Molecular Nature of X(3872) in B 0 → K 0 X(3872) and B + K + X(3872) Decays

Abstract

We investigate the decays of B 0 → K 0 X(3872) and B + → K + X(3872) based on the picture where the X(3872) resonance is strongly coupled to the D D ¯ * + c . c . channel. In addition to the decay mechanism where the X(3872) resonance is formed from the c c ¯ pair hadronization with the short-distance interaction, we have also considered the D D ¯ * rescattering diagrams in the long-distance scale, where D and D ¯ * are formed from c and c ¯ separately. Because of the difference of the mass thresholds of charged and neutral D D ¯ * channels, and the rather narrow width of the X(3872) resonance, at the X(3872) mass, the loop functions of D 0 D ¯ * 0 and D + D ¯ * − are much different. Taking this difference into account, the ratio of ℬ [ B 0 → K 0 X ( 3872 ) ] / ℬ [ B + → K + X ( 3872 ) ] ≃ 0.5 can be naturally obtained. Based on this result, we also evaluate the decay widths of B s 0 → η ( η ′ ) X ( 3872 ) . It is expected that future experimental measurements of these decays can be used to elucidate the nature of the X(3872) resonance.