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More about the $B$ and $D$ mesons in nuclear matter

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.