Pseudoscalar boson and standard model-like Higgs boson productions at the LHC in the simplest little Higgs model

In the framework of the simplest little Higgs model, we perform a comprehensive study for the pair productions of the pseudoscalar boson eta and standard model-like Higgs boson h at LHC, namely gg(b (b) over bar) -> eta eta, gg(q (q) over bar) -> eta h, and gg(b (b) over bar) -> hh. These production processes provide a way to probe the couplings between Higgs bosons. We find that the cross section of gg -> eta eta always dominates over that of b (b) over bar -> eta eta. When the Higgs boson h which mediates these two processes is on-shell, their cross sections can reach several thousand fb and several hundred fb, respectively. When the intermediate state h is off-shell, those two cross sections are reduced by 2 orders of magnitude, respectively. The cross sections of gg -> eta h and q (q) over bar -> eta h are about in the same order of magnitude, which can reach O(10(2) fb) for a light eta boson. Besides, compared with the standard model prediction, the cross section of a pair of standard model-like Higgs bosons production at LHC can be enhanced sizably. Finally, we briefly discuss the observable signatures of eta eta, eta h, and hh at the LHC.