Pith. Sign in

REVIEW

Hidden-heavy Pentaquarks in the Born-Oppenheimer Approximation for QCD

PaperPDF from arXiv

data files

ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Fareed Alasiri, Eric Braaten, Roberto Bruschini

High Energy Physics - Phenomenology · Submitted 5 Oct 2026 · 49 references

Pith's verdict: A clean, honest framework paper whose headline predictions — 5/2− for P(4457)+ and "only four" hidden-charm pentaquarks — rest on an assumed potential shape nobody has computed; referee it, but flag the binding assumption and the weak mass fit.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on October 6, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

  1. T0 AI review An AI read the paper and answered a fixed list of questions.
  2. T1 Audit Automatic checks that the references and files the paper relies on exist and match.
  3. T2 Compute The paper's code or calculations re-run with the same results.
  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 2 major objections · 4 minor · Ask about this paper · The compiled record · Read the full review →
Challenge this review Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2610.06009 (version 1)
Pith IDQJ5MWYQD, Pith's permanent record of this paper and its review
CitationEric Braaten, Fareed Alasiri, Roberto Bruschini. "Hidden-heavy Pentaquarks in the Born-Oppenheimer Approximation for QCD." arXiv:2610.06009 (2026). https://pith.science/paper/QJ5MWYQD
Cite this reviewBibTeX for Pith's review of this paper
Claim paper

Why Pith says this

Highlight any text to comment on it.

Referee report

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The four observed charmed pentaquarks form one bound quartet, with $J^P = \frac{1}{2}^-$, $\frac{3}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$, arising from two coupled Born-Oppenheimer potentials of a spin-$\frac{3}{2}$ adjoint baryon.

The reading

This paper argues that the four observed nonstrange hidden-charm pentaquarks $P_{c\bar{c}}(4312)^+$, $P_{c\bar{c}}(4337)^+$, $P_{c\bar{c}}(4440)^+$, and $P_{c\bar{c}}(4457)^+$ are a single bound quartet: the ground state of a $c\bar{c}$ pair in the two coupled Born-Oppenheimer potentials that attach at short distance to a spin-$\frac{3}{2}^+$ adjoint (color-octet) baryon and at long distance approach the $\Sigma_c^{(*)}\bar{D}^{(*)}$ threshold. Their predicted quantum numbers are $\frac{1}{2}^-$, $\frac{3}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$ respectively, and the $\frac{5}{2}^-$ assignment for $P_{c\bar{c}}(4457)^+$ differs from almost every prior molecular or constituent-model prediction, which cluster on $\frac{1}{2}^-$ or $\frac{3}{2}^-$. Because the competing $\left(\frac{1}{2}^{+'}\right)_{\frac{1}{2}}$ potential attached to the same-parity orbital excitation of the $\frac{1}{2}^+$ adjoint baryon (about 600 MeV higher) is assumed not to bind, the paper predicts exactly four nonstrange hidden-charm pentaquarks rather than the seven that simple molecular models produce. The strange partners $P_{c\bar{c}s}(4338)^0$ and $P_{c\bar{c}s}(4459)^0$ are placed as two members of a ground-state triplet in the potential of a spin-$\frac{1}{2}$ strange adjoint baryon, and the paper gives model-independent ratios of decay rates into charmonium plus a light baryon and into charm-hadron pairs as the testable consequences.

What carries the argument

The central object is the diabatic Born-Oppenheimer potential for QCD with static color-triplet and color-antitriplet sources: a discrete energy level of light QCD that behaves as a repulsive color-Coulomb potential offset by an adjoint (color-octet) baryon energy at short distance and approaches a heavy-hadron-pair threshold at long distance. The argument runs on a bookkeeping of these potentials, since 17 adjoint-baryon potentials exist at short distance but 29 static-hadron-pair potentials at long distance, forcing about half the long-distance potentials to connect through same-parity orbital excitations of adjoint baryons. The load-bearing piece is the couple of potentials $\left(\frac{3}{2}^{+}\right)_{\frac{3}{2},\frac{1}{2}}$ of the spin-$\frac{3}{2}$ adjoint baryon, assumed to dip below the $\Sigma_c^{(*)}\bar{D}^{(*)}$ threshold and to support a quartet of bound states, while the single $\left(\frac{1}{2}^{+'}\right)_{\frac{1}{2}}$ potential of the about-600-MeV-higher orbital excitation approaches the same threshold from above and binds nothing; that asymmetry is what reduces the count from seven (molecular dominance) to four. First-order perturbation theory in the charm-hadron spin-splitting term $V_{SS}$ then splits the quartet into the four observed masses and fixes the quantum numbers, with the $\frac{5}{2}^-$ state pure $\Sigma_c^*\bar{D}^*$.

