Unravelling Pentaquarks with Born--Oppenheimer effective theory

Abstract

The hidden-charm pentaquark states $P_{c\bar{c}}{\left(4312\right)}^{+}$, $P_{c\bar{c}}{\left(4380\right)}^{+}$, $P_{c\bar{c}}{\left(4440\right)}^{+}$, and $P_{c\bar{c}}{\left(4457\right)}^{+}$, all with isospin $I=1/2$, were discovered by the LHCb collaboration in the decay process ${\Lambda }_b^0\to J/\psi p{K}^{-}$. 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 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 ${\Sigma }_c\bar{D}$ threshold. We further incorporate $\mathcal{O}(1/m_Q)$ spin-dependent corrections to compute pentaquark multiplet spin splittings. Based on the spectrum, semi-inclusive decay widths to $J/\psi$ and ${\eta }_c$, and the decay width ratios to ${\Lambda }_c\bar{D}$ and ${\Lambda }_c{\bar{D}}^{\ast }$, 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 $P_{c\bar{c}}{\left(4312\right)}^{+}$, $(3/2{)}^{-}$ for $P_{c\bar{c}}{\left(4380\right)}^{+}$, $(1/2{)}^{-}$ for $P_{c\bar{c}}{\left(4457\right)}^{+}$, and $(3/2{)}^{-}$ for $P_{c\bar{c}}{\left(4440\right)}^{+}$. We also present results for the lowest bottom pentaquarks.

59 pages, 8 figures, 7 tables

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