Quark-model search for compact $c\bar c uds$ pentaquark states

A potential quark model is used to search for a $P_{c\bar{c}s}^0=(c\bar{c}uds)^0$, $J^P=1/2^-$ pentaquark state that has recently been observed experimentally by the LHCb collaboration at 4338.2 MeV, with a width of 7.0 MeV and high statistical significance $>15\sigma$. Our model Hamiltonian reproduces the masses of the low-lying charmed and strange hadrons. We use the Gaussian expansion method {to solve the} five-body Schr\"odinger equation. Employing the real scaling method {including} the relevant meson-baryon thresholds explicitly, sharp resonances are distinguished from the meson-baryon scattering states. We incorporate new color states of the color-octet meson and baryon configurations as well as the color-singlet configurations for the five-quark states. We find no $J^P=1/2^-$ resonance close to the observed state, and also none in the $J^P=3/2^-$ state. This increases the likelihood that $P^0_{c\bar{c}s}$ is a $\Xi_c\bar{D}$ hadronic molecule rather than a compact state.