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

Abstract

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 K L → γγ comply with the general behaviour of the matrix elements expected in the pairing boundstate 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(p 4 ) directdecay piece, whereas the non-diagonal magnetic-moment term belongs to the order O(p 6 ).

New Dipole Penguin Contribution to K --> pi pi decays

“…Despite being a model approach, such a treatment has some unique features: Besides weakening the destructive interference between the matrix elements of Q 6 and Q 8 operators (which we explicate in the next section), it enables the evaluation of the matrix elements for all the relevant operators within a single framework. Let us stress that in the chiral quark model we could evaluate the mentioned off-shell effects in K-meson decays [1,2,15] and to account for the off-shell, off-diagonal self energy contribution to the CP-violating ratio ε ′ /ε [16]. We believe that the off-shell chromomagnetic effect, calculated in this Letter, presents an interesting new piece in illuminating the K → ππ puzzle.…”