  The recent LHCb data on $B_s^0\to J/\psi p\bar{p}$ revealed a new
pentaquark-like $P_c(4337)^+$ structure, while finding no evidence for
$P_c(4312)^+$ discovered earlier in $\Lambda_b^0\to J/\psi p K^-$. Though
puzzling, the data actually offer an important hint to understand the nature of
the pentaquark candidates. We develop a model to analyze the $B_s^0\to J/\psi
p\bar{p}$ data. We find that a $\Sigma_c\bar{D}$ one-loop mechanism causes a
threshold cusp that fits well the $P_c(4337)^+$ peak. Also, the
$\Sigma_c\bar{D}$ and $\Lambda_c\bar{D}^{*}$ threshold cusps interfere with
each other to reproduce an oscillating behavior in the proton helicity angle
distribution. These results combined with our earlier analysis on
$\Lambda_b^0\to J/\psi p K^-$ indicate that $P_c(4312)^+$ and $P_c(4337)^+$ are
created by different interference patterns between the $\Sigma_c\bar{D}$ and
$\Lambda_c\bar{D}^{*}$ (anomalous) threshold cusps. The proposed scenario
consistently explains why the $P_c(4312)^+$ and $P_c(4337)^+$ peaks appear in
$\Lambda_b^0\to J/\psi p K^-$ and $B_s^0\to J/\psi p\bar{p}$, respectively, but
not vice versa or both.
