Effective-field-theory arguments for pursuing lepton-flavor-violating K decays at LHCb

We provide general effective-theory arguments relating present-day discrepancies in semileptonic B-meson decays to signals in kaon physics, in particular lepton-flavor violating ones of the kind K→(π)e±μ?. We show that K-decay branching ratios of around 10-12-10-13 are possible, for effective-theory cutoffs around 5-15 TeV compatible with discrepancies in B→K(∗)μμ decays. We perform a feasibility study of the reach for such decays at LHCb, taking K+→π+μ±e? as a benchmark. In spite of the long lifetime of the K+ compared to the detector size, the huge statistics anticipated as well as the overall detector performance translate into encouraging results. These include the possibility to reach the 10-12 ballpark, and thereby significantly improve current limits. Our results advocate LHC's high-luminosity Upgrade phase, and support analogous sensitivity studies at other facilities. Given the performance uncertainties inherent in the Upgrade phase, our conclusions are based on a range of assumptions we deem realistic on the particle identification performance as well as on the kinematic reconstruction thresholds for the signal candidates.