REVIEW
Coupled-channel study of crypto-exotic baryons with charm
High Energy Physics - Phenomenology · Submitted 6 Jul 2005 · 47 references
Pith's verdict: A solid extension of the GSI coupled-channel program with genuinely parameter-free charm -1 predictions, but the two headline zero-charm states are tuned to the bubble-chamber signals and the abstract presents them as found.
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Referee report
The paper
The paper claims
A single force — t-channel vector-meson exchange — is claimed to bind mesons and baryons into a whole spectrum of narrow hidden-charm baryons, including a 3.52 GeV nucleon and a 3.17 GeV hyperon only about 1 MeV wide.
The reading
What carries the argument
The load-bearing object is the s-wave projected coupled-channel kernel built from t-channel vector-meson exchange, $V^{(I,S,C)}(sqrt s) = sum_V C^{(I,S,C)}_V /(8 m_V^2) ,(2sqrt s - M - bar M + (bar M - M)(bar m^2 - m^2)/m_V^2)$, unitarized by the diagonal loop matrix $J$ with a subtraction scale $mu = sqrt{m_{rm th}^2 + M_{rm th}^2}$ chosen so that the lightest channel's loop vanishes at the matching point. That subtraction choice is what keeps heavy channels such as $eta_c N$ from contaminating the low-energy $pi N$ amplitude and spoiling the chiral prediction. The matrices $C^{(I,S,C)}_V$ carry all the group theory: summing over the light vector nonet reproduces the Weinberg–Tomozawa structure, and the full SU(4) decomposition $15 otimes 20 = 4 oplus 20_1 oplus 20_2 oplus 20_s oplus 36 oplus 60 oplus 140$ shows where attraction lives — strongest in the $bar 4$, repulsive in the $140$, absent in the $60$, with the exotic $36$ also attractive. Resonance positions and channel couplings are read off generalized speed plots, $mathrm{Speed}_{ab} = |d M_{ab}/d sqrt s|$, which separate a genuine pole from a threshold cusp.
Extended reading notes
Core claim
The central claim is that crypto-exotic baryons — baryons containing a $cbar c$ pair but no net charm — exist as hadronic molecules, bound by the t-channel exchange of light vector mesons between a pseudoscalar meson and a baryon ground state. The authors set up coupled-channel s-wave scattering over all channels required by $u,d,s,c$ quarks, with the interaction kernel taken as vector-meson exchange and the coupling constants fixed by chiral symmetry, the KSFR relation and leading-order large-$N_c$ relations; only the charmed-vector-meson vertices are left to SU(4) estimates. Solving the resulting matrix equation $M = [1 - V J]^{-1} V$ produces an SU(3) octet of hidden-charm states decaying predominantly through $eta'$ channels, with members at 3.52 GeV $(I,S)=(tfrac12,0)$, 3.58 GeV $(0,-1)$, 3.80 GeV $(tfrac12,-2)$ and 3.93 GeV $(1,-1)$, plus a more strongly bound SU(3) singlet formed from the $(bar D_s Lambda_c)$, $(bar D Xi_c)$ system near 3.17 GeV whose width comes out around 1 MeV. The same machinery reproduces the two known s-wave charmed baryons, $Lambda_c(2593)$ and $Xi_c(2790)$, and predicts about ten further narrow open-charm states below 3 GeV; the authors use this to argue that the $Lambda_c(2880)$ cannot be an s-wave state, since its observed narrow width is incompatible with the large coupling to the $eta Lambda_c$ channel that an s-wave assignment would require.
Load-bearing premise
The masses of every hidden-charm state rest on SU(4)-symmetric estimates for how charmed vector mesons couple to charmed mesons and baryons — estimates the authors themselves say are only good to a factor of two and which they then adjust by hand to place the nucleon resonance at 3.52 GeV with a 7 MeV width.
Editorial extensions
If this is right
- A narrow peak should appear in the $eta' N$ channel near 3.52 GeV, with a formation cross section in $pi^- p$ of roughly $600 ,mu$barn per MeV of total width, against a total cross section of about 25 mbarn.
- A narrow $eta' Lambda$ or $bar D_s Lambda_c$ structure should appear near 3.17 GeV, with a $K^- p$ formation cross section of order $36 ,mu$barn per MeV of width, compatible with the old bubble-chamber limit of under 20 MeV.
- The octet partners at 3.58, 3.80 and 3.93 GeV should be visible in the corresponding strangeness and isospin channels, all with widths clustered near 7 MeV and all decaying preferentially into channels containing an $eta'$.
