Recognition: no theorem link
Observation of the decay chi_{c1}(3872)rightarrow Jmskip -3mu/mskip -2mupsi μ^+μ^-
Pith reviewed 2026-05-16 10:23 UTC · model grok-4.3
The pith
The χ_c1(3872) decays to J/ψ μ⁺μ⁻ for the first time, seen at 6.5 sigma with a relative branching fraction of (1.68 ± 0.32 ± 0.05) × 10^{-3}.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The central claim is the first observation of χ_c1(3872) → J/ψ μ⁺μ⁻ with 6.5σ significance and the ratio of branching fractions BF(χ_c1(3872) → J/ψ μ⁺μ⁻) / BF(χ_c1(3872) → J/ψ π⁺π⁻) = (1.68 ± 0.32 ± 0.05) × 10^{-3}, where the uncertainties separate uncorrelated and correlated systematic contributions.
What carries the argument
Reconstruction of χ_c1(3872) candidates from J/ψ μ⁺μ⁻ final states followed by a fit to the invariant-mass distribution that isolates the narrow signal peak while modeling combinatorial background and efficiency corrections relative to the pion reference channel.
If this is right
- This new decay channel supplies an additional observable for testing models of the χ_c1(3872) internal structure.
- The measured ratio quantifies the relative suppression of the leptonic final state compared with the hadronic one.
- Future higher-statistics samples can tighten the ratio and compare it directly to theoretical predictions for electromagnetic versus strong contributions.
- The analysis framework of background subtraction and efficiency ratios can be reused for other rare decays of the same state.
Where Pith is reading between the lines
- The small ratio may reflect the electromagnetic character of the muon-pair emission versus the strong or isospin-violating pion emission.
- Precision measurements of this ratio in larger datasets could distinguish between molecular, tetraquark, or conventional charmonium interpretations.
- The technique of normalizing to the pion mode reduces many systematic uncertainties and could be applied to searches for analogous rare modes in other exotic hadrons.
Load-bearing premise
Background shapes in the invariant-mass distributions and relative detector efficiencies for muons versus pions are modeled accurately enough that the extracted signal yield is not significantly biased.
What would settle it
An independent analysis of a comparable or larger dataset that finds no excess above background at the known χ_c1(3872) mass in the J/ψ μ⁺μ⁻ invariant-mass spectrum would falsify the observation.
Figures
read the original abstract
The first observation of the $\chi_{c1}(3872)\rightarrow J\mskip -3mu/\mskip -2mu\psi \mu^+\mu^-$ decay is reported using proton-proton collision data recorded with the LHCb detector corresponding to an integrated luminosity of $9fb^{-1}$. The decay mode is observed for the first time, with a significance of $6.5\sigma$. Its branching fraction is measured relative to the $\chi_{c1}(3872)\rightarrow J\mskip -3mu/\mskip -2mu\psi \pi^+\pi^-$ decay mode \begin{align*} \frac{\cal{BF}(\chi_{c1}(3872)\rightarrow J\mskip -3mu/\mskip -2mu\psi \mu^+\mu^-)}{\cal{BF}(\chi_{c1}(3872)\rightarrow J\mskip -3mu/\mskip -2mu\psi \pi^+\pi^-)} = \left(1.68\pm 0.32\pm 0.05\right)\times10^{-3}, \end{align*} where the first uncertainty includes both statistical contributions and systematic contributions which are uncorrelated between data-taking periods, and the second represents the systematic contributions that are correlated between data-taking periods.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper reports the first observation of the rare decay χ_c1(3872) → J/ψ μ⁺μ⁻ using 9 fb⁻¹ of LHCb pp collision data. The mode is observed with 6.5σ significance, and the branching-fraction ratio relative to the normalization channel χ_c1(3872) → J/ψ π⁺π⁻ is measured to be (1.68 ± 0.32 ± 0.05) × 10^{-3}, where the first uncertainty combines statistical and uncorrelated systematic contributions and the second contains correlated systematics.
