An exploratory lattice study of DI=3/2 K ->pi pi decays at next-to-leading order in the chiral expansion

We present the first direct evaluation of ∆ I = 3 / 2 K → ππ matrix elements with the aim of determining all the low-energy constants results for the quenched matrix elements of the electroweak penguin operators ( I =2 h ππ |O 8 | K 0 i = (0 . 68 ± 0 . 09) GeV 3 and I =2 h ππ |O 7 | K 0 i = (0 . 12 ± 0 . 02) GeV in the NDR-MS scheme at the scale 2 GeV), but not for the matrix elements of O 4 (for which there are too many Low-Energy Constants at NLO for a reliable extrapolation). For all three operators we find that the effect of including the NLO corrections is significant (typically about 30%). We present a detailed discussion of the status of the prospects for the reduction of the systematic uncertainties.