Evading no-go for PBH formation and production of SIGWs using Multiple Sharp Transitions in EFT of single field inflation

Deploying $\mathit{\text{multiple}}\mathit{\text{sharp}}\mathit{\text{transitions}}$ (MSTs) under a unified framework, we investigate the formation of Primordial Black Holes (PBHs) and the production of Scalar Induced Gravitational Waves (SIGWs) by incorporating one-loop corrected renormalized-resummed scalar power spectrum. With effective sound speed parameter, $1\le c_s\le 1.17$, the direct consequence is the generation of PBH masses spanning $M_{\mathrm{P}\mathrm{B}\mathrm{H}}\sim \mathcal{O}({10}^{-31}{M}_{\odot }-{10}^4{M}_{\odot })$, thus evading well known $\mathit{\text{No-go}}\mathit{\text{theorem}}$ on PBH mass. Our results align coherently with the extensive NANOGrav 15-year data and the sensitivities outlined by other terrestrial and space-based experiments (e.g.: LISA, HLVK, BBO, HLV(O3), etc.).