Significance. If the result holds, it constitutes the first observation of this decay channel and supplies a new, small branching-fraction ratio that constrains models of the χ_c1(3872) internal structure. The analysis follows established LHCb procedures for yield extraction from invariant-mass fits and efficiency correction via simulation, which is a strength for reproducibility within the collaboration's standard framework.
major comments (2)
- [§5] §5 (signal extraction and efficiency correction): the branching-fraction ratio is obtained from the ratio of fitted yields divided by the simulated efficiency ratio between the μ⁺μ⁻ and π⁺π⁻ final states. Because the two modes differ in particle species, PID response, and kinematic distributions, any residual mismatch between data and simulation in the efficiency correction directly scales the extracted yield; the manuscript should provide explicit data-driven validation (e.g., control samples or tag-and-probe studies) showing that the correction uncertainty is not underestimated at the level of the quoted 0.32 × 10^{-3} statistical-plus-uncorrelated error.
- [§4.2] §4.2 (invariant-mass fit): the background in the J/ψ μ⁺μ⁻ mass distribution is modeled with a parametric function on top of a low-statistics signal. The paper must demonstrate that alternative background shapes (e.g., polynomial of different order or sideband interpolation) do not shift the signal yield by more than the quoted uncertainty, as even a 15 % relative bias would move the significance below 5σ.
minor comments (2)
- [Figure 3] Figure 3 (mass-fit projections): the legend and axis labels should explicitly state the integrated luminosity and data-taking periods used for each component.
- [Abstract and §1] The abstract and §1 use inconsistent spacing in the particle names (J/ψ vs. J msip -3mu/ msip -2mu ψ); adopt a uniform notation throughout.
Simulated Author's Rebuttal
We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below. Revisions have been made to incorporate additional validation studies for the efficiency corrections and background modeling robustness checks.
read point-by-point responses
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Referee: [§5] §5 (signal extraction and efficiency correction): the branching-fraction ratio is obtained from the ratio of fitted yields divided by the simulated efficiency ratio between the μ⁺μ⁻ and π⁺π⁻ final states. Because the two modes differ in particle species, PID response, and kinematic distributions, any residual mismatch between data and simulation in the efficiency correction directly scales the extracted yield; the manuscript should provide explicit data-driven validation (e.g., control samples or tag-and-probe studies) showing that the correction uncertainty is not underestimated at the level of the quoted 0.32 × 10^{-3} statistical-plus-uncorrelated error.
Authors: We appreciate the referee's emphasis on rigorous validation of the efficiency corrections. The efficiency ratio was evaluated using simulation, with systematic uncertainties determined from variations in the simulation parameters (e.g., tracking and PID response) and cross-checked against data control samples. In the revised manuscript we have added an explicit subsection detailing tag-and-probe studies performed on a large sample of J/ψ → μ⁺μ⁻ decays in data to validate the muon identification efficiencies. We also include comparisons of the relevant kinematic distributions between data and simulation for both decay modes. These studies confirm that any residual data-simulation discrepancies are covered within the quoted 0.32 × 10^{-3} uncertainty; no additional component is required. revision: yes
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Referee: [§4.2] §4.2 (invariant-mass fit): the background in the J/ψ μ⁺μ⁻ mass distribution is modeled with a parametric function on top of a low-statistics signal. The paper must demonstrate that alternative background shapes (e.g., polynomial of different order or sideband interpolation) do not shift the signal yield by more than the quoted uncertainty, as even a 15 % relative bias would move the significance below 5σ.
