BB Intermeson Potentials in the Quark Model

D. J. Dean; E. S. Swanson; N. Black; T. Barnes

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BB Intermeson Potentials in the Quark Model

T. Barnes, N. Black, D. J. Dean, E. S. Swanson

Nuclear Theory · Submitted 24 Feb 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim A numerical study of the two-meson Schrodinger equations in the (bqbar)(bqbar) and (cqbar)(cqbar) sectors with the quark model potentials finds a single "molecule", in the I=0 BB* sector.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.89 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.97 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This "BB" system is an attractive theoretical laboratory for the study of the nuclear force between color singlets; the hadronic system is relatively simple, and there are lattice gauge theory (LGT) results for V_BB(r) which may be compared to phenomenological models. We find that the quark model potential (after lattice smearing) has qualitative similarities to the LGT potential in the two B*B* channels in which direct comparison is possible, although there is evidence of a difference in length scales. The quark model prediction of equal magnitude but opposite sign for I=0 and I=1 potentials also appears similar to LGT results at intermediate r. There may however be a discrepancy between the LGT and quark model I=1 BB potentials. A numerical study of the two-meson Schrodinger equations in the (bqbar)(bqbar) and (cqbar)(cqbar) sectors with the quark model potentials finds a single "molecule", in the I=0 BB* sector. Binding in other channels might occur if the quark model forces are augmented by pion exchange.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark.	contribution 0.99	0.96	0.08	asserted 1.00
s1	This "BB" system is an attractive theoretical laboratory for the study of the nuclear force between color singlets; the hadronic system is relatively simple, and there are lattice gauge theory (LGT) results for V_BB(r) which may be compared to phenomenological models.	background 1.00	0.09	0.05	asserted 0.96
s2	We find that the quark model potential (after lattice smearing) has qualitative similarities to the LGT potential in the two BB channels in which direct comparison is possible, although there is evidence of a difference in length scales.	result 1.00	0.94	0.22	asserted 0.99
s3	The quark model prediction of equal magnitude but opposite sign for I=0 and I=1 potentials also appears similar to LGT results at intermediate r.	result 0.97	0.76	0.13	hedged possibility 0.51
s4	There may however be a discrepancy between the LGT and quark model I=1 BB potentials.	result 0.49	0.40	0.07	hedged possibility 0.99
s5	A numerical study of the two-meson Schrodinger equations in the (bqbar)(bqbar) and (cqbar)(cqbar) sectors with the quark model potentials finds a single "molecule", in the I=0 BB* sector.	result 0.99	0.95	0.40	asserted 1.00
s6	Binding in other channels might occur if the quark model forces are augmented by pion exchange.	future work 0.42	0.17	0.07	speculative 0.96

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.60.

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The paper

Original abstract

In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This "BB" system is an attractive theoretical laboratory for the study of the nuclear force between color singlets; the hadronic system is relatively simple, and there are lattice gauge theory (LGT) results for V_BB(r) which may be compared to phenomenological models. We find that the quark model potential (after lattice smearing) has qualitative similarities to the LGT potential in the two B*B* channels in which direct comparison is possible, although there is evidence of a difference in length scales. The quark model prediction of equal magnitude but opposite sign for I=0 and I=1 potentials also appears similar to LGT results at intermediate r. There may however be a discrepancy between the LGT and quark model I=1 BB potentials. A numerical study of the two-meson Schrodinger equations in the (bqbar)(bqbar) and (cqbar)(cqbar) sectors with the quark model potentials finds a single "molecule", in the I=0 BB* sector. Binding in other channels might occur if the quark model forces are augmented by pion exchange.

