  We analyse the corrections to factorization for the $B-\bar B$ mixing
amplitude assuming that non-factorizable soft gluon exchanges can be described
by the local gluon condensate. Within this approximation the $<\alpha_s
GG>$-correction to the mixing amplitude can be expressed through the $B$-meson
transition form factors at zero momentum transfer. The correction is negative
independent of the particular values of the form factors.
  As a next step, we study these form factors making use of the relativistic
dispersion approach based on the constituent quark picture. We obtain spectral
representations for the form factors in terms of the $B$-meson soft wave
function and the propagator of the color-octet $b\bar q$ system. The $B$-meson
wave function has been determined previously from weak exclusive B decays, so
the main uncertainty in our estimates comes from the unknown details of the
propagator in the nonperturbative region. We obtain $\Delta
B_{B_d}(m_b)=-0.06\pm 0.035 $ and $\Delta B_{B_s}(m_b)=-0.05\pm 0.03 $.
