Unraveling pentaquarks with the Born-Oppenheimer effective theory

The hidden-charm pentaquark states P c c ¯ ( 4312 ) + , P c c ¯ ( 4380 ) + , P c c ¯ ( 4440 ) + , and P c c ¯ ( 4457 ) + , all with isospin I = 1 / 2 , were discovered by the LHCb Collaboration in the decay process Λ b 0 → 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 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 D ¯ and Λ c 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 /<