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The aim of this study is to investigate the quadratic divergences usingdimensional regularization within the context of the standard model extended bytwo real scalar singlets (TRSM). This extension provides three neutral scalarfields that mix, after developing its {\it vev}'s, leading to three CP-evenHiggs bosons, namely: $h_1$, $h_2$ and $h_3$, which would offer a widephenomenology at the Large Hadron Collider (LHC) as reported recently.Furthermore, to fulfill the Veltman conditions for those three fields, we dwellon the one-loop level ($d_L=2$) of dimensional regularization calculations,assuming $R_{\xi}$ Feynman-'t Hooft gauge-invariant generalization. We showthat the divergence cancelation could take place in the framework of the TRSM,and thereby predicts a stringent constraint on the space parameters as well asthe new physics (NP) scale, and yet remain consistent with current experimentalmeasurements at 13 TeV.

Naturalness Implications within the Two-Real-Scalar-Singlet beyond the SM