Authors: We agree that explicit demonstration of background-model robustness is necessary given the limited signal statistics. We have performed the requested checks using alternative background parametrizations: first- and second-order polynomials, an exponential function, and a sideband-interpolation approach. The extracted signal yield varies by at most 9 % across these models, which remains well within the statistical uncertainty of the nominal fit. The significance stays above 6σ in every case. A summary of these studies, including the range of yields obtained, has been added to Section 4.2 of the revised manuscript together with a brief justification of the nominal background choice. revision: yes
Circularity Check
Direct experimental extraction of branching fraction ratio with no definitional or self-referential reduction
full rationale
The branching fraction ratio is computed from the ratio of fitted signal yields in the two decay channels, scaled by the ratio of reconstruction efficiencies obtained from simulation. This is a standard data-driven measurement; the reported central value is not presupposed in any input parameter or prior self-citation. Background modeling is performed by fitting parametric shapes to sidebands in the same dataset, providing an independent constraint rather than a closed loop. No equation equates the final result to a fitted input by construction, and the 6.5σ significance arises from the excess over the fitted background in the new channel. The analysis therefore remains self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
free parameters (1)
- signal yield in mass fit
axioms (1)
- domain assumption LHCb detector simulation accurately reproduces muon and pion efficiencies
Reference graph
Works this paper leans on
-
[1]
N. H¨ usken, E. S. Norella, and I. Polyakov,A brief guide to exotic hadrons, Mod. Phys. Lett.A40(2025) 253002,arXiv:2410.06923
-
[2]
Belle collaboration, S. K. Choiet al.,Observation of a narrow charmoniumlike state in exclusive B± →K ±π+π−J/ψ decays, Phys. Rev. Lett.91(2003) 262001, arXiv:hep-ex/0309032
work page internal anchor Pith review Pith/arXiv arXiv 2003
-
[3]
D0 collaboration, V. M. Abazovet al.,Observation and properties of the X(3872) decaying to J/ψπ +π− in p¯pcollisions at √s = 1.96 TeV, Phys. Rev. Lett.93(2004) 162002,arXiv:hep-ex/0405004
work page internal anchor Pith review Pith/arXiv arXiv 2004
-
[4]
A study of B->X(3872) K, with X(3872)->J/Psi pi+ pi-
BaBar collaboration, B. Aubertet al.,Study of B→χ c1(3872)K, with χc1(3872)→J/ ψπ +π−, Phys. Rev.D77(2008) 111101,arXiv:0803.2838
work page internal anchor Pith review Pith/arXiv arXiv 2008
-
[5]
Precision Measurement of the X(3872) Mass in J/psi pi+ pi- Decays
CDF collaboration, T. Aaltonenet al.,Precision measurement of the X(3872)Mass inJ/ψπ +π− decays, Phys. Rev. Lett.103(2009) 152001,arXiv:0906.5218
work page internal anchor Pith review Pith/arXiv arXiv 2009
-
[6]
Observation of X(3872) production in pp collisions at sqrt(s)= 7 TeV
LHCb collaboration, R. Aaijet al.,Observation of X(3872)production in pp collisions at √s=7 TeV, Eur. Phys. J.C72(2012) 1972,arXiv:1112.5310
work page internal anchor Pith review Pith/arXiv arXiv 2012
-
[7]
Observation of $e^{+} e^{-} \to \gamma X(3872)$ at BESIII
BESIII collaboration, M. Ablikimet al.,Observation of e+e− →γX (3872)at BESIII, Phys. Rev. Lett.112(2014) 092001,arXiv:1310.4101
work page internal anchor Pith review Pith/arXiv arXiv 2014
-
[8]
Determination of the X(3872) meson quantum numbers
LHCb collaboration, R. Aaijet al.,Determination of the X(3872)meson quantum numbers, Phys. Rev. Lett.110(2013) 222001,arXiv:1302.6269
work page internal anchor Pith review Pith/arXiv arXiv 2013
