Abstract

Rare K rightarrow pi nu bar{nu } decays, being dominated by short distance contributions within the standard model (SM), open a window for new physics (NP) searches at low energies. The K rightarrow pi nu bar{nu } branching ratios are expected to be measured with sim 10% accuracies by NA62/CERN and KOTO/JPARC. The theoretical uncertainties of branching ratios within the SM are well under control. In the B sector, it is tentative to explain the B-meson anomalies R_{D^{(*)}} and/or R_{K^{(*)}} by effects of physics beyond the SM. Although NP seems to be present in the third fermion generation it might also manifest in the flavor changing neutral current transition s rightarrow d . Together with the anticipated good experimental sensitivities and accurate theoretical predictions for Krightarrow pi nu bar{nu }, this motivates studies of correlated effects of NP in rare Krightarrow pi nu bar{nu } and B rightarrow K^{(*)} mu ^+ mu ^- decays. Here we consider the loop induced effects in K rightarrow pi nu bar{nu } in two leptoquark models designed to address lepton-flavor universality violation in the R_{K^{(*)}} anomalies.

Highlights

  • new physics (NP) seems to be present in the third fermion generation it might manifest in the flavor changing neutral current transition s → d

  • New effects in flavor changing neutral current (FCNC) b → s and/or charged current b → c semi-leptonic decays are likely to be accompanied by new effects in other quarkflavor transitions

  • In [34] there is no contribution at tree-level to s → dνν. This is not valid anymore after one-loop corrections are taken into account

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Summary

Introduction

New effects in flavor changing neutral current (FCNC) b → s and/or charged current b → c semi-leptonic decays are likely to be accompanied by new effects in other quarkflavor transitions. [21] explored the flavor structure of custodial Randall–Sundrum (RS) models in the light of observed deviations in the B decays and found that the K → π ννdecays might distinguish among different scenarios of lepton compositeness. Motivated by these efforts, we are interested here in FCNC s → dνν (and s → d + −) transitions. The branching ratio for K ± → π ±ννhas been measured with ∼ 100% uncertainty, while for the KL → π 0ννdecay rate only an upper bound two orders of magnitude above the SM expectation value is known at present This situation will improve in the coming years, since the experiments NA62 at CERN and KOTO at JPARC will achieve experimental accuracies of around ten-percent. In Appendix A we provide some numerical values and in Appendix B we discuss technical issues related to the loop-functions, together with a brief discussion of the process K ± → π ±μ+μ− in the light of the two LQ models

Framework
Scalar leptoquarks
Leptoquarks in rare K decays
Tree-level effects
Radiative Yukawas and boxes
Comparison of models
Conclusion
Box diagrams
Findings
Gauge invariance
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