Searching for the Signal of a Primordial Black Hole from CMB Lensing and γ-Ray Emissions

In this letter, we search for the signal of primordial black holes (PBHs) by correlating the γ-ray emissions in the MeV energy band produced by the Hawking evaporation and the lensing effect of the cosmic microwave background (CMB). We use the conservative case of the astrophysical model as much as possible in the calculations, since the potential astrophysical origins dominate the observed emission in the MeV energy band. By carefully discussing the appropriate energy bands corresponding to different PBH masses, it is worth expecting a tight constraint on the fraction of the Schwarzschild PBHs in the mass range of 1016-5 × 1017 g by simulations of the sensitivity of the future CMB-S4 project and the γ-ray telescope e-ASTROGAM. Furthermore, we also consider the PBH model with spins and find that the constraining ability of the PBH fraction from the correlation between CMB lensing and γ-ray emissions can be improved by another order of magnitude, which could importantly fill the gaps with PBH fraction limits in the mass range of 5 × 1017-2 × 1018 g.