply only to invisible or long-lived dark photons, since the title itself does not specify this.
  3. [Sec. 3.2; Sec. 5.2; Fig. 8] The numerical constraints rely on NDA estimates for the hadronic LECs c3 and c4, as explicitly acknowledged in Sec. 3.2 ('there is no available lattice result, and we use NDA estimates') and in the discussion of Fig. 8 ('the potential underestimate of its corresponding LEC c3 based on the NDA'). Since the bounds on operators in the 6⊗3 and 10⊗1 irreps are linear in κ3=c3/c1 or κ4=c4/c1, the resulting Λ_eff limits carry O(1) uncertainties. The paper should quantify this dependence, either by showing the variation of the limits with κ3,κ4 or by quoting a range. Without this, the stated precision of the effective-scale constraints in Fig. 8 is overstated.
minor comments (4)
  1. [Sec. 2; Table 1] The text first defines case A operators as dimension-7, but later the m_X insertion makes them dimension-8. The terminology 'dim-7 operators' in Table 1 and the Abstract should be harmonized with the effective dimension used in the width calculation.
  2. [Sec. 5.1.2; Fig. 6] The recast of n→ℓ+π− data for n→ℓ−π+X assumes equal efficiencies for π+ and π− intranuclear interactions. The text invokes Ref. [43], but the actual charge dependence of π− absorption near the Cherenkov threshold is not shown; a short justification or a conservative uncertainty on this assumption would be helpful.
  3. [Sec. 4.3; Figs. 2–3] The figures show normalized distributions for several operators and dark-photon masses, but the caption does not define the line styles and colors clearly. A legend or explicit matching of curves to operators would improve readability.
  4. [App. A.1; Eq. (A.1a)] The width expressions are presented with three significant figures, but they depend on central-value LECs and NDA κ3,κ4. It would be clearer to quote fewer digits or indicate the parametric uncertainties in the prefactors.

Circularity Check

0 steps flagged

No significant circularity: the operator basis, chiral matching, width formulas, and recast bounds are derived from stated EFT/ChPT inputs and external Super-K data, not from the results they purport to predict.

full rationale

The paper's derivation chain—XLEFT operator basis (Section 2), chiral matching (Section 3.2), decay-width formulas (Section 4), and reinterpretation of Super-K two-body data (Section 5)—does not reduce to its inputs. The operator basis is constructed from chiral fermion fields with Fierz identities; completeness there is a basis-construction claim, not a prediction obtained from the later bounds. The chiral Lagrangian in Eq. (3.9) is adopted from Ref. [11], which shares two present authors, but that is an independent published framework with lattice LECs c1,c2 from Ref. [33] and stated NDA estimates for c3,c4; it is not fitted to the Super-K data used in this paper. The widths depend only on Wilson coefficients and hadronic LECs, and the numerical constraints come from external Super-K two-body searches and Ref. [12]'s recast of p→l+phi. No fitted parameter is relabeled as a prediction. The correlated-mode lifetime bounds in Section 5.3 follow from single-operator dominance applied to externally derived WC limits, so they are logical consequences rather than constructed outputs. The explicit case-A m_X factor is a stated normalization convention ('we introduce an operational factor of m_X for each operator'), not a hidden input; it makes the Λ_eff bounds convention-dependent for case A, but that is a model/UV-completeness caveat rather than circularity. The invisibility assumption underlying the recasts is an experimental-signature assumption, also not circular.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 0 invented entities

The paper rests on the completeness of its Fierz-reduced operator bases, the validity of leading-order ChPT matching with lattice/NDA LECs, and the experimental assumption that X is invisible. No new particles are invented; the dark photon is the assumed external state.

