Testing dark energy models with $H(z)$ data
  $Om(z)$ is a diagnostic approach to distinguish dark energy models. However,
there are few articles to discuss what is the distinguishing criterion. In this
paper, firstly we smooth the latest observational $H(z)$ data using a
model-independent method -- Gaussian processes, and then reconstruct the
$Om(z)$ and its fist order derivative $\mathcal{L}^{(1)}_m$. Such
reconstructions not only could be the distinguishing criteria, but also could
be used to estimate the authenticity of models. We choose some popular models
to study, such as $\Lambda$CDM, generalized Chaplygin gas (GCG) model,
Chevallier-Polarski-Linder (CPL) parametrization and Jassal-Bagla-Padmanabhan
(JBP) parametrization. We plot the trajectories of $Om(z)$ and
$\mathcal{L}^{(1)}_m$ with $1 \sigma$ confidence level of these models, and
compare them to the reconstruction from $H(z)$ data set. The result indicates
that the $H(z)$ data does not favor the CPL and JBP models at $1 \sigma$
confidence level. Strangely, in high redshift range, the reconstructed
$\mathcal{L}^{(1)}_m$ has a tendency of deviation from theoretical value, which
demonstrates these models are disagreeable with high redshift $H(z)$ data. This
result supports the conclusions of Sahni et al. \citep{sahni2014model} and Ding
et al. \citep{ding2015there} that the $\Lambda$CDM may not be the best
description of our universe.
