In the littlest Higgs model with T-parity (LHT), the mirror quarks have flavor structures and will contribute to the top quark flavor changing neutral current. In this work, we perform an extensive investigation of the top quark rare three-body decays t → cV V (V = γ, Z, g) and t → cff (f = b, τ, µ, e) at one-loop level. Our results show that the branching ratios of t → cgg and t → cbb could reach O(10 −3 ) in the favorite parameter space of the littlest Higgs model with T-parity, which implies that these decays may be detectable at the LHC or ILC, while for the other decays, their rates are too small to be observable at the present or future colliders. PACS numbers: 14.65.Ha,12.60.-i, 12.15.Mm I.
II.A BRIEF REVIEW OF THE LHT One of the major motivations for the little Higgs model [29,30] is to resolve the little hierarchy problem [31], in which the quadratic divergence of the Higgs mass term at one-loop level was canceled by the new diagrams with additional gauge bosons and a heavy top-quark partner. It was soon recognized that the scale of the new particles should be in the multi-TeV range in order to satisfy the constraints from electroweak precision measurements, which in turn reintroduces the little hierarchy problem [32]. This problem has been eased in the LHT model where a new Z 2 discrete symmetry called "T-parity" is introduced, and in this way, all dangerous tree level contribution to the precision measurements are forbidden [26].Just like the little Higgs model, in the LHT model the assumed global symmetry SU (5) is spontaneously broken down to SO(5) at a scale f ∼ O(T eV ), and the embedded [SU (2) ⊗ U (1)] 2 gauge symmetry is simultaneously broken at f to the diagonal subgroup SU (2) L ⊗ U (1) Y , which is identified with the SM gauge group.