-
[9]
Diquark-Antidiquarks with Hidden or Open Charm and the Nature of X(3872)
L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer,Diquark-antidiquarks with hidden or open charm and the nature of X(3872), Phys. Rev.D71(2005) 014028, arXiv:hep-ph/0412098
work page internal anchor Pith review Pith/arXiv arXiv 2005
-
[10]
N. A. Tornqvist,Isospin breaking of the narrow charmonium state of Belle at 3872MeV as a deuson, Phys. Lett.B590(2004) 209,arXiv:hep-ph/0402237
work page internal anchor Pith review Pith/arXiv arXiv 2004
-
[11]
Interplay of quark and meson degrees of freedom in a near-threshold resonance: multi-channel case
C. Hanhart, Y. S. Kalashnikova, and A. V. Nefediev,Interplay of quark and meson degrees of freedom in a near-threshold resonance: multi-channel case, Eur. Phys. J. A47(2011) 101,arXiv:1106.1185. 10
work page internal anchor Pith review Pith/arXiv arXiv 2011
-
[12]
LHCb collaboration, R. Aaijet al.,Probing the nature of the χc1(3872)state using radiative decays, JHEP11(2024) 121,arXiv:2406.17006
-
[13]
Aaijet al.,Observation of sizeable ω contribution to χc1 →π +π−J/ ψdecays, Phys
LHCb collaboration, R. Aaijet al.,Observation of sizeable ω contribution to χc1 →π +π−J/ ψdecays, Phys. Rev.D108(2023) L011103,arXiv:2204.12597
-
[14]
Navaset al.,Review of particle physics, Phys
Particle Data Group, S. Navaset al.,Review of particle physics, Phys. Rev.D110 (2024) 030001
work page 2024
-
[15]
P. Colangelo, F. De Fazio, and R. Pinto,Two-lepton tales: Dalitz decays of heavy quarkonia,arXiv:2512.17672
-
[16]
Belle collaboration, K. Abeet al.,Observation of a near-threshold ωJ/ ψmass en- hancement in exclusive B+ →K +ωJ/ ψdecays, Phys. Rev. Lett.94(2005) 182002, arXiv:hep-ex/0408126
-
[17]
Observation of a charmonium-like enhancement in the gamma gamma --> omega J/psi process
Belle collaboration, S. Ueharaet al.,Observation of a charmonium-like enhancement in theγγ→J/ ψωprocess, Phys. Rev. Lett.104(2010) 092001,arXiv:0912.4451
work page internal anchor Pith review Pith/arXiv arXiv 2010
-
[18]
Evidence for the decay X(3872) --> J/psi omega
BaBar collaboration, P. del Amo Sanchezet al.,Evidence for the decay X(3872)→J/ψω, Phys. Rev.D82(2010) 011101,arXiv:1005.5190
work page internal anchor Pith review Pith/arXiv arXiv 2010
-
[19]
BaBar collaboration, J. P. Leeset al.,Study of X(3915)→J/ ψω in two-photon collisions, Phys. Rev.D86(2012) 072002,arXiv:1207.2651
work page internal anchor Pith review Pith/arXiv arXiv 2012
-
[20]
LHCb collaboration, R. Aaijet al.,Observation of muonic Dalitz decays of χb mesons and precise spectroscopy of hidden-beauty states, JHEP10(2024) 122, arXiv:2408.05134
-
[21]
$\chi_{c1}$ and $\chi_{c2}$ resonance parameters with the decays $\chi_{c1,c2}\to J/\psi\mu^+\mu^-$
LHCb collaboration, R. Aaijet al., χc1 and χc2 resonance parameters with the decays χc1,c2 →J/ ψµ+µ−, Phys. Rev. Lett.119(2017) 221801,arXiv:1709.04247
work page internal anchor Pith review Pith/arXiv arXiv 2017
-
[22]
A. A. Alves Jr.et al.,Performance of the LHCb muon system, JINST8(2013) P02022,arXiv:1211.1346
work page internal anchor Pith review Pith/arXiv arXiv 2013
-
[23]
LHCb collaboration, R. Aaijet al.,LHCb detector performance, Int. J. Mod. Phys. A30(2015) 1530022,arXiv:1412.6352
work page internal anchor Pith review Pith/arXiv arXiv 2015
-
[24]
Precision measurement of D meson mass differences
LHCb collaboration, R. Aaijet al.,Precision measurement of D meson mass differ- ences, JHEP06(2013) 065,arXiv:1304.6865
work page internal anchor Pith review Pith/arXiv arXiv 2013
-
[25]
Design and performance of the LHCb trigger and full real-time reconstruction in Run 2 of the LHC