Extended reading notes

Core claim

The central claim is that the count and quantum numbers of the observed hidden-charm pentaquarks are fixed by the low-energy spectrum of adjoint (color-octet) baryons, not by molecular dynamics. Reading the short-distance ends of the relevant Born-Oppenheimer potentials off the lowest adjoint baryons and matching them, through the diabatic representation, to the long-distance heavy-hadron-pair thresholds, the authors identify the four states $P_{c\bar{c}}(4312)^+$, $P_{c\bar{c}}(4337)^+$, $P_{c\bar{c}}(4440)^+$, and $P_{c\bar{c}}(4457)^+$ as the ground-state quartet of a $c\bar{c}$ pair in the two coupled potentials $\left(\frac{3}{2}^{+}\right)_{\frac{3}{2},\frac{1}{2}}$ of the spin-$\frac{3}{2}$ adjoint baryon, with $J^P = \frac{1}{2}^-$, $\frac{3}{2}^-$, $\frac{3}{2}^-$, $\frac{5}{2}^-$ respectively. The mismatch in counting—17 adjoint-baryon potentials at short distance against 29 static-hadron-pair potentials at long distance—forces nearly half the long-distance potentials to connect through same-parity orbital excitations of the adjoint baryon, and it is this matching constraint that keeps the $\left(\frac{1}{2}^{+'}\right)_{\frac{1}{2}}$ potential from binding, so only four nonstrange hidden-charm pentaquarks exist. Because $P_{c\bar{c}}(4457)^+$ is predicted to be $\frac{5}{2}^-$, this framework separates from nearly all prior molecular and constituent-model assignments for that state, and the predicted ratios of decay rates into charmonium plus proton, into constituent charm-hadron pairs, and into the lower-energy $\Lambda_c \bar{D}^{(*)}$ pairs give the sharpest experimental way to tell the two pictures apart.

Load-bearing premise

The identification rests on the assumed qualitative shapes of the B-O potentials: the two coupled $\left(\frac{3}{2}^{+}\right)$ potentials must cross below the $\Sigma_c^{(*)}\bar{D}^{(*)}$ threshold and support bound states, while the $\left(\frac{1}{2}^{+'}\right)_{\frac{1}{2}}$ potential tied to the orbital excitation about 600 MeV higher must approach the same threshold from above and bind nothing; if that potential binds, there are seven pentaquarks instead of four and the central claim collapses.

Editorial extensions

If this is right

  • If $P_{c\bar{c}}(4457)^+$ is measured to have $J^P = \frac{5}{2}^-$, the quartet assignment is confirmed and almost all prior molecular and constituent-model predictions for its spin, which cluster on $\frac{1}{2}^-$ or $\frac{3}{2}^-$, are excluded.
  • No additional nonstrange hidden-charm pentaquarks should appear near the $\Sigma_c^*\bar{D}^*$ threshold at about 4526.7 MeV, where molecular dominance predicts three; observation of any such state would favor the molecular picture over this one.
  • The predicted decay ratios are large and testable, e.g., $\Gamma[P_{c\bar{c}}(4440)\to\eta_c p]/\Gamma[P_{c\bar{c}}(4440)\to J/\psi p]\approx 9.2$, and the combined partial widths into $\Lambda_c\bar{D}^{(*)}$ are 17, 310, and 370 times that of $P_{c\bar{c}}(4312)$.
  • In the strange sector, $P_{c\bar{c}s}(4459)^0$ should have $J^P = \frac{1}{2}^-$ or $\frac{3}{2}^-$, and a third $c\bar{c}s$ pentaquark of the complementary quantum number should lie near it, close to the $\Xi_c\bar{D}^*$ threshold.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the same potential-shape logic carries over to the $b\bar{b}$ sector, the four-versus-seven counting should reappear in hidden-bottom pentaquarks with smaller spin splittings, giving an independent test of the framework.
  • The four-versus-seven difference can be probed by scanning the $J/\psi p$ invariant-mass distributions near the $\Sigma_c^*\bar{D}^*$ threshold for the three extra states that molecular dominance predicts but this model excludes, without waiting for a definitive $J^P$ measurement.
  • Because the argument hinges on the relative height of the $\frac{3}{2}^+$ versus $\frac{1}{2}^{+'}$ adjoint-baryon energies, which the paper estimates only through the roughly 600 MeV orbital-excitation heuristic, a single lattice computation of the adjoint-baryon spectrum would either confirm or overturn the central claim.
Original abstract

