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On the Spin of the X(3872)
High Energy Physics - Phenomenology · Submitted 5 Apr 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our analysis returns a probability of 5.5% and 0.1% for the agreement with data of the 1++ and 2-+ hypotheses, respectively, once we combine the whole information (angular and mass distributions) from both channels.
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The abstract, sentence by sentence
Whether the much studied X(3872) is an axial or tensor resonance makes an important difference to its interpretation. A recent paper by the BaBar collaboration raised the viable hypothesis that it might be a 2-+ state based on the 3 pions spectrum in the X -> J/psi omega decays. Furthermore, the Belle collaboration published the 2 pions invariant mass and spin-sensitive angular distributions in X -> J/psi rho decays. Starting from a general parametrization of the decay amplitudes for the axial and tensor quantum numbers of the X, we re-analyze the whole set of available data. The level of agreement of the two spin hypotheses with data is interpreted with a rigorous statistical approach based on Monte Carlo simulations in order to be able to combine all the distributions regardless of their different levels of sensitivity to the spin of the X. Our analysis returns a probability of 5.5% and 0.1% for the agreement with data of the 1++ and 2-+ hypotheses, respectively, once we combine the whole information (angular and mass distributions) from both channels. On the other hand, the separate analysis of J/psi rho (angular and mass distributions) and J/psi omega (mass distribution) indicates that the 2-+ assignment is excluded at the 99.9% C.L. by the former case, while the latter excludes at the same level the 1++ hypothesis. There are therefore indications that the two decay modes behave in a different way.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Whether the much studied X(3872) is an axial or tensor resonance makes an important difference to its interpretation. | background 0.96 | 0.06 | 0.04 | asserted 0.98 |
| s1 | A recent paper by the BaBar collaboration raised the viable hypothesis that it might be a 2-+ state based on the 3 pions spectrum in the X -> J/psi omega decays. | background 0.99 | 0.03 | 0.03 | hedged possibility 0.55 |
| s2 | Furthermore, the Belle collaboration published the 2 pions invariant mass and spin-sensitive angular distributions in X -> J/psi rho decays. | background 0.97 | 0.04 | 0.02 | asserted 1.00 |
| s3 | Starting from a general parametrization of the decay amplitudes for the axial and tensor quantum numbers of the X, we re-analyze the whole set of available data. | method 0.73 | 0.89 | 0.03 | asserted 0.74 |
| s4 | The level of agreement of the two spin hypotheses with data is interpreted with a rigorous statistical approach based on Monte Carlo simulations in order to be able to combine all the distributions regardless of their different levels of sensitivity to the spin of the X. | method 0.99 | 0.85 | 0.03 | asserted 0.95 |
| s5 | Our analysis returns a probability of 5.5% and 0.1% for the agreement with data of the 1++ and 2-+ hypotheses, respectively, once we combine the whole information (angular and mass distributions) from both channels. | result 1.00 | 0.95 | 0.73 | asserted 1.00 |
| s6 | On the other hand, the separate analysis of J/psi rho (angular and mass distributions) and J/psi omega (mass distribution) indicates that the 2-+ assignment is excluded at the 99.9% C.L. by the former case, while the latter excludes at the same level the 1++ hypothesis. | result 1.00 | 0.87 | 0.21 | asserted 0.92 |
| s7 | There are therefore indications that the two decay modes behave in a different way. | interpretation 0.95 | 0.78 | 0.13 | hedged possibility 1.00 |
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The paper
Original abstract
Whether the much studied X(3872) is an axial or tensor resonance makes an important difference to its interpretation. A recent paper by the BaBar collaboration raised the viable hypothesis that it might be a 2-+ state based on the 3 pions spectrum in the X -> J/psi omega decays. Furthermore, the Belle collaboration published the 2 pions invariant mass and spin-sensitive angular distributions in X -> J/psi rho decays. Starting from a general parametrization of the decay amplitudes for the axial and tensor quantum numbers of the X, we re-analyze the whole set of available data. The level of agreement of the two spin hypotheses with data is interpreted with a rigorous statistical approach based on Monte Carlo simulations in order to be able to combine all the distributions regardless of their different levels of sensitivity to the spin of the X. Our analysis returns a probability of 5.5% and 0.1% for the agreement with data of the 1++ and 2-+ hypotheses, respectively, once we combine the whole information (angular and mass distributions) from both channels. On the other hand, the separate analysis of J/psi rho (angular and mass distributions) and J/psi omega (mass distribution) indicates that the 2-+ assignment is excluded at the 99.9% C.L. by the former case, while the latter excludes at the same level the 1++ hypothesis. There are therefore indications that the two decay modes behave in a different way.
