REVIEW
Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson
High Energy Physics - Phenomenology · Submitted 23 Feb 2004 · 31 references
Pith's verdict: The qualitative claim — large isospin breaking makes J/psi rho allowed and J/psi sigma forbidden — is correct and became the standard reading of the X(3872); the numbers attached to it are tuned to an assumed binding energy and should be read as estimates.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
The narrow 3872 MeV state seen by Belle and confirmed by CDF may be a deuteron-like bound pair of two heavy mesons, held together by pion exchange, rather than a conventional charmonium level.
The reading
What carries the argument
The machinery is the one-pion-exchange potential written in the same central-plus-tensor form used for the deuteron, $C(r)=e^{-m_π r}/(m_π r)$ and $T(r)=C(r)[1+3m_π r+3(m_π r)^2]$, applied to heavy mesons with a spin-isospin-C-parity factor $γ$. For the $1^{++}$ system the potential is a $2×2$ matrix in the $^3S_1$ and $^3D_1$ orbitals, and the two charge modes $|D^0$-$D^{*0}$ and $|D^+$-$D^{*-}$ are coupled through the matrix with rows $(1,2)$ and $(2,1)$, whose eigenvalues are $3$ (the attractive $I=0$ combination) and $-1$ (the weaker, repulsive $I=1$ combination). The calculation then solves four coupled channels, two spin orbitals times two charge modes, with the mass splittings of $D$, $D^*$ and $π$ included. The tensor term is load-bearing: without it the deuteron, and by analogy this state, would not bind. The same potential, with the tensor term adding directly to the central term rather than through off-diagonal iteration, is what the paper uses to argue that a $0^{-+}$ P-wave molecule is still possible.
Extended reading notes
Core claim
The central claim is that the 3872 MeV state is a $D$-antimeson-$D$-star molecule bound mainly by one-pion exchange, in the same way the deuteron is bound by pion exchange between nucleons, and that its isospin is strongly broken. In the exact-isospin limit the state would be the pure $I=0$ combination $(|D^0$-$D^{*0}$ plus $|D^+$-$D^{*-}$)/$√2$ with $J^{PC}=1^{++}$ or $0^{-+}$. Because the neutral threshold lies 8.1 MeV below the charged one, the neutral component dominates the wave function and the state acquires a substantial $I=1$ piece. The concrete consequence the author draws is that the decay to $J/ψρ$ is not forbidden, while $σJ/ψ$ for any isoscalar dipion $σ$ is forbidden by C-parity and spin-parity, so the $π^+π^-$ in the Belle signal should come from $ρ$ and no $J/ψπ^0π^0$ should appear. The paper also estimates a $D^0$-$D^0π^0$ width of order 30-40 keV, with a $D^0$-$D^0γ$ to $D^0$-$D^0π^0$ ratio of about 62%.
Load-bearing premise
The binding energy is put in by hand at 0.5 MeV below the neutral threshold, and the short-distance cutoff (between roughly 1.36 and 1.53 GeV across the figures) is then chosen to reproduce it, so the predicted size of the isospin breaking follows from that calibration rather than from first principles.
Editorial extensions
If this is right
- If the identification holds, the 3872 MeV state is a multiquark object rather than a $c$-antiquark-$c$ level, opening a spectroscopy of heavy-meson molecules.
- The same pion-exchange mechanism should produce the predicted $D^*$-$D^*$ states near 4015 MeV, and more deeply bound $B$-$B^*$ and $B^*$-$B^*$ states roughly 50 MeV below their thresholds.
- The dipion in $J/ψπ^+π^-$ should be purely $ρ$-like, and no $J/ψπ^0π^0$ should appear in the decays.
- The $D^0$-$D^0π^0$ channel should be significant, of order tens of keV, with $D^0$-$D^0γ$ at roughly 62% of it.
- A pseudoscalar $0^{-+}$ assignment is not excluded, but only if the regularized tensor force is strong enough to overcome the P-wave angular-momentum barrier.
Reading between the lines
- The threshold-splitting argument generalizes: any molecule sitting within a few MeV of a threshold inherits isospin violation from the charge splitting of its constituents, so the $ρ$-versus-$σ$ test is a template for other near-threshold candidates.
