Revisiting the constraints on primordial black hole abundance with the isotropic gamma ray background

We revisit the constraints on primordial black holes (PBHs) in the mass range $10^{13}-10^{18}$ g by comparing the 100\,keV-5\,GeV gamma-ray background with isotropic flux from PBH Hawking radiation (HR). We investigate three effects that may update the constraints on the PBH abundance; i) reliably calculating the secondary spectra of HR for energy below 5\,GeV, ii) the contributions to the measured isotropic flux from the Galactic PBH HR and that from annihilation radiation due to evaporated positrons, iii) inclusion of astrophysical background from gamma-ray sources. The conservative constraint is significantly improved by more than an order of magnitude at $2\times10^{16}$g$\lesssim M\lesssim 10^{17}$g over the past relevant work, where the effect ii is dominant. After further accounting for the astrophysical background, more than a tenfold improvement extends to a much wider mass range $10^{15}$g$\lesssim M\lesssim 2\times 10^{17}$g.