Deploying \textit{multiple sharp 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, 1β€csββ€1.17, the direct consequence is the
generation of PBH masses spanning MPBHββΌO(10β31Mβββ104Mββ), thus evading well known \textit{No-go 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.).Comment: 14 pages, 3 figures, Comments are welcom