  We study Galileon scalar field model by considering the lowest order Galileon
term in the lagrangian, $(\partial_{\mu} \phi)^2 \Box\phi$ by invoking a field
potential. We use Statefinder hierarchy to distinguish the light mass galileon
models with different potentials amongst themselves and from the $\Lambda$CDM
behaviour. The $Om$ diagnostic is applied to cosmological dynamics and
observational constraints on the model parameters are studied using
SN+Hubble+BAO data.