Human review
References
How the literature uses it
10 arXiv papers cite this in 13 sentences
Papers citing it · 9 sentences without a confident label
Uses its method or tool 3 papers
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In order to quantify the significance of the second structure included in the fits, we have adopted the statistical approach described in detail in Ref. [ref] : from the fit to the data performed assuming only one exotic structure, we have simulated a large number of mock experiments, correctly accounting for statistical fluctuations.
A J^PG=1++ Charged Resonance in the Y(4260) to pi+pi- J/psi Decay? · Interpretation of the $Z_c(3900)$ state · 1.00
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To properly compare the quality of one model fit vs another we use the $Δχ^2$ estimator on a number of MC generated datasets [ref] .
Amplitude analysis and the nature of the Zc(3900) · Fit results · 0.97
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A likelihood ratio test does not give rejections larger than $3σ$ [ref] .
Novel approaches in Hadron Spectroscopy · The Zc(3900) · 0.89
Cites it as background 1 paper
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There have been two previous theoretical analyses [ref] of the $M_3π$ distribution shown in Fig. [ref].
The J/{\psi} {\omega} Decay Channel of the X(3872) Charm Meson Molecule · Previous theoretical analyses · 0.96
What it cites · 19 sentences without a confident label
Uses the method or tool of 3 papers
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In particular, in the $X →J/ψ π^+π^-$ sample we consider the di-pion invariant mass ($m_2π$) and the angles defined in the $X$ rest frame in Ref. [ref] and described in Fig [ref]: the angle between the $J/ψ$ and the direction opposite to $K$ ($θ_X$), the angle between the $π^+$ and the direction opposite to $K$ ($χ$), and the angle between the $l^+$ produced by the decay of the $J/ψ$ and the $z$-axis of a coordinate system where the $x$-axis is the direction opposite to the $K$ and the $y$-axis is the component of $π^+$ orthogonal to $K$ ($θ_l$).
Angular distributions in $J/\psi(\rho,\omega)$ states near threshold · Data re-analysis · 0.95
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The matrix elements describing the amplitudes $X→J/ψ V$ (where $V=ρ,ω$) are obtained by Lorentz, gauge invariance and parity considerations leading to the formulae reported below [ref] .
Strong Couplings of X(3872)_{J=1,2} and a New Look at J/psi Suppression in Heavy Ion Collisions · Matrix elements · 0.93
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Following Ref. [ref] , we describe the decay $ω→2π$, as the oscillation $ω→ρ→2π$, as explained in Fig. [ref].
Remarks on the quantum numbers of X(3872) from the invariant mass distributions of the rho J/psi and omega J/psi final states · Rho-omega mixing · 0.99
Uses data or values from 3 papers
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In order to extract information on the spin of the $X$ particle, we re-analyze the $B→X K$ data published in Ref. [ref] (for $X→J/ψ π^+π^-$) and in Ref. [ref] (for $X→J/ψ π^+π^-π^0$).
Bounds on the width, mass difference and other properties of X(3872) --> pi+pi-J/psi decays · Data re-analysis · 1.00
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In order to extract information on the spin of the $X$ particle, we re-analyze the $B→X K$ data published in Ref. [ref] (for $X→J/ψ π^+π^-$) and in Ref. [ref] (for $X→J/ψ π^+π^-π^0$).
Evidence for the decay X(3872) --> J/psi omega · Data re-analysis · 1.00
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To account for the $X$ width in the invariant mass distributions, we extract randomly the values of the mass of the $X$ from a Breit-Wigner centered at $m_X = 3872 MeV$ with $Γ_X = 1.7 MeV$ [ref] , accepting only those values kinematically consistent with the decay of interest.
New Hadronic Spectroscopy · Data re-analysis · 0.97
Compares with 1 paper
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Finally, in order to compare directly with Ref. [ref] we report in Tab. [ref] also the results performed using exclusively the two invariant mass distributions or the three angular distributions.
Remarks on the quantum numbers of X(3872) from the invariant mass distributions of the rho J/psi and omega J/psi final states · Fits on sub-samples · 1.00
Cites as background 1 paper
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The CDF collaboration concluded from the analysis of the angular distributions and correlations of the $X$ decay products that the possible quantum numbers are $J^PC= 1^++$ or $2^-+$ [ref] .
Analysis of the Quantum Numbers $J^{PC}$ of the X(3872) Particle · Introduction · 0.87
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