Abstract
The weak form factor associated with the pure annihilation decay D 0 → K 0ϕ is evaluated assuming factorization of the hadronic matrix element and using single-pole approximation and experimental data for ϕ→ KK . Chiral SU(3)×SU(3) current algebra and PCAC extrapolated to large q 2 = m D 2 imply a very small branching ratio B( D 0 → K 0ϕ) = O(10 −3%) , far below the experimental value O(1%). The recently suggested large- N approximation enhances this estimate considerably, but in order to fully reproduce the data either non-leading in 1 N terms have to be included (breakdown of factorization) or PCAC has to be strongly violated at such large value of q 2. Indeed moderate violations of PCAC give B( D 0 → K 0ϕ) = O(10−3%) in the large- N limit. In the presence of strong violations of PCAC at q 2 = m F 2 the branching ratio for F + → ϱπ +, another pure annihilation channel, could be as large as 10%.
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