- In the open-charm sector, roughly ten additional narrow s-wave states below 3 GeV are predicted, including a $Sigma_c(2620)$ coupling to $(D N)$ and $(D_s Sigma)$, a $Lambda_c(2815)$ formed from $(eta Lambda_c)$ and $(K Xi_c)$, and narrow $Xi_c$ states near 2672 and 2793 MeV.
- Lattice QCD simulations with dynamical charm quarks should either confirm or exclude bound states in these quantum-number channels, since the prediction is a statement about the spectrum itself, not about a particular decay.
Reading between the lines
- The mechanism is generic enough that the same vector-exchange attraction should bind other heavy-meson/heavy-baryon combinations not tabulated here — for instance states built on $Omega_c$ or on the doubly charmed $Xi_{cc}$ with a $bar D_s$ — so the paper's tables are probably a subset of a larger molecular spectrum.
- If the widths really are set by OZI violation through the $eta'$, then the crypto-exotic states are a direct experimental handle on the $U_A(1)$ anomaly's mixing of $eta'$ with gluonic operators, a connection the authors note but do not exploit quantitatively.
- The claim that $Lambda_c(2880)$ is not s-wave is testable independently of the model: measuring its coupling to $eta Lambda_c$ relative to $pi Sigma_c$ would either show the suppression an s-wave assignment forbids or reveal the state as a higher partial wave.
- Because the headline masses depend on couplings the authors tune by hand, a useful extension would be to treat those couplings as fit parameters against the two known charmed baryons and then postdict, rather than tune, the hidden-charm masses.
Original abstract
Identifying the t-channel exchange of vector mesons as the driving force for the s-wave scattering of pseudo-scalar mesons off the baryon ground states, a surprisingly rich spectrum of molecules is formed. We argue that chiral symmetry and large- N_c considerations determine that part of the interaction which generates the spectrum. All channels that are required by the existence of (u,d,s,c) quarks are considered. A bound state with exotic quantum numbers is predicted at mass 2.78 GeV. It couples strongly to the (bar D_s N),(bar D Lambda),(bar D Sigma) channels. A further charm minus-one system is predicted at mass 2.84 GeV as a result of (bar D_s Lambda), (bar D Xi) interactions. We suggest the existence of strongly bound crypto-exotic baryons, which contain a charm-anti-charm pair. Such states are narrow since they can decay only via OZI-violating processes. A narrow nucleon resonance is found at mass 3.52 GeV. It is a coupled-channel bound state of the (eta_c N), (bar D Sigma_c) system, which decays dominantly into the (eta' N) channel. Furthermore two isospin singlet hyperon states at mass 3.23 GeV and 3.58 GeV are observed as a consequence of coupled-channel interactions of the (bar D_s Lambda_c), (bar D Xi_c) and (eta_c Lambda),(bar D Xi_c') states. Most striking is the small width of about 1 MeV of the lower state. The upper state may be significantly broader due to a strong coupling to the (eta' Lambda) state. The two so far observed s-wave baryons with charm one are recovered. We argue that the Lambda_c(2880) is not a s-wave state. In addition to those states we predict the existence of about ten narrow s-wave baryon states with masses below 3 GeV.
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
Identifying the t-channel exchange of vector mesons as the driving force for the s-wave scattering of pseudo-scalar mesons off the baryon ground states, a surprisingly rich spectrum of molecules is formed. We argue that chiral symmetry and large- N_c considerations determine that part of the interaction which generates the spectrum. All channels that are required by the existence of (u,d,s,c) quarks are considered. A bound state with exotic quantum numbers is predicted at mass 2.78 GeV. It couples strongly to the (bar D_s N),(bar D Lambda),(bar D Sigma) channels. A further charm minus-one system is predicted at mass 2.84 GeV as a result of (bar D_s Lambda), (bar D Xi) interactions. We suggest the existence of strongly bound crypto-exotic baryons, which contain a charm-anti-charm pair. Such states are narrow since they can decay only via OZI-violating processes. A narrow nucleon resonance is found at mass 3.52 GeV. It is a coupled-channel bound state of the (eta_c N), (bar D Sigma_c) system, which decays dominantly into the (eta' N) channel. Furthermore two isospin singlet hyperon states at mass 3.23 GeV and 3.58 GeV are observed as a consequence of coupled-channel interactions of the (bar D_s Lambda_c), (bar D Xi_c) and (eta_c Lambda),(bar D Xi_c') states. Most striking is the small width of about 1 MeV of the lower state. The upper state may be significantly broader due to a strong coupling to the (eta' Lambda) state. The two so far observed s-wave baryons with charm one are recovered. We argue that the Lambda_c(2880) is not a s-wave state. In addition to those states we predict the existence of about ten narrow s-wave baryon states with masses below 3 GeV.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Identifying the t-channel exchange of vector mesons as the driving force for the s-wave scattering of pseudo-scalar mesons off the baryon ground states, a surprisingly rich spectrum of molecules is formed. | method 0.42 | 0.60 | 0.21 | asserted 1.00 |