Hidden-heavy pentaquarks can be identified as bound states in diabatic Born-Oppenheimer potentials that are repulsive color-Coulomb potentials at short distance, cross below a heavy-hadron-pair threshold, and then approach that threshold at long distance. We identify the pentaquarks $P_{c\bar{c}}(4312)^+$, $P_{c\bar{c}}(4337)^+$, $P_{c\bar{c}}(4440)^+$, and $P_{c\bar{c}}(4457)^+$ as the ground-state quartet for $c \bar c$ in the two coupled potentials associated with a spin-$3/2$ adjoint baryon. We predict that their $J^P$ quantum numbers are $\frac{1}{2}^-$, $\frac{3}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$, respectively. Our prediction for $P_{c\bar{c}}(4457)^+$ differs from almost all previous predictions. Our prediction that there are only four hidden-charm pentaquarks differs qualitatively from that of simple molecular models that there should be seven. We identify the strange hidden-charm pentaquarks $P_{c\bar{c}s}(4338)^0$ and $P_{c\bar{c}s}(4459)^0$ as two members of the ground-state triplet for $c \bar c$ in the potential associated with a spin-$1/2$ strange adjoint baryon. We also present model-independent predictions for pentaquark decays into charmonium plus a light baryon and into a charm baryon and a charm meson.

