Primordial black holes and primordial nucleosynthesis: Effects of hadron injection from low mass holes

We investigate the influence of hadron injection from evaporating primordial black holes (PBHs) in the early stage of the primordial nucleosynthesis era $\left(t\simeq {10}^{-3}-{10}^4\hspace{0.5em}\sec \right).\mathrm{}$ The emitted quark-antiquark pairs or gluons immediately fragment into a lot of hadrons and scatter off the thermal plasma which is constituted by photons, electrons, and nucleons. For the relatively low mass holes we point out that the dominant effect is the interconversion between an ambient proton and neutron through the strong interaction induced by the emitted hadrons. Even after the freeze-out time of the weak interactions between the neutron and proton, more neutrons are produced and the synthesized light element abundances could be drastically changed. Comparing the theoretical predictions with the observational data, we constrain the PBH’s density and their lifetime. We obtain the upper bound for PBH’s initial mass fraction, $\beta \lesssim {10}^{-20}$ for ${10}^8\hspace{0.5em}\mathrm{g}\lesssim M\lesssim {10}^{10}$ g, and $\beta \lesssim {10}^{-22}$ for ${10}^{10}\hspace{0.5em}\mathrm{g}\lesssim M\lesssim 3\times {10}^{10}$ g.