  In the Next-to-Minimal Supersymmetric Standard Model (NMSSM), it is possible
to have strong mass degeneracies between the new singlet-like scalar and the
heavy doublet-like scalar, as well as between the singlet-like and doublet-like
pseudoscalar Higgs states. When the difference in the masses of such states is
comparable with the sum of their widths, the quantum mechanical interference
between their propagators can become significant. We study these effects by
taking into account the full Higgs boson propagator matrix in the calculation
of the production process of $\tau^+\tau^-$ pairs in gluon fusion at the Large
Hadron Collider (LHC). We find that, while these interference effects are
sizeable, they are not resolvable in terms of the distributions of differential
cross sections, owing to the poor detector resolution of the $\tau^+\tau^-$
invariant mass. They are, however, identifiable via the inclusive cross
sections, which are subject to significant variations with respect to the
standard approaches, wherein the propagating Higgs bosons are treated
independently from one another. We quantify these effects for several
representative benchmark points, extracted from a large set of points, obtained
by numerical scanning of the NMSSM parameter space, that satisfy the most
important experimental constraints currently available.
