  Neutrino emission significantly affects the evolution of the accretion tori
formed in black hole-neutron star mergers. It removes energy from the disk,
alters its composition, and provides a potential power source for a gamma-ray
burst. To study these effects, simulations in general relativity with a hot
microphysical equation of state and neutrino feedback are needed. We present
the first such simulation, using a neutrino leakage scheme for cooling to
capture the most essential effects and considering a moderate mass (1.4
M_{\odot} neutron star, 5.6 M_{\odot} black hole), high spin (black hole
J/M^2=0.9) system with the K_0=220 MeV Lattimer-Swesty equation of state. We
find that about 0.08 M_{\odot} of nuclear matter is ejected from the system,
while another 0.3 M_{\odot} forms a hot, compact accretion disk. The primary
effects of the escaping neutrinos are (i) to make the disk much denser and more
compact, (ii) to cause the average electron fraction Y_e of the disk to rise to
about 0.2 and then gradually decrease again, and (iii) to gradually cool the
disk. The disk is initially hot (T~6 MeV) and luminous in neutrinos
(L_{\nu}~10^{54} erg s^{-1}), but the neutrino luminosity decreases by an order
of magnitude over 50 ms of post-merger evolution.
