Title: Revisiting Bounds on Primordial Black Hole as Dark Matter with X-ray Background

Abstract: Within the mass range of $10^{16}-5\times 10^{18}$ g, primordial black holes (PBHs) persist as plausible candidates for dark matter. Our study involves a reassessment of the constraints on PBHs through a comparative analysis of the cosmic X-ray background (CXB) and the emissions arising from their Hawking evaporation. We identify previously overlooked radiation processes across the relevant energy bands, potentially refining the bounds on PBHs. These processes encompass the direct emission from Hawking radiation, in-flight annihilation, the final state of radiation, and positronium annihilation. Thorough consideration is given to all these processes and their respective emission fractions, followed by a precise calculation of the $\mathcal{D}$ factor for observations directed towards the high-latitude Galactic contribution. Furthermore, we integrate the flux originating from extragalactic sources, both of which contribute to the measured isotropic flux. Through a comparative analysis of data derived from previous CXB observations utilizing an Active Galactic Nuclei (AGN) double power-law model, we establish the most stringent constraints for PBHs, thereby excluding the possibility of PBHs constituting the entire dark matter mass within the range of $2.5\times 10^{17}-3 \times 10^{17} $g.