  The LHCb discovery of the two baryonic states $P_c^+(4380)$ and
$P_c^+(4450)$, having $J^{P}=3/2^-$ and $J^{P}=5/2^+$, respectively, in the
process $pp \to b \bar{b} \to \Lambda_b X$, followed by the decay $\Lambda_b
\to J/\psi\; p\; K^-$, has motivated a number of theoretical models.
Interpreting them as compact $\{\bar{c}\; [c u] \; [ud]; L_{\mathcal{P}}=0,1\}$
objects, the mass spectroscopy of the $J^P=3/2^-$ and $J^P=5/2^+$ pentaquarks
was worked out by us for the pentaquarks in the $SU(3)_F$ multiplets, using an
effective Hamiltonian based on constituent diquarks and quarks. Their possible
discovery modes in $b$-baryon decays were also given using the heavy quark spin
symmetry. In this paper, we calculate the mass spectrum of the hidden
$c\bar{c}$ pentaquarks having $J^{P}=\frac{1}{2}^\pm$ for the $SU(3)_F$
multiplets and their anticipated discovery modes in $b$-baryon decays. Some of
the $P_c^+(J^P=1/2^\pm$) pentaquarks, produced in the $\Lambda_{b}$ decays may
have their masses just below the $J/\psi\, p$ threshold, in which case they
should be searched for in the modes $ P_c^+(J^P=1/2^\pm) \to \eta_c\; p,\;\;
\mu^+ \mu^- \;p,\;\; e^+ e^-\; p$.