- If the state really has a large radius, its production in $B$ decays and in proton-antiproton collisions should differ in ways set by the long-range part of the wave function, which gives a handle beyond the mass alone.
- The $ωJ/ψ$ channel just above the state, which the paper deliberately leaves out of the coupled-channel system, would add an attractive higher-order coupling that could shift the required binding and change the predicted isospin admixture.
- The paper's own check that it reproduces the measured $D^{*+}$ width from the same normalization suggests the same potential could be used to postdict the binding of the analogous bottom-meson molecules, where the predicted binding is much larger and the isospin admixture correspondingly smaller.
Original abstract
The narrow charmonium state near 3872 MeV reported by the Belle collaboration and confirmedby CDF lies almost exactly at the neutral D anti-D* threshold. As was predicted many years ago it can be a deuteronlike meson-meson state called a deuson. If so, it should be an axial, or possibily a pseudoscalar state with C=0, and isospin predominantly 0. Large isospin breaking is expected because of the isospin mass splitting between the neutral and charged D (D*) mesons. Because of this large isospin breaking the decay X(3872) to J/psi rho would be allowed, while J/psi sigma would be forbidden by C-parity, as indicated by the present data.
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.
The abstract, sentence by sentence
The narrow charmonium state near 3872 MeV reported by the Belle collaboration and confirmedby CDF lies almost exactly at the neutral D anti-D* threshold. As was predicted many years ago it can be a deuteronlike meson-meson state called a deuson. If so, it should be an axial, or possibily a pseudoscalar state with C=0, and isospin predominantly 0. Large isospin breaking is expected because of the isospin mass splitting between the neutral and charged D (D*) mesons. Because of this large isospin breaking the decay X(3872) to J/psi rho would be allowed, while J/psi sigma would be forbidden by C-parity, as indicated by the present data.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The narrow charmonium state near 3872 MeV reported by the Belle collaboration and confirmedby CDF lies almost exactly at the neutral D anti-D* threshold. | background 0.98 | 0.05 | 0.08 | asserted 0.97 |
| s1 | As was predicted many years ago it can be a deuteronlike meson-meson state called a deuson. | interpretation 0.65 | 0.05 | 0.30 | hedged possibility 0.76 |
| s2 | If so, it should be an axial, or possibily a pseudoscalar state with C=0, and isospin predominantly 0. | interpretation 0.91 | 0.11 | 0.20 | hedged possibility 0.90 |
| s3 | Large isospin breaking is expected because of the isospin mass splitting between the neutral and charged D (D*) mesons. | interpretation 0.71 | 0.08 | 0.14 | asserted 0.66 |
| s4 | Because of this large isospin breaking the decay X(3872) to J/psi rho would be allowed, while J/psi sigma would be forbidden by C-parity, as indicated by the present data. | interpretation 0.95 | 0.20 | 0.43 | asserted 0.56 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Showing 3 of the paper's 5 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0402237 by the authors.
References
How later papers used it
99 later papers cite it
1 later paper by other authors is listed below: 1 compared its own results with it.
Compares with it 1 of 3 papers with this label
-
Compared its own masses for 1S qcqc and 1S qbqb tetraquarks with this paper's one-pion exchange masses for D*D*bar and B*B*bar and found them in good agreement.
Nonrelativistic model of tetraquarks and predictions for their masses from fits to charmed and bottom meson data (2020) · 0.97 · paraphrased: the licence does not allow quoting
How the literature uses it
95 arXiv papers cite this in 118 sentences
Papers whose main result relates to this one's
States the same result 1 paper
-
It is pointed out that the narrow charmonium state at 3871.8 MeV reported by the Belle collaboration is likely to be a $D\bar D^*$ deuteronlike meson-meson state called a deuson.
Comment on the narrow charmonium state of Belle at 3871.8 MeV as a deuson · 0.91
Papers citing it · 68 sentences without a confident label
Contests it 1 paper
-
The early assignment of the $X(3872)$ as the pure $P$-wave charmonium [ref] or pure $D^0-D^0*$ molecular state [ref] seems in conflict with the experimental data.
