Non-factorizable contributions in hadronic weak decays of charm mesons

Abstract

Two body decays of charm mesons are studied by describing their amplitude in terms of a sum of factorizable and non-factorizable ones. The former is estimated by using a naive factorization while the latter is calculated by using a hard pseudo-scalar-meson approximation. The hard pseudo-scalar-meson amplitude is given by a sum of the so-called equal-time commutator term and surface term which contains all possible pole contributions of various mesons, not only the ordinary $\{q\bar q\}$ but also four-quark $\{qq\bar q\bar q\}$, hybrid $\{q\bar qg\}$ and glue-balls. Naively factorized amplitudes for the spectator decays which lead to too big rates can interfere destructively with exotic meson pole amplitudes and the total amplitudes can reproduce their observed rates. The non-factorizable contributions can supply sufficiently large contributions to the color suppressed decays which are strongly suppressed in the naive factorization. A possible solution to the long standing puzzle that the ratio of decay rates for $D^0\to K^+K^-$ to $D^0\to π^+π^-$ is around 2.5 is given by different contributions of exotic meson poles.