free parameters (4)
  • Hadronic LEC c3 (κ3 = c3/c1) = NDA estimate from [11], no lattice value
    Controls all 6_L⊗3_R operator contributions; paper notes potential underestimate affecting fig. 8 bounds for those operators.
  • Hadronic LEC c4 (κ4 = c4/c1) = NDA estimate from [11], no lattice value
    Controls 10⊗1 operator contributions in case B (e.g., Õ_SL,TL); enters three-body modes only.
  • Non-kinematic signal efficiencies for recast modes = e.g., 0.10 (e+K0), 0.12 (µ+K0), 0.32 (νπ0); ring-ID efficiencies 0.94/0.764/0.917
    Assumed equal to two-body analyses; no three-body validation, affecting all partial-lifetime bounds.
  • Case-A m_X operational factor = 1×m_X per operator
    Introduced by hand to regularize the m_X→0 limit; changes case-A operator dimensions and redefines WCs, so effective-scale bounds are on this rescaled operator.
axioms (7)
  • domain assumption Leading-order chiral Lagrangian [11] is sufficient; vector-meson and higher-order chiral corrections are negligible.
    Section 3.2; all width derivations rely on this.
  • domain assumption Dark photon X is invisible and escapes the detector, so three-body N→lMX events resemble two-body N→lM events modulo kinematics.
    Section 5 intro; required for all Super-K recasts.
  • standard math Operator bases in tables 1 and 2 are complete after Fierz reductions.
    Completeness argued with Fierz identities; standard technique.
  • ad hoc to paper NDA estimates for c3,c4 are adequate at O(1).
    No lattice results; adopted for fig. 8 constraints.
  • domain assumption Single-operator dominance for correlated decay-mode limits.
    Section 5.3; used to convert WC bounds into lifetime limits for other channels.
  • ad hoc to paper Case-A m_X insertion factor defines the physical normalization of the operators.
    Section 4 before §4.1; changes operator dimension and WC interpretation.
  • domain assumption Super-K selection efficiencies for two-body modes transfer unchanged to three-body modes.
    Section 5.1.1; no dedicated simulation for three-body signal efficiency.

pith-pipeline@v1.3.0-alltime-deepseek · 62066 in / 12957 out tokens · 130550 ms · 2026-08-01T04:40:38.040090+00:00 · methodology

0 comments
read the original abstract

Baryon-number-violating (BNV) nucleon decays into a light new particle represent an exciting yet experimentally unexplored frontier. In this work, we systematically study nucleon decays into a dark photon using a low-energy effective field theory extended with a dark photon $X$, referred to as $X$LEFT. We first construct a complete set of leading-order BNV $X$LEFT operators and then perform a systematic matching onto the chiral perturbation theory for operators involving light $u,d,s$ quarks that dominantly contribute to nucleon decays. Within the chiral framework, we derive general expressions for the decay widths of both two- and three-body nucleon decays and analyze the momentum distributions in the latter. Finally, we thoroughly reinterpret the existing experimental data on conventional two-body modes (into a lepton and a meson) to set lower bounds on partial lifetimes of the corresponding three-body modes involving an additional dark photon. These bounds allow us to further set stringent constraints on the $X$LEFT operators and other correlated decay modes. Our results provide a toolkit for future experimental and theoretical studies of these exotic nucleon decays.

discussion (0)

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Reference graph

Works this paper leans on

31 extracted references · 23 linked inside Pith

  1. [5]

    Heeck,Light particles with baryon and lepton numbers,Phys

    J. Heeck,Light particles with baryon and lepton numbers,Phys. Lett. B813(2021) 136043, [2009.01256]

    Pith/arXiv arXiv 2021

  2. [6]

    Fridell, C

    K. Fridell, C. Hati and V. Takhistov,Noncanonical nucleon decays as window into light new physics,Phys. Rev. D110(2024) L031701, [2312.13740]

    Pith/arXiv arXiv 2024

  3. [7]

    Domingo, H

    F. Domingo, H. K. Dreiner, D. K¨ ohler, S. Nangia and A. Shah,A novel proton decay signature at DUNE, JUNO, and Hyper-K,JHEP05(2024) 258, [2403.18502]

    Pith/arXiv arXiv 2024

  4. [8]

    T. Li, M. A. Schmidt and C.-Y. Yao,Baryon-number-violating nucleon decays in ALP effective field theories,JHEP08(2024) 221, [2406.11382]

    Pith/arXiv arXiv 2024

  5. [9]

