Probing the CP-even Higgs Sector via $H_3\to H_2{H}_1$ in the Natural NMSSM

After the discovery of a Standard Model (SM) like Higgs boson, naturalness strongly favors the next to the Minimal Supersymmetric SM (NMSSM). In this letter, we point out that the most natural NMSSM predicts the following CP-even Higgs $H_i$ sector: (A) $H_2$ is the SM-like Higgs boson with mass pushed-upward by a lighter $H_1$ with mass overwhelmingly within $[m_{H_2}\mathrm{/}2,m_{H_2}]$; (B) $m_{H_3}\simeq 2\mu \mathrm{/}\sin 2\beta \gtrsim 300$ GeV; © $H_3$ has a significant coupling to top quarks and can decay to $H_1{H}_2$ with a large branching ratio. Using jet substructure we show that all the three Higgs bosons can be discovered via $gg\to H_3\to H_1{H}_2\to b\bar{b}\mathrm{\ell }\nu jj$ at the 14 TeV LHC. Especially, the LEP-LHC scenario with $H_1\simeq 98$ GeV has a very good discovery potential.