The strange side of LHCb

Abstract

We provide general effective-theory arguments relating present-day discrepancies in semi-leptonic $B$-meson decays to signals in kaon physics, in particular lepton-flavour violating ones of the kind $K\to (\pi )e^{\pm }{\mu }^{\mp }$. 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 $B\to K^{(\ast )}\mu \mu$ decays. We perform a feasibility study of the reach for such decays at LHCb, taking $K^{+}\to {\pi }^{+}{\mu }^{\pm }{e}^{\mp }$ 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.

Comments: 7 pages, 3 figures, 2 tables. v2: text made shorter and crispier. No change in conclusions. Matches published (for some time already) version