Effects from the charm scale in K+ -> pi+ nu nubar

Abstract

We consider contributions to the rare decay K+ -> pi+ nu nubar which become nonlocal at the charm scale. Compared to the leading term, such amplitudes are suppressed by two powers of mK/mc and could potentially give corrections at the level of 15%. We compute the leading coefficients of the subleading dimension eight operators in the effective theory below the charm mass. The matrix elements of these operators cannot all be calculated from first principles and some must be modeled. We find that these contributions are likely to be small, but the estimate is sufficiently uncertain that the result may be as large as the existing theoretical uncertainty from other sources.