Non-factorizable effects in the $B-\bar B$ mixing

Abstract

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 $.