  Statistics of lensed arcs in clusters of galaxies serve as a powerful probe
of both the non-sphericity and the inner slope of dark matter halos. We develop
a semi-analytic method to compute the number of arcs in triaxial dark matter
halos. This combines the lensing cross section from the Monte Carlo ray-tracing
simulations, and the probability distribution function (PDF) of the axis ratios
evaluated from cosmological N-body simulations. This approach enables one to
incorporate both asymmetries in the projected mass density and elongations
along the line-of-sight analytically, for the first time in cosmological lensed
arc statistics. As expected, triaxial dark matter halos significantly increase
the number of arcs relative to spherical models; the difference amounts to more
than one order of magnitude while the value of enhancement depends on the
specific properties of density profiles. Then we compare our theoretical
predictions with the observed number of arcs from 38 X-ray selected clusters.
In contrast to the previous claims, our triaxial dark matter halos with inner
density profile \rho \propto r^{-1.5} in a Lambda-dominated cold dark matter
(CDM) universe reproduces well the observation. Since both the central mass
concentration and triaxial axis ratios (minor to major axis ratio ~0.5)
required to account for the observed data are consistent with cosmological
N-body simulations, our result may be interpreted to lend strong support for
the collisionless CDM paradigm at the mass scale of clusters.
