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.