    T. Li, M. A. Schmidt and C.-Y. Yao,Baryon-number-violating nucleon decays in sterile neutrino effective field theories,2502.14303

    Pith/arXiv arXiv

  6. [10]

    W.-Q. Fan, Y. Liao, X.-D. Ma and H.-L. Wang,Comprehensive investigation on baryon number violating nucleon decays involving an axion-like particle*,Chin. Phys. C50(2026) 033103, [2507.11844]

    arXiv 2026

  7. [11]

    Liao, X.-D

    Y. Liao, X.-D. Ma and H.-L. Wang,New Chiral Structures for Baryon Number Violating Nucleon Decays,Phys. Rev. Lett.135(2025) 161801, [2504.14855]

    arXiv 2025

  8. [12]

    X.-D. Ma, M. A. Schmidt and W. Zhang,Baryon-number-violating nucleon decays in SMEFT extended with a light scalar,JHEP02(2026) 175, [2511.02169]

    arXiv 2026

  9. [13]

    Heeck and I

    J. Heeck and I. M. Shoemaker,Nucleon Decays into Light New Particles in Neutrino Detectors,Phys. Rev. Lett.135(2025) 111804, [2506.08090]

    Pith/arXiv arXiv 2025

  10. [14]

    J. C. Helo, T. Ota and M. Hirsch,Invisible neutron decay and light BSM particles,Phys. Rev. D113(2026) 035002, [2510.14940]

    arXiv 2026

  11. [15]

    Adolf, C

    P. Adolf, C. Hati, M. Hirsch and V. Takhistov,Echoes of Nucleon Decay from Long-Lived Particles,2605.21583

    Pith/arXiv arXiv

  12. [16]

    Fornal, A

    B. Fornal, A. Hewitt and Y. Zhao,Baryonic and Leptonic GeV Dark Matter,Phys. Lett. B 815(2021) 136151, [2011.09014]

    Pith/arXiv arXiv 2021

  13. [17]

    G. Elor, M. Escudero and A. Nelson,Baryogenesis and Dark Matter fromBMesons,Phys. Rev. D99(2019) 035031, [1810.00880]

    Pith/arXiv arXiv 2019

  14. [18]

    Fornal and B

    B. Fornal and B. Grinstein,Dark Matter Interpretation of the Neutron Decay Anomaly, Phys. Rev. Lett.120(2018) 191801, [1801.01124]

    Pith/arXiv arXiv 2018

  15. [19]

    Liang, Y

    J.-H. Liang, Y. Liao, X.-D. Ma and H.-L. Wang,Dark sector effective field theory,JHEP12 (2023) 172, [2309.12166]

    Pith/arXiv arXiv 2023

  16. [20]

    Claudson, M

    M. Claudson, M. B. Wise and L. J. Hall,Chiral Lagrangian for Deep Mine Physics,Nucl. Phys. B195(1982) 297–307. – 48 – [21]Super-Kamiokandecollaboration, V. Takhistov et al.,Search for Nucleon and Dinucleon Decays with an Invisible Particle and a Charged Lepton in the Final State at the Super-Kamiokande Experiment,Phys. Rev. Lett.115(2015) 121803, [1508.05...

    Pith/arXiv arXiv 1982

  17. [27]

    Liao, X.-D

    Y. Liao, X.-D. Ma and H.-L. Wang,Effective field theory approach to lepton number violating decaysK ± →π ∓l±l±: short-distance contribution,JHEP01(2020) 127, [1909.06272]

    Pith/arXiv arXiv 2020

  18. [28]

    Grojean, J

    C. Grojean, J. Kley and C.-Y. Yao,Hilbert series for ALP EFTs,JHEP11(2023) 196, [2307.08563]

    Pith/arXiv arXiv 2023

  19. [29]

    H. Song, H. Sun and J.-H. Yu,Complete EFT operator bases for dark matter and weakly-interacting light particle,JHEP05(2024) 103, [2306.05999]

    Pith/arXiv arXiv 2024

  20. [30]

    W.-Q. Fan, Y. Liao, X.-D. Ma and H.-L. Wang,Baryon number violating hydrogen decay, Phys. Lett. B862(2025) 139335, [2412.20774]