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.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-06: 1 request, 6,122 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Hidden-heavy pentaquarks can be identified as bound states in diabatic Born-Oppenheimer potentials that are repulsive color-Coulomb potentials at short distance, cross below a heavy-hadron-pair threshold, and then approach that threshold at long distance. We identify the pentaquarks $P_{c\bar{c}}(4312)^+$, $P_{c\bar{c}}(4337)^+$, $P_{c\bar{c}}(4440)^+$, and $P_{c\bar{c}}(4457)^+$ as the ground-state quartet for $c \bar c$ in the two coupled potentials associated with a spin-$3/2$ adjoint baryon. We predict that their $J^P$ quantum numbers are $\frac{1}{2}^-$, $\frac{3}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$, respectively. Our prediction for $P_{c\bar{c}}(4457)^+$ differs from almost all previous predictions. Our prediction that there are only four hidden-charm pentaquarks differs qualitatively from that of simple molecular models that there should be seven. We identify the strange hidden-charm pentaquarks $P_{c\bar{c}s}(4338)^0$ and $P_{c\bar{c}s}(4459)^0$ as two members of the ground-state triplet for $c \bar c$ in the potential associated with a spin-$1/2$ strange adjoint baryon. We also present model-independent predictions for pentaquark decays into charmonium plus a light baryon and into a charm baryon and a charm meson.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Hidden-heavy pentaquarks can be identified as bound states in diabatic Born-Oppenheimer potentials that are repulsive color-Coulomb potentials at short distance, cross below a heavy-hadron-pair threshold, and then approach that threshold at long distance. method 0.54 0.32 0.25 asserted 0.78
s1 We identify the pentaquarks $P_{c\bar{c}}(4312)^+$, $P_{c\bar{c}}(4337)^+$, $P_{c\bar{c}}(4440)^+$, and $P_{c\bar{c}}(4457)^+$ as the ground-state quartet for $c \bar c$ in the two coupled potentials associated with a spin-$3/2$ adjoint baryon. result 0.91 0.95 0.35 asserted 1.00
s2 We predict that their $J^P$ quantum numbers are $\frac{1}{2}^-$, $\frac{3}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$, respectively. result 0.99 0.93 0.20 asserted 0.98
s3 Our prediction for $P_{c\bar{c}}(4457)^+$ differs from almost all previous predictions. result 0.56 0.84 0.07 asserted 1.00
s4 Our prediction that there are only four hidden-charm pentaquarks differs qualitatively from that of simple molecular models that there should be seven. result 0.64 0.85 0.17 asserted 1.00
s5 We identify the strange hidden-charm pentaquarks $P_{c\bar{c}s}(4338)^0$ and $P_{c\bar{c}s}(4459)^0$ as two members of the ground-state triplet for $c \bar c$ in the potential associated with a spin-$1/2$ strange adjoint baryon. result 0.96 0.94 0.11 asserted 1.00
s6 We also present model-independent predictions for pentaquark decays into charmonium plus a light baryon and into a charm baryon and a charm meson. contribution 0.66 0.93 0.07 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from argument 0.34.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. The observed cc¯ pentaquarks (left) and ccs¯ pentaquarks (right) considered in this work and the relevant baryon-meson thresholds. In 2020, the LHCb Collaboration presented evidence with a significance of 3.1σ for a strange hidden-charm (ccs¯ ) pentaquark as a peak near 4450 MeV in the J/ψ Λ invariant￾mass distribution from the decay Ξ − b → J/ψ Λ K− [30]. In 2022, LHCb discovered a ccs¯ pentaquark as a peak near 4338 MeV in the J/ψ Λ invariant-mass distribution from the decay B− → J/ψ Λ ¯p [31]. Its J P quantum numbers were determined to be 1 2 − . The properties of the two ccs¯…
Figure 2. The light-quark flavors in the j π = 1 2 + ¯3-mesons form a triplet in the (I3, S) plane. We refer to the energy increase of a hadron from replacing an up or down quark by a strange quark as a strangeness splitting. Strangeness splittings can be calculated using lattice QCD or lattice NRQCD. We refer to the energy difference between two members of an HQSS multiplet as a spin splitting. The spin splittings of heavy hadrons scale as 1/mQ, where mQ is the heavy quark mass. Spin splittings of heavy hadrons cannot be calculated using lattice simulations of light QCD only. 3.2 Antitriplet…
Figure 3. The light-quark flavors in the j π = 0+ and 1 + 3-baryons form an antitriplet (left) and a sextet (right) in the (I3, S) plane. Brackets { · · · } or [ · · · ] indicate a symmetric or antisymmetric combination of the flavors enclosed. 1 2 + . For charm baryons, the HQSS singlets with (I, S) = (0, 0) and ( 1 2 , −1) are Λc and Ξc. They form the two rows of the antitriplet in
Figure 4. The light-quark flavors in the j π = 1 2 + 8-baryons form a singlet 1A (left), an octet 8M (middle), and a decuplet 10S (right) in the (I3, S) plane. The light-quark flavors in the j π = 3 2 + 8-baryons form an additional octet 8M. Brackets { · · · }, [ · · · ], or (· · ·) indicate a symmetric, antisymmetric, or mixed-symmetry combination of the flavors enclosed, respectively. three SU(3)-flavor triplets can be decomposed into one antisymmetric singlet, two mixed￾symmetry octets, and one symmetric decuplet: 3⊗3⊗3 = 1A ⊕8M ⊕8M ⊕10S. The direct product of three SU(2)-spin doublets can…
Figure 5. Plausible qualitative behaviors of the lowest-energy B-O potentials with (I, S) = 1 2 , 0  . The 1 2 + 1 2 and 1 2 +′ 1 2 potentials approach the ΛcD¯(∗) and Σ (∗) c D¯(∗) thresholds from above at large r. The 3 2 + 1 2 and 3 2 + 3 2 potentials cross below the Σ (∗) c D¯(∗) threshold before approaching it at large r. The dots on the vertical axis are adjoint-baryon energies. The dotted curves are the potentials with the color-Coulomb potential set to zero, which change smoothly from the adjoint￾baryon energy at small r to a static-hadron-pair threshold at large r. r → 0.…
Figure 6. Plausible qualitative behavior of the lowest-energy B-O potentials with (I, S) = (0, −1). The 1 2 + 1 2 potential approaches the ΛcD¯ (∗) s threshold from above at large r. The 1 2 +′ 1 2 potential crosses below the ΞcD¯(∗) threshold before approaching it at large r. The dots on the vertical axis are adjoint-baryon energies. The dotted curves are the potentials with the color-Coulomb potential set to zero, which change smoothly from the adjoint-baryon energy at small r to a static-hadron-pair threshold at large r. The octet 8-baryon is expected to be lower in energy, because it…
Figure 7. Energy-level diagram for the ground-state quartet of isospin- 1 2 cc¯pentaquarks associated with the 3 2 + 8-baryon. The dashed horizontal lines are thresholds for a charm baryon and a charm meson. The shaded boxes are the error bands for the measured masses, with the central value highlighted by a thin line. The thick bars are predictions given by the sum of a ground-state energy and spin splittings. The ground-state energy is equal to the spin-weighted average of the central values of the observed masses assuming the predicted spins. The spin splittings are from first order pertu
Figure 8. Energy-level diagram for the isospin- 1 2 cc¯ pentaquarks associated with the 3 2 + and 1 2 +′ 8-baryons under the assumption of molecular dominance with ideal mixing. The dashed horizontal lines are the thresholds for a charm baryon and a charm meson. The shaded boxes are the error bars for the measured masses, with the central value highlighted by a thin line. The quantum numbers of Pcc¯(4440)+ and Pcc¯(4457)+ were chosen to be 1 2 − and 3 2 − (Scenario 1), but the opposite assignment 3 2 − and 1 2 − (Scenario 2) is also possible. The blue bars are the predictions of molecular…
Figure 9. Energy-level diagram for the ground-state triplet of isospin-0 ccs¯ pentaquarks associated with the 1 2 +′ 8-baryon. The dashed horizontal lines are the thresholds for a charm baryon and a charm meson. The shaded boxes are the error bands for the measured masses, with the central value highlighted by a thin line. For illustration purposes, we assign the quantum numbers 3 2 − to Pccs¯ (4459)0 , but the assignment 1 2 − is also possible. The thick bars are predictions given by the sum of a ground-state energy and spin splittings. The ground-state energy is equal to the spin￾weigh

Figures reproduced from arXiv:2610.06009 by the authors.

References

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.