| s1 | We argue that chiral symmetry and large- N_c considerations determine that part of the interaction which generates the spectrum. | interpretation 0.64 | 0.50 | 0.08 | asserted 0.70 |
| s2 | All channels that are required by the existence of (u,d,s,c) quarks are considered. | method 0.75 | 0.80 | 0.03 | asserted 0.96 |
| s3 | A bound state with exotic quantum numbers is predicted at mass 2.78 GeV. | result 1.00 | 0.89 | 0.27 | asserted 0.91 |
| s4 | It couples strongly to the (bar D_s N),(bar D Lambda),(bar D Sigma) channels. | result 1.00 | 0.84 | 0.08 | asserted 1.00 |
| s5 | A further charm minus-one system is predicted at mass 2.84 GeV as a result of (bar D_s Lambda), (bar D Xi) interactions. | result 1.00 | 0.89 | 0.06 | asserted 0.96 |
| s6 | We suggest the existence of strongly bound crypto-exotic baryons, which contain a charm-anti-charm pair. | result 0.63 | 0.61 | 0.58 | hedged possibility 0.89 |
| s7 | Such states are narrow since they can decay only via OZI-violating processes. | interpretation 0.95 | 0.41 | 0.09 | asserted 0.98 |
| s8 | A narrow nucleon resonance is found at mass 3.52 GeV. | result 1.00 | 0.92 | 0.07 | asserted 1.00 |
| s9 | It is a coupled-channel bound state of the (eta_c N), (bar D Sigma_c) system, which decays dominantly into the (eta' N) channel. | result 1.00 | 0.94 | 0.07 | asserted 1.00 |
| s10 | Furthermore two isospin singlet hyperon states at mass 3.23 GeV and 3.58 GeV are observed as a consequence of coupled-channel interactions of the (bar D_s Lambda_c), (bar D Xi_c) and (eta_c Lambda),(bar D Xi_c') states. | result 1.00 | 0.86 | 0.09 | asserted 1.00 |
| s11 | Most striking is the small width of about 1 MeV of the lower state. | result 0.99 | 0.88 | 0.06 | asserted 1.00 |
| s12 | The upper state may be significantly broader due to a strong coupling to the (eta' Lambda) state. | interpretation 0.56 | 0.81 | 0.04 | hedged possibility 1.00 |
| s13 | The two so far observed s-wave baryons with charm one are recovered. | result 0.72 | 0.55 | 0.07 | asserted 1.00 |
| s14 | We argue that the Lambda_c(2880) is not a s-wave state. | interpretation 0.88 | 0.69 | 0.06 | asserted 0.89 |
| s15 | In addition to those states we predict the existence of about ten narrow s-wave baryon states with masses below 3 GeV. | result 0.97 | 0.88 | 0.26 | asserted 0.69 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:hep-ph/0507071 by the authors.
References
How the literature uses it
47 arXiv papers cite this in 121 sentences
Papers citing it · 69 sentences without a confident label
Contests it 2 papers
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As commented in Ref. [ref] , the subtraction scales $μ$ used in Ref. [ref] is unreasonably large to ensure that the heavy channel has a negligible effect on the low-energy scattering of the light channel.
Molecular-type $QQss\bar{s}$ pentaquarks predicted by an extended hidden gauge symmetry approach · Numerical results · contest 0.76
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Subsequent works [ref] introduced some improvements, but they failed to provide a scheme fully consistent with HQSS.
Lowest-lying ${\frac{1}{2}}^-$ and ${\frac{3}{2}}^-$ $\Lambda_{Q}$ resonances: from the strange to the bottom sectors · Extended molecular schemes · contest 0.84
Builds on it 1 paper
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For the pseudoscalar $P$ and vector $V^μ$ meson fields, they are easily extended from the SU(3) to the SU(5) case following the work of [ref] ,
Molecular-type $QQss\bar{s}$ pentaquarks predicted by an extended hidden gauge symmetry approach · The molecular-type double-heavy pentaquarks with three strange quarks · 0.85
Uses its method or tool 10 papers
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In Ref. [ref] , the medium effect for the $D/D̅$ meson is studied within the self-consistent framework developed in Ref. [ref] , together with the SU(4) contact interaction model of Ref. [ref] .
