  We compute the $K$ and $L_{3}$ -edge resonant inelastic x-ray scattering
(RIXS) spectrum of the columnar and the staggered quantum dimer states
accessible to the square lattice Heisenberg magnet. Utilizing a bond operator
representation mean field theory we investigate the RIXS features of the one-
and two-triplon excitation spectrum supported by the quantum dimer model in the
background of condensed singlet excitation. We find that the two-triplon
excitation boundary lies within a 124 (78) meV to (414) 345 meV energy range
for the columnar (staggered) phase. We estimated the two-triplon gap to be 124
(78) meV for the columnar (staggered) dimer phase. The highest intensity of the
$K$ -edge RIXS spectrum is centralized approximately around the $(\pi/2,\pi/2)$
point for both the columnar and the staggered phases. At the $L_{3}$ -edge we
study the one- and two- triplon signal considering experimental scattering
geometry, polarization restriction, and experimental resolution effects. Our
calculations find an additional contribution to the two-triplon RIXS signal,
not previously reported in the literature, that originates from the local
hard-core dimer constraint. This leads to a finite non-zero signal at the (0,0)
momentum transfer which can offer an explanation for the existing ladder RIXS
experiments and also predicts a non-zero signal for the two-dimensional quantum
dimer system. We find that the $L_3$ edge RIXS response of the one- and
two-triplon signal could exist in antiphase rung modulation for zero and $\pi$
as found in inelastic neutron scattering. We also consider static crystal
twinning at the $L_3$ -edge RIXS signal to mimic realistic crystal effects.
Since the disordered phase has the potential to harbor a variety of quantum
paramagnetic states, our RIXS calculations provide useful signatures to
identify the true nature of the ordering pattern.
