  We report on the measurement of the Central Exclusive Production of charged
particle pairs $h^{+}h^{-}$ ($h = \pi, K, p$) with the STAR detector at RHIC in
proton-proton collisions at $\sqrt{s} = 200$ GeV. The charged particle pairs
produced in the reaction $pp\to p^\prime+h^{+}h^{-}+p^\prime$ are reconstructed
from the tracks in the central detector, while the forward-scattered protons
are measured in the Roman Pot system. Differential cross sections are measured
in the fiducial region, which roughly corresponds to the square of the
four-momentum transfers at the proton vertices in the range $0.04~\mbox{GeV}^2
< -t_1 , -t_2 < 0.2~\mbox{GeV}^2$, invariant masses of the charged particle
pairs up to a few GeV and pseudorapidities of the centrally-produced hadrons in
the range $|\eta|<0.7$. The measured cross sections are compared to
phenomenological predictions based on the Double Pomeron Exchange (DPE) model.
Structures observed in the mass spectra of $\pi^{+}\pi^{-}$ and $K^{+}K^{-}$
pairs are consistent with the DPE model, while angular distributions of pions
suggest a dominant spin-0 contribution to $\pi^{+}\pi^{-}$ production. The
fiducial $\pi^+\pi^-$ cross section is extrapolated to the Lorentz-invariant
region, which allows decomposition of the invariant mass spectrum into
continuum and resonant contributions. The extrapolated cross section is well
described by the continuum production and at least three resonances, the
$f_0(980)$, $f_2(1270)$ and $f_0(1500)$, with a possible small contribution
from the $f_0(1370)$. Fits to the extrapolated differential cross section as a
function of $t_1$ and $t_2$ enable extraction of the exponential slope
parameters in several bins of the invariant mass of $\pi^+\pi^-$ pairs. These
parameters are sensitive to the size of the interaction region.