R. Aaijet al.,Design and performance of the LHCb trigger and full real-time recon- struction in Run 2 of the LHC, JINST14(2019) P04013,arXiv:1812.10790
work page internal anchor Pith review Pith/arXiv arXiv 2019
-
[26]
N. Grieseret al.,The LHCb stripping project: Sustainable legacy data processing for high-energy physics, Comput. Softw. Big. Sci.9(2025) 21,arXiv:2509.05294
-
[27]
A Brief Introduction to PYTHIA 8.1
T. Sj¨ ostrand, S. Mrenna, and P. Skands,A brief introduction to PYTHIA 8.1, Comput. Phys. Commun.178(2008) 852,arXiv:0710.3820
work page internal anchor Pith review Pith/arXiv arXiv 2008
-
[28]
I. Belyaevet al.,Handling of the generation of primary events in Gauss, the LHCb simulation framework, J. Phys. Conf. Ser.331(2011) 032047. 11
work page 2011
-
[29]
D. J. Lange,The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A462(2001) 152
work page 2001
-
[30]
Allisonet al.,Geant4 developments and applications, IEEE Trans
Geant4 collaboration, J. Allisonet al.,Geant4 developments and applications, IEEE Trans. Nucl. Sci.53(2006) 270; Geant4 collaboration, S. Agostinelliet al.,Geant4: A simulation toolkit, Nucl. Instrum. Meth.A506(2003) 250
work page 2006
-
[31]
Clemencicet al.,The LHCb simulation application, Gauss: Design, evolution and experience, J
M. Clemencicet al.,The LHCb simulation application, Gauss: Design, evolution and experience, J. Phys. Conf. Ser.331(2011) 032023
work page 2011
-
[32]
W. D. Hulsbergen,Decay chain fitting with a Kalman filter, Nucl. Instrum. Meth. A552(2005) 566,arXiv:physics/0503191
work page internal anchor Pith review Pith/arXiv arXiv 2005
-
[33]
L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone,Classification and regression trees, Wadsworth international group, Belmont, California, USA, 1984
work page 1984
-
[34]
Y. Freund and R. E. Schapire,A decision-theoretic generalization of on-line learning and an application to boosting, J. Comput. Syst. Sci.55(1997) 119
work page 1997
-
[35]
H. Voss, A. Hoecker, J. Stelzer, and F. Tegenfeldt,TMVA - Toolkit for multi- variate data analysis with ROOT, PoSACAT(2007) 040; A. Hoeckeret al., TMVA 4 — Toolkit for Multivariate Data Analysis with ROOT. Users Guide., arXiv:physics/0703039
work page internal anchor Pith review Pith/arXiv arXiv 2007
-
[36]
Aaijet al.,Study of the line shape of the χc1(3872)state, Phys
LHCb collaboration, R. Aaijet al.,Study of the line shape of the χc1(3872)state, Phys. Rev.D102(2020) 092005,arXiv:2005.13419
-
[37]
K¨ all´ en,Elementary particle physics, Science147(1964) 1133
G. K¨ all´ en,Elementary particle physics, Science147(1964) 1133
work page 1964
-
[38]
LHCb collaboration, R. Aaijet al.,Study of the ψ2(3823)and χc1(3872)states in B+ →(J/ ψπ+π−)K + decays, JHEP08(2020) 123,arXiv:2005.13422
-
[39]
T. Skwarnicki,A study of the radiative cascade transitions between the Upsilon-prime and Upsilon resonances, PhD thesis, Institute of Nuclear Physics, Krakow, 1986, DESY-F31-86-02
work page 1986
-
[40]
S. S. Wilks,The large-sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Stat.9(1938) 60
work page 1938
-
[41]
Measurement of the track reconstruction efficiency at LHCb
LHCb collaboration, R. Aaijet al.,Measurement of the track reconstruction efficiency at LHCb, JINST10(2015) P02007,arXiv:1408.1251
work page internal anchor Pith review Pith/arXiv arXiv 2015
-
[42]
R. Nisius,BLUE: combining correlated estimates of physics observables within ROOT using the Best Linear Unbiased Estimate method, SoftwareX11(2020) 100468, arXiv:2001.10310. 12 LHCb collaboration R. Aaij38 , A.S.W. Abdelmotteleb 58 , C. Abellan Beteta 52 , F. Abudin´ en58 , T. Ackernley62 , A. A. Adefisoye 70 , B. Adeva48 , M. Adinolfi 56 , P. Adlarson86 ...
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