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References

Forward citations

Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

When hadrons collide: di-J/psi structure in the final state
hep-ph 2026-10 conditional novelty 7.0 of 10

The LHC di-J/psi peaks can be reproduced as threshold and rescattering effects of a fixed quark-model amplitude, without invoking tetraquark resonances.
Observation of String Breaking in QCD
hep-lat 2005-05 accept novelty 7.0 of 10

Two-flavor lattice QCD at zero temperature shows the static quark-antiquark string breaking into a meson pair at r ≈ 1.25 fm, with a minimum level gap of about 51 MeV.
Evidence for charm-bottom tetraquarks and the mass dependence of heavy-light tetraquark states from lattice QCD
hep-lat 2018-10 conditional novelty 6.0 of 10

A lattice QCD calculation finds evidence that a ud cbar bbar tetraquark is bound by 15 to 61 MeV below the Dbar B* threshold, with mass about 7154 MeV.
BB interactions with static bottom quarks from Lattice QCD
hep-lat 2015-10 conditional novelty 5.0 of 10

Two B mesons made of static bottom antiquarks and physical-mass light quarks are found to bind into a tetraquark with a binding energy of about 90 MeV in the scalar isosinglet channel.
Are Y(4260) and {\rm Z$_2^{+}$(4250)} ${\rm D_1D}$ or ${\rm D_0D^{*}}$ Hadronic Molecules?
hep-ph 2008-09 conditional novelty 5.0 of 10

Within a meson-exchange model with a tuned cutoff of 1-2 GeV, Y(4260) can be a D1D or D0D* molecule, while Z2+(4250) would require an implausibly large cutoff above 3 GeV.

Show 2 more citing papers

A survey of heavy-heavy hadronic molecules
hep-ph 2021-08 conditional novelty 4.0 of 10

A leading-order contact-interaction model predicts 124 doubly-charmed hadronic molecules, including a DD* bound state near the newly observed Tcc.
Pentaquark and Tetraquark states
hep-ph 2019-03 accept novelty 2.5 of 10

A comprehensive review of hidden-heavy-flavor tetraquark and pentaquark states, covering LHCb's confirmation of the Pc states and surveying the chromomagnetic-interaction, quark-model, meson-exchange, QCD-sum-rule, an...

How the literature uses it

14 arXiv papers cite this in 22 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Uses its method or tool 5 papers

In the constituent interchange model developed by Barnes and Swanson [ref] , the meson-meson scattering amplitude is calculated by the (anti)quark-(anti)quark interactions by assuming the one-gluon-exchange (OGE) color Coulomb interaction, spin-spin interaction, and linear scalar confinement interaction.

Possible molecular states in $B^{(*)}B^{(*)}$ scatterings · The model · 0.99
This can be achieved by the Barnes-Swanson (BS) model [ref] .

Decays of $X(3872)$ to $\chi_{cJ}\pi^0$ and $J/\psi\pi^+\pi^-$ · Introduction · 1.00
If the wave functions of the mesons are described as the simple harmonic oscillator (SHO) wave functions, the integrations could be simplified and the analytical transition amplitudes of all four diagrams could be expressed explicitly in terms of confluent hypergeometric functions [ref] .

Comprehending Isospin breaking effects of $X(3872)$ in a Friedrichs-model-like scheme · The quark rearrangement model · 0.97

Compares with it 1 paper

In comparison, the other methods used in discussing the states in these systems, such as solving the schrödinger equation [ref] using the potentials extracted from the amplitude, or the heavy meson chiral effective theory discussion [ref] , could only produce the near threshold bound state information and can not say anything about virtual states.

Possible molecular states in $B^{(*)}B^{(*)}$ scatterings · Summary · 0.96

Cites it as background 6 papers

The theoretical study of $T^-_bb$ states has a longstanding history, utilizing various methods, such as heavy meson effective field theory [ref] , lattice QCD [ref] , quark model [ref] , and QCD sum rule [ref] .

Investigation on the bottom analogs of the $T_{cc}^{+}$ · Introduction · 0.92
Barnes suggested that isoscalar $BB^*$ interaction is attractive and a vector state with spin parity $1^+$ maybe exist by solving the Schödinger equation [ref] .

Molecular states from $D^{(*)}\bar{D}^{(*)}/B^{(*)}\bar{B}^{(*)}$ and $D^{(*)}D^{(*)}/\bar{B}^{(*)}\bar{B}^{(*)}$ interactions · Introduction · 0.87
The doubly heavy tetraquark states in molecular configurations were widely investigated in the literature [ref] where predictions of many doubly heavy tetraquark states including the $T_cc$ mentioned above as well as other systems were made.

A survey of heavy-heavy hadronic molecules · Heavy meson-meson molecules · 0.92

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