    Pith/arXiv arXiv 2025

  21. [31]

    Liao, X.-D

    Y. Liao, X.-D. Ma and H.-L. Wang,Chiral perturbation theory for baryon-number-violating nucleon decay into a vector meson,Phys. Rev. D112(2025) L031704, [2506.05052]. [32]Particle Data Groupcollaboration, S. Navas et al.,Review of particle physics,Phys. Rev. D110(2024) 030001

    Pith/arXiv arXiv 2025

  22. [33]

    J.-S. Yoo, Y. Aoki, P. Boyle, T. Izubuchi, A. Soni and S. Syritsyn,Proton decay matrix elements on the lattice at physical pion mass,Phys. Rev. D105(2022) 074501, [2111.01608]

    Pith/arXiv arXiv 2022

  23. [34]

    E. E. Jenkins and A. V. Manohar,Baryon chiral perturbation theory using a heavy fermion Lagrangian,Phys. Lett. B255(1991) 558–562

    1991

  24. [35]

    Bijnens, H

    J. Bijnens, H. Sonoda and M. B. Wise,On the Validity of Chiral Perturbation Theory for Weak Hyperon Decays,Nucl. Phys. B261(1985) 185–198

    1985

  25. [36]

    J. A. Oller, M. Verbeni and J. Prades,Meson-baryon effective chiral lagrangians to O(q**3), JHEP09(2006) 079, [hep-ph/0608204]. – 49 – [37]RQCDcollaboration, G. S. Bali, S. Collins, W. S¨ oldner and S. Weish¨ aupl,Leading order mesonic and baryonic SU(3) low energy constants from Nf=3 lattice QCD,Phys. Rev. D105 (2022) 054516, [2201.05591]

    Pith/arXiv arXiv 2006

  26. [38]

    Shtabovenko, R

    V. Shtabovenko, R. Mertig and F. Orellana,FeynCalc 9.3: New features and improvements, Comput. Phys. Commun.256(2020) 107478, [2001.04407]

    Pith/arXiv arXiv 2020

  27. [39]

    M. G. Mayer and J. H. D. Jensen,Elementary Theory of Nuclear Shell Structure. Wiley, New York, 1955

    1955

  28. [40]

    Nakamura, S

    K. Nakamura, S. Hiramatsu, T. Kamae, H. Muramatsu, N. Izutsu and Y. Watase,The Reaction C-12 (e, e’ p) at 700-MeV and DWIA Analysis,Nucl. Phys. A268(1976) 381–407. [41]Super-Kamiokandecollaboration, K. Abe et al.,Search for Nucleon Decay vian→¯νπ 0 andp→¯νπ + in Super-Kamiokande,Phys. Rev. Lett.113(2014) 121802, [1305.4391]. [42]Super-Kamiokandecollaborat...

    Pith/arXiv arXiv 1976

  29. [43]

    Saunders, S

    A. Saunders, S. Hoeibraten, J. J. Kraushaar, B. J. Kriss, R. J. Peterson, R. A. Ristinen et al.,Reaction and total cross-sections for low-energy pi+ and pi- on isospin zero nuclei, Phys. Rev. C53(1996) 1745–1752

    1996

  30. [44]

    Numao, Y

    T. Numao, Y. I. Davydov, J.-M. Poutissou, T. C. Awes, V. Cianciolo, S. Berridge et al., Search for free decay of negative pions in water and light materials,Phys. Rev. D73(2006) 092004, [hep-ex/0605121]

    Pith/arXiv arXiv 2006

  31. [45]

    Learned, F

    J. Learned, F. Reines and A. Soni,Limits on Nonconservation of Baryon Number,Phys. Rev. Lett.43(1979) 907. [46]SNO+collaboration, A. Allega et al.,Improved search for invisible modes of nucleon decay in water with the SNO+detector,Phys. Rev. D105(2022) 112012, [2205.06400]. [47]JUNOcollaboration, A. Abusleme et al.,JUNO sensitivity to invisible decay mode...

    Pith/arXiv arXiv 1979