  Low-luminosity gamma-ray bursts (GRBs) with luminosity . 10^49erg/s probably
consititute a distinct population from the classic high-luminosity GRBs. They
are the most luminous objects detected so far within ~ 100 Mpc, the horizon
distance of ultra-high energy cosmic rays (UHECRs), so they are considered to
be candidate sources of UHECRs. It was recently argued that the energy
production rate in UHECRs is much larger than that in gamma-ray photons of long
GRBs measured by the Fermi satellite, which, if true, would challenge the view
that GRBs can be the sources of UHECRs. We here suggest that many of the low
luminosity GRBs, due to their low luminosity, can not trigger the current GRB
detectors and hence their contribution to the local gamma-ray energy production
rate is missing. We find that the real local energy production rate by
low-luminosity GRBs, taking into account the missing part, which constitutes a
dominant fraction of the total amount, could be sufficient to account for the
flux of UHECRs. Due to the low-luminosity, only intermediate-mass or heavy
nuclei can be accelerated to ~ 10^20 eV. We discuss the acceleration and
survival of these UHE nuclei in low-luminosity GRBs, especially in those
missing low-luminosity GRBs. At last, the accompanying diffuse neutrino flux
from the whole low-luminosity GRB population is calculated.
