  The LHCb pentaquarks -- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ -- have
been theorized to be $\Sigma_c \bar{D}$ and $\Sigma_c \bar{D}^*$ S-wave
molecules. Here we explore the possibility that two of these pentaquarks -- the
$P_c(4440)$ and $P_c(4457)$ -- contain in addition a $\Lambda_c(2595) \bar{D}$
component in P-wave. We will analyze the effects of this extra channel within
two effective field theories: the first one will be a standard contact-range
effective field theory and the second one will include the non-diagonal pion
dynamics connecting the $\Sigma_c \bar{D}^*$ and $\Lambda_c(2595) \bar{D}$
channels, which happens to be unusually long-ranged. The impact of the
coupled-channel dynamics between the $\Sigma_c \bar{D}^*$ and $\Lambda_c(2595)
\bar{D}$ components is modest at best for the $P_c(4440)$ and $P_c(4457)$,
which will remain to be predominantly $\Sigma_c \bar{D}^*$ molecules. However,
if the quantum numbers of the $P_c(4457)$ are $J^P = \frac{1}{2}^-$, the
coupled-channel dynamics is likely to induce the binding of a $\Lambda_c(2595)
\bar{D}$ S-wave molecule (coupled to $\Sigma_c \bar{D}^*$ in P-wave) with $J^P
= \frac{1}{2}^+$ and a mass similar to the $P_c(4457)$. If this is the case,
the $P_c(4457)$ could actually be a double peak containing two different
pentaquark states.
