Roles of Higgs decay into two pseudoscalar bosons in the search of intermediate-mass Higgs Boson

The dominance of $h\to \eta \eta$ decay mode for the intermediate mass Higgs boson is highly motivated to solve the little hierarchy problem and to ease the tension with the precision data. However, the discovery modes for $m_h \alt 150$ GeV, $h \to \gamma\gamma$ and $W/Z h \to (\ell\nu/\ell \bar \ell) (b\bar b)$, will be substantially affected. We show that $h \to \eta \eta \to 4b$ is complementary and we can use this decay mode to detect the intermediate Higgs boson at the LHC, via $Wh$ and $Zh$ production. Requiring at least one charged lepton and 4 $B$-tags in the final state, we can identify a clean Higgs boson signal for $m_h \alt 150$ GeV with a high significance and with a full Higgs mass reconstruction. We use the next-to-minimal supersymmetric standard model and the simplest little Higgs model for illustration.