A tale of Bethe logarithms: leptonic widths of $\chi_{cJ}$ and Lamb shift · Numerical results · contest 0.76
Uses its method or tool 1 paper
-
To estimate the D-wave mixing, We will use the pion exchange type of potential between $D-D̅^̅*̅$ and $D-D^*$ for the $X(3872)$ and $T_cc$ quantum numbers, respectively, that were used in Ref. [ref] .
$X(3872)$ and $T_{cc}$: structures and productions in heavy ion collisions · D-wave mixing · 0.96
Uses its data or values 3 papers
-
One of its most salient features is that the mass coincides exactly with the $D̅^*0 D^0/D̅^0 D^*0$ threshold as $m_D^0+m_D^*0-m_X(3872)=(0.00±0.18)$ MeV [ref] , which naturally inspired the molecular interpretations [ref] .
Revisit the isospin violating decays of $X(3872)$ · Introduction · 0.80
-
Given the proximity of the observed mass ($m_X(3872)=3871.64±0.06$ [ref] ) to the $D^0D̅^*0$ ($D̅^0D^*0$) threshold ($m_D^0+m_D̅^*0=3871.69±0.07$), a natural interpretation is that of a shallow $D^0D̅^*0$ molecular bound state [ref] with a very narrow width ($Γ_X(3872)=1.19±0.21$ [ref] ).
Hadron properties at finite temperature · Doubly heavy exotic mesons · 0.99
-
This is a charmonium-like state with an extremely narrow width ($Γ=1.19 ±0.21$ Mev [ref] ) and uncharacteristic decays breaking the isospin ($Br(X(3872) →ωJ/ψ)/Br(X(3872) →π^+π^- J/ψ) = 1.1 ±0.4$ [ref] ).
Fully-heavy tetraquark spectroscopy in the relativistic quark model · Introduction · 0.98
Compares with it 2 papers
-
The observed states can be compared to predictions for molecular states based upon a one-pion exchange model [ref] which are listed in Table [ref].
Exotics: Heavy Pentaquarks and Tetraquarks · Interpretation of the $X$(3872) · 0.93
-
Actually, the value of $g$ is about four times bigger than the coupling constant $γV_0/m_πħc=5.7$ MeV fm used in [ref] to describe $χ_c1(3872)$ as a deuson with a binding energy of 500 keV from pion exchange assuming isospin invariance.
$\chi_{c1}(2p)$: an overshadowed charmoniumlike resonance · Diabatic toy model with pion exchange · 0.86
Cites it as support 3 papers
-
In the literatures, this idea has been tested and shown to be indeed the case for heavy quark systems [ref] .
Exotic baryons from a heavy meson and a nucleon - Positive parity states - · Introduction · 0.97
-
These features suggest that this state is a hadronic molecule [ref] (see Ref. [ref] for a review).
Predicting isovector charmonium-like states from X(3872) properties · Introduction · 0.98
-
Nevertheless, the extreme closeness of the $X(3872)$ mass to the $D^0 D̅^*0$ threshold makes it extremely compelling to model as a molecule of these mesons [ref] .
Heavy-Quark QCD Exotica · Dynamics of Binding · 0.97
Cites it as background 38 papers
-
The $X(3872)$ [ref] , also known as $χ_c1(3872)$, and the $Z_c(3900)$ [ref] have been proposed as candidates of isoscalar and isovector $DD̅^*$ hadronic molecules, respectively, since long [ref] .
Establishing the heavy quark spin and light flavor molecular multiplets of the $X(3872)$, $Z_c(3900)$ and $X(3960)$ · Introduction · 0.89
-
Long ago [ref] the idea of $π$ exchange between flavored mesons, in particular charm, was suggested as a source of potential “deusons" [ref] .
On the possibility of Deeply Bound Hadronic Molecules from single Pion Exchange · Introduction · 0.94
-
In the one pion exchange model, Tornqvist suggested that X(3872) is a $1^++$ $DD̅^*/D̅D^*$ molecule and isospin is strongly broken [ref] .
Dynamics of Hadronic Molecule in One-Boson Exchange Approach and Possible Heavy Flavor Molecules · Possible $DD̅^*/D̅D^*$ hadronic molecule and X(3872) · 0.86
Discussion
Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.