Hidden-Heavy Pentaquarks and Where to Find Them

Abstract

We provide a simple explanation for the observed hidden-charm pentaquarks as bound states in Born-Oppenheimer potentials. We identify $P_{c\bar{c}}(4312)^+$, $P_{c\bar{c}}(4440)^+$, and $P_{c\bar{c}}(4457)^+$ as heavy-quark spin states in a quartet of $c \bar{c}$ pentaquarks with $J^P$ quantum numbers $\frac{1}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$. The quantum numbers of $P_{c\bar{c}}(4457)^+$ differ from most previous predictions. We also predict a fourth $c\bar{c}$ pentaquark with quantum numbers $\frac{3}{2}^-$ near the $Σ_c^\ast\bar{D}$ threshold. We identify $P_{c\bar{c}s}(4338)^0$ and $P_{c\bar{c}s}(4459)^0$ as heavy-quark spin states in a triplet of $c \bar{c}s$ pentaquarks with quantum numbers $\frac{1}{2}^-$ and either $\frac{1}{2}^-$ or $\frac{3}{2}^-$. We also predict a third $c\bar{c}s$ pentaquark with quantum numbers either $\frac{3}{2}^-$ or $\frac{1}{2}^-$ near the $Ξ_c\bar{D}^\ast$ threshold. We explain why the observed hidden-charm pentaquarks have narrow widths.

Figures (4)

• Figure 1: Exotic hidden-heavy hadrons and other fantastic beasts (image by Jam-Di, https://www.deviantart.com/jam-di).
• Figure 2: A B-O potential for exotic hidden-heavy hadrons (thick curve) may support bound states (thin horizontal line) only if it crosses below the heavy-hadron-pair threshold before approaching it.
• Figure 3: Energy levels for the ground-state quartet of $c \bar{c}$ pentaquarks in the $\bigl(\frac{3}{2}^+\bigr)\Lambda$ potentials with $(I,S)=\bigl(\frac{1}{2},0\bigr)$ (thick bars) versus the measured masses (shaded boxes with thin lines).
• Figure 4: Energy levels for the ground-state triplet of $c \bar{c}s$ pentaquarks in the $\bigl(\frac{1}{2}^{+\prime}\bigr)\frac{1}{2}$ potential with $(I,S)=(0,-1)$ (thick bars) versus the measured masses (shaded boxes with thin lines). The predicted quantum numbers of $P_{c\bar{c}s}(4459)^0$ are either $\frac{1}{2}^-$ or $\frac{3}{2}^-$.