Production and decays of the light pseudoscalar boson $\eta$ at the LHC in the simplest little Higgs model

In many extensions of the standard model, the Higgs sector often contains an additional pseudoscalar boson. A good example is the SU(3) simplest little Higgs model, which accommodates a light pseudoscalar boson $\eta$ with quite different characteristics from those in other multi-Higgs-doublet models. We study various phenomenological signatures of the $\eta$ at the LHC. In particular, we calculate in details both production and decays in the Drell-Yan type channel $q\bar{q}\to Z\mathrm{/}{Z}^{\mathrm{\prime }}\to h\eta$, and in the associated production with a $t\bar{t}$ pair, $gg(q\bar{q})\to t\bar{t}\eta$. We emphasize the ${\tau }^{+}{\tau }^{-}$ decay mode of the $\eta$ boson when its mass is below the $b\bar{b}$ threshold. We show that $t\bar{t}\eta$ production is in fact large enough to give a sizable number of events while suppressing the backgrounds. We also comment on the direct gluon fusion process and the indirect decay from the heavy $T$ quark ($T\to t\eta$)