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We compute the $K$ and $L_{3}$ -edge resonant inelastic x-ray scattering(RIXS) spectrum of the columnar and the staggered quantum dimer statesaccessible to the square lattice Heisenberg magnet. Utilizing a bond operatorrepresentation mean field theory we investigate the RIXS features of the one-and two-triplon excitation spectrum supported by the quantum dimer model in thebackground of condensed singlet excitation. We find that the two-triplonexcitation boundary lies within a 124 (78) meV to (414) 345 meV energy rangefor 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 westudy the one- and two- triplon signal considering experimental scatteringgeometry, polarization restriction, and experimental resolution effects. Ourcalculations find an additional contribution to the two-triplon RIXS signal,not previously reported in the literature, that originates from the localhard-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 RIXSexperiments and also predicts a non-zero signal for the two-dimensional quantumdimer system. We find that the $L_3$ edge RIXS response of the one- andtwo-triplon signal could exist in antiphase rung modulation for zero and $\pi$as found in inelastic neutron scattering. We also consider static crystaltwinning at the $L_3$ -edge RIXS signal to mimic realistic crystal effects.Since the disordered phase has the potential to harbor a variety of quantumparamagnetic states, our RIXS calculations provide useful signatures toidentify the true nature of the ordering pattern.

$K$ -edge and $L_{3}$ -edge RIXS study of columnar and staggered quantum dimer phases of the square lattice Heisenberg model