Quark off-shell contributions to KL → γγ in a bound-state approach

We present a new piece of evidence in favour of the importance of the quark off-shellness in the kaon. The matrix elements of the flavour-changing operators for KL → γγ comply with the general behaviour of the matrix elements expected in the pairing bound-state model used here. The present calculation in essence agrees with previous chiral-quark results. The off-shell contribution turns out to be dominant (the model on-shell amplitude being at the 10% level). Compared with the chiral perturbation-theory approach, our off-shell contribution is an entirely new O(p4) direct-decay piece, whereas the non-diagonal magnetic-moment term belongs to the order O(p6).