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.
Highlights
Data on b → sll and b → clν transitions display persistent deviations with respect to Standard-Model (SM) expectations [1,2,3,4,5,6,7], suggesting a sizable violation of lepton universality (LUV)
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
Without further assumptions observable LUV is accompanied by leptonflavor violation (LFV), whose expected size is related to the measured amount of LUV [12]
Summary
Data on b → sll and b → clν transitions display persistent deviations with respect to Standard-Model (SM) expectations [1,2,3,4,5,6,7], suggesting a sizable violation of lepton universality (LUV). Our aim is to relate predictions for these modes, which are mediated by the s → d current, to the present theory understanding of B-decay discrepancies, that occur in b → s transitions. In order to relate these two currents as model independently as possible, we focus on an effective-theory picture, forgoing the introduction of new degrees of freedom. To first approximation, such an approach does not require any discussion of b → c discrepancies instead. Let us first consider the thirdgeneration effective interaction, HNP 1⁄4 Gðb 0Lγαb0LÞðτ0Lγατ0LÞ; ð1Þ where G ≪ GF, GF is the Fermi constant, the subscript L denotes left-handed fields, and primes identify the gauge
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