Open Access

Unraveling pentaquarks with the Born-Oppenheimer effective theory

Nora Brambilla ^1,2,3,*, Abhishek Mohapatra ^1,†, and Antonio Vairo ^1,‡

¹Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Strasse 1, 85748 Garching, Germany
²Technical University of Munich, Institute for Advanced Study, Lichtenbergstrasse 2 a, 85748 Garching, Germany
³Technical University of Munich, Munich Data Science Institute, Walther-von-Dyck-Strasse 10, 85748 Garching, Germany

^*Contact author: nora.brambilla@tum.de
^†Contact author: abhishek.mohapatra@tum.de
^‡Contact author: antonio.vairo@tum.de

Phys. Rev. D 112, 114037 – Published 23 December, 2025

DOI: https://doi.org/10.1103/5z3t-rq5f

Abstract

The hidden-charm pentaquark states $P_{c \bar{c}} {(4312)}^{+}$ , $P_{c \bar{c}} {(4380)}^{+}$ , $P_{c \bar{c}} {(4440)}^{+}$ , and $P_{c \bar{c}} {(4457)}^{+}$ , all with isospin $I = 1 / 2$ , were discovered by the LHCb Collaboration in the decay process $Λ_{b}^{0} \to J / ψ p K^{-}$ . Although their quantum numbers remain undetermined, these states have generated significant theoretical interest. We analyze their spectrum and decay patterns—including those of their spin partners—within the Born-Oppenheimer (BO) effective field theory (BOEFT), a framework grounded in QCD. At leading order in BOEFT, we identify these pentaquark states as bound states in BO potentials that exhibit at short distance a repulsive octet behavior and a nonperturbative shift due to the adjoint baryons masses, while asymptotically approaching the $Σ_{c} \bar{D}$ threshold. We further incorporate $O (1 / m_{Q})$ spin-dependent corrections to compute pentaquark multiplet spin splittings. Based on the spectrum, semi-inclusive decay widths to $J / ψ$ and $η_{c}$ , and the decay width ratios to $Λ_{c} \bar{D}$ and $Λ_{c} {\bar{D}}^{*}$ , we provide the first theoretical predictions for the adjoint baryon masses, which can be confirmed by future lattice QCD studies. Moreover, our analysis supports the quantum number assignments: $J^{P} = (1 / 2)^{-}$ for $P_{c \bar{c}} {(4312)}^{+}$ , $(3 / 2)^{-}$ for $P_{c \bar{c}} {(4380)}^{+}$ , $(1 / 2)^{-}$ for $P_{c \bar{c}} {(4457)}^{+}$ , and $(3 / 2)^{-}$ for $P_{c \bar{c}} {(4440)}^{+}$ . We also present results for the lowest bottom pentaquarks.

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Phys. Rev. D 112, 114037– Published 23 December, 2025

Vol. 112, Iss. 11 — 1 December 2025

Received 26 August 2025
Accepted 28 October 2025

DOI: https://doi.org/10.1103/5z3t-rq5f

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Unraveling pentaquarks with the Born-Oppenheimer effective theory

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