  We calculate the shifts in decay constants of the pseudoscalar $B$ and $D$
mesons in nuclear medium in the frame work of QCD sum rules. We write those
shifts in terms of the $B-N$ and $D-N$ scattering lengths and an extra
phenomenological parameter entered to calculations. Computing an appreciate
forward scattering correlation function, we derive the QCD sum rules for the
$B-N$ and $D-N$ scattering lengths and the extra phenomenological parameter in
terms of various operators in nuclear medium. We numerically find the values of
the shifts in the decay constants compared to their vacuum values. Using the
sum rules obtained, we also determine the shifts in the masses of these
particles due to nuclear matter and compare the results obtained with the
previous predictions in the literature.
