  In the Littlest Higgs model with T-parity, the heavy photon ($A_{H}$) is
supposed to be a possible dark matter (DM) candidate. A direct proof of
validity of the model is to produce the heavy photon at accelerator. In this
paper, we study the production rate of $ e^ + e^ - \to A_{H}A_{H}$ at the
international $e^ + e^ -$ linear collider (ILC) in the Littlest Higgs model
with T-parity and show the distributions of the transverse momenta of $A_{H}$.
The numerical results indicate that the heavy photon production rate could
reach the level of $10^{-1} fb$ at some parameter space, so it can be a good
chance to observe the heavy photon via the pair production process with the
high luminosity at the ILC (500 $fb^{-1}$) . We know that DM is composed of
weakly-interacting massive particles (WIMPs), so the interactions with standard
model (SM) particles are weakness, how to detect heavy photon at a collider and
distinguish it from other DM candidates are simply discussed in the final
sector of the paper.

High Energy Physics - Phenomenology