Probing the CP-even Higgs sector via H-3 -> H2H1 in the natural next-to-minimal supersymmetric standard modelg

fter the discovery of a standard model (SM)-like Higgs boson, naturalness strongly favors the next-to-minimal supersymmetric SM. In this letter, we point out that the natural next-to-minimal supersymmetric SM usually 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(H2)/2, m(H2)]; (B) m(H3) similar or equal to 2 mu/sin 2 beta greater than or similar to 300 GeV; (C) H-3 has a significant coupling to the top quark and can decay to H1H2 with a large branching ratio. Using a jet substructure we show that these three Higgs bosons can be discovered via gg -> H-3 -> H1H2 -> b (b) over barl nu jj at the 14 TeV LHC. In particular, the LEP-LHC scenario with H-1 similar or equal to 98 GeV has a very good discovery potential.