  We investigate the spectral shape of a high-energy diffuse photon emitted by
evaporating primordial black holes (PBHs) in the Randall-Sundrum type II (RS2)
braneworld. In their braneworld scenario, the nature of small PBHs is
drastically modified from the ordinary four-dimensional case for the following
two reasons. (i) dropping Hawking temperature, which equivalently lengthens the
lifetime of the individual PBH due to the change of space-time topology and
(ii) the effective increase of the total amount of PBHs caused by accretion
during the earliest part of the radiation-dominated epoch, the brane
high-energy phase. From studies of the expected spectral shape and its
dependence on braneworld parameters, we obtain two qualitatively distinctive
possibilities of constraints on the braneworld PBHs from the observations of
diffuse high-energy photon background. If the efficiency of accretion in the
high-energy phase exceeds a critical value, the existence of the extra
dimension gives a more stringent upper bound on the abundance of PBHs than the
4D case and a small length scale for the extra dimension is favored. On the
contrary, in the case below the critical accretion efficiency, we find that the
constraint on the PBH abundance can be relaxed by a few orders of magnitude in
exchange for the existence of the large extra dimension; its size may be even
bounded in the region above 10^{19} times 4D Planck length scale provided the
rest mass energy density of the PBHs relative to energy density of radiation is
actually larger than 10^{-27} (4D upper bound) at their formation time. The
above analytical studies are also confirmed numerically, and an allowed region
for braneworld parameters and PBH abundance is clearly obtained.
