  The ampitude of the $B\to\rho\gamma$ decay induced by the flavour-changing
neutral currents contains the penguin contribution and the weak-annihilation
contribution generated by the 4-quark operators in the effective Hamiltonian.
The penguin contribution is known quite well. We analyse the weak-annihilation
which is suppressed by the heavy-quark mass compared to the penguin
contribution.
  In the factorization approximation, the weak annihilation amplitude is
represented in terms of the leptonic decay constants and the meson-photon
matrix elements of the weak currents. The latter contain the $B\gamma$,
$\rho\gamma$ transition form factors and contact terms determined by the
equations of motion. We calculate the $B\gamma$ and $\rho\gamma$ form factors
within the relativistic dispersion approach and obtain numerical estimates for
the weak annihilation amplitude.
