  Heavy neutral Higgs boson production and decay into neutralino and chargino
pairs is studied at the Large Hadron Collider in the context of the Minimal
Supersymmetric Standard Model. Higgs boson decays into the heavier neutralino
and chargino states, i.e., H^0 or A^0 to tilde{chi}_i^0 tilde{chi}_j^0 (i,j =
2,3,4) as well as H^0 or A^0 to tilde{chi}_1^{pm} tilde{chi}_2^{mp},
tilde{chi}_2^+ tilde{chi}_2^- (all leading to four-lepton plus missing
transverse energy final states), is found to improve the possibilities of
discovering such Higgs states beyond those previously identified by considering
H^0 or A^0 to tilde{chi}_2^0 tilde{chi}_2^0 decays only. In particular, H^0,A^0
bosons with quite heavy masses, approaching ~800 GeV in the so-called
`decoupling region' where no clear SM signatures for the heavier MSSM Higgs
bosons are known to exist, can now be discerned, for suitable but not
particularly restrictive configurations of the low energy supersymmetric
parameters. The high M_A discovery reach for the H^0 and A^0 may thus be
greatly extended. Full event-generator level simulations, including realistic
detector effects and analyses of all significant backgrounds, are performed to
delineate the potential H^0,A^0 discovery regions. The wedgebox plot technique
is also utilized to further analyze the 4l plus missing transverse energy
signal and background events. This study marks the first thorough and
reasonably complete analysis of this important class of MSSM Higgs boson
signature modes. In fact, this is the first time discovery regions including
all possible neutralino and chargino decay modes of the Higgs bosons have ever
been mapped out.
