Unravelling Pentaquarks with Born--Oppenheimer effective theory

TL;DR

This paper uses the Born--Oppenheimer effective field theory to analyze the spectrum, decay patterns, and quantum numbers of hidden-charm pentaquarks, providing theoretical predictions and supporting specific quantum number assignments.

Contribution

It applies BOEFT to pentaquarks, offering the first predictions for adjoint baryon masses and detailed quantum number assignments, advancing understanding of their structure within QCD.

Findings

Identifies pentaquarks as bound states in BO potentials with specific short-distance behavior.

Provides the first theoretical predictions for adjoint baryon masses.

Supports quantum number assignments: (1/2)^- for P_c(4312), (3/2)^- for P_c(4380), (1/2)^- for P_c(4457), (3/2)^- for P_c(4440).

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 ${\cal O}(1/m_Q)$ 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 $\Lambda_c\bar{D}^*$, 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.