Abstract
We analyse the prospects to detect at the LHC the neutral Higgs particles of the Minimal Supersymmetric Standard Model, when the masses of the two CP-even $h,H$ and of the CP-odd $A$ boson are close to one another, and the value of $\tb$ is large. In this "intense-coupling regime", the Higgs bosons have strongly enhanced couplings to isospin down-type fermions and large total decay widths, so that the $\gamma \gamma, WW^*$ and $ZZ^*$ decay modes of the three Higgs bosons are strongly suppressed. We advocate the use of the decays into muon pairs, $h,H,A \to \mu^+ \mu^-$, to resolve the three Higgs boson peaks: although the branching ratios are small, ${\cal O}(10^{4})$, the resolution on muons is good enough to allow for their detection, if the mass splitting is large enough. Using an event generator analysis and a fast detector simulation, we show that only the process $pp \to b\bar{b} \mu^+ \mu^-$, when at least one of the $b$-quarks is detected, is viable.