Heavy Hadrons in Nuclear Matter · Nuclear matter · 0.87
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A coupled-channel BSE, with a $SU(6)_lsf×$HQSS-extended WT meson-baryon interaction, is solved in [ref] within the on–shell approximation, and adopting a one-subtraction RS at fixed scale for all channels, as advocated in Refs. [ref] .
$\Omega_c$ excited states within a ${\rm SU(6)}_{\rm lsf}\times$HQSS model · Conclusions · 0.80
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To describe the interaction we employ effective Lagrangians that describe the couplings of the vector meson to pseudoscalar mesons $(VPP)$ and baryons $(VBB)$, which are obtained using the hidden gauge formalism and assuming $SU(4)$ symmetry [ref] : [equation] [equation] where $ϕ$ and $V_μ$ represent the 16-plet pseudo-scalar field and the 16-plet vector field, respectively, and $⟨ ⟩$ denotes the $SU(4)$ trace in flavour space.
Double strangeness pentaquarks and other exotic hadrons in the $\Xi_b \to \Xi\ J/\Psi\ \phi$ decay · Meson-Baryon interaction · 0.98
Uses its data or values 3 papers
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[ref] are provided directly, while for the other models [ref] they are evaluated by employing a Gaussian potential whose strength is adjusted to describe the corresponding published $I=0$ and $I=1$ scattering lengths listed in Table [ref].
First study of the two-body scattering involving charm hadrons · Results · 0.80
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Regarding the coupling constants related to baryons, the following values are utilized [ref] [equation] Other coupling constants of those type can be derived from $SU(4)$ symmetry.
Strong decays of the $\Lambda_{c}(2910)$ and $\Lambda_{c}(2940)$ in the $ND^{*}$ molecular frame · Coupling constants under SU(4) symmetry · 1.00
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We consider two possibles models: in the first one, which is based in the latest experimental results (Refs. [ref] ), we assume existence of only one broad $X(4140)$ resonance with a pole position of $M_R=4146.5 MeV$ and a width of $Γ=83 MeV$; while the second model assumes the existence of a narrow $X(4140)$ plus a wide $X(4160)$ resonance, based on earlier experimental results [ref] and a recent theoretical model [ref] .
Double strangeness pentaquarks and other exotic hadrons in the $\Xi_b \to \Xi\ J/\Psi\ \phi$ decay · The $J/ψ ϕ$ mass distribution · 0.90
Compares with it 9 papers
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In total 200 and 221 pairs contribute to $N_same()$ in the region of $< 200$, where model calculations [ref] predict a deviation from unity.
First study of the two-body scattering involving charm hadrons · The correlation function · 0.84
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In addition, there appears a subthreshold mode, located around 75 MeV below the $D_s$ mass, related to an additional $D_s N$ resonance found in [ref] and not in [ref] , in spite of the similar kernels employed, which include a null or negligible $D_sN$ interaction.
Properties of the $D_{s0}^*(2317)^\pm$ in hot and dense nuclear matter · In-medium and finite-temperature loop function · 0.96
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From the analysis of the amplitude on the real axis, the quasi-bound states are found at qualitatively similar positions with Ref. [ref] , while the $I=1$ state becomes broader.
Heavy Hadrons in Nuclear Matter · Two-body interaction with nucleon · 0.97
Cites it as support 1 paper
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These phenomena mentioned above give us sufficient reason to believe that there should be double-charm molecular pentaquarks [ref] , which is the starting point of the present work.
Molecular-type $QQss\bar{s}$ pentaquarks predicted by an extended hidden gauge symmetry approach · Introduction · 0.99
Cites it as background 14 papers
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For $J^P=(1/2)^-$ $D̅N$ system, the $D̅N$ interaction is either insufficient to form the loosely bound state [ref] or only capable of forming very shallow bound states [ref] for $J^P=1/2^-(I=0)$ $D̅N$ system.
Finding Interaction Mechanism between Exotic Molecule and Conventional Hadron · Model for Interaction Dynamics · 0.83
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The hadronic molecules have been studied by the meson-baryon coupled-channel approach [ref] and the QCD sum rules [ref] .
Hidden-charm pentaquarks as a meson-baryon molecule with coupled channels for $\bar{D}^{(\ast)}\Lambda_{\rm c}$ and $\bar{D}^{(\ast)}\Sigma^{(\ast)}_{\rm c}$ · Introduction · 0.94
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Baryons with hidden charm, structured as a meson-baryon molecule, had been predicted in some earlier works [ref] , prior to their discovery, but the existence of a hidden charm pentaquark with double strangeness was not addressed until recently.
Double strangeness pentaquarks and other exotic hadrons in the $\Xi_b \to \Xi\ J/\Psi\ \phi$ decay · Introduction · 0.84
Discussion
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