Little Higgs model with new Z-parity and Dark matter

It has been known that Little Higgs models with T-parity, which can give a dark matter candidate, suffer from the anomalies of given models through the Wess-Zumino-Witten term, which in turn can violate the T-parity. Here we thus introduce a new kind of discrete symmetry called Z-parity, which is a residual gauge symmetry of an additional U(1) symmetry of the extended gauge group of the Little Higgs models. Because Z-parity comes from the gauge symmetry, this discrete symmetry not only remains unbroken under the anomalies but also can give the lightest Z-parity particle, which is stable and becomes a viable dark matter candidate. We also show that there is an allowed parameter space in the global symmetry breaking scale f versus the mass of the dark matter, which satisfies the current relic density of the cold dark matter.