Weak Annihilation Topologies and Final State Interactions in D -> PP Decays

Abstract

We study two-body D -> PP decays, assuming that each decay process go through the bare amplitude followed by elastic SU(3) rescattering, where the bare amplitude consists of (i) the color-allowed and color-suppressed factorization amplitudes and (ii) the short-distance weak annihilation amplitudes. We have performed the χ^2 fit on 14 branching ratios of D -> PP decays in the formalism of the above mentioned model. The final state interactions can be well accounted for by the short-distance annihilation topologies and SU(3) rescatterings. The two SU(3) rescattering phase differences are δ\equiv δ_{27}-δ_{8} \simeq -46^\circ and σ\equiv δ_{27}-δ_{1} \simeq -21^\circ, where δ_{27}, δ_{8} and δ_{1}are the rescattering phases of final states corresponding to the representations 27, 8 and 1, respectively. We find that the D^0 -> K^0 \bar{K}^0 decay occurs mainly due to the nonzero short-distance weak annihilation effects, originating from SU(3) symmetry-breaking corrections to the distribution amplitudes of the final-state kaons, but receives tiny effects from other modes via SU(3) rescattering. Our results are in remarkable accordance with the current data.