# Search for the lepton-flavour violating decays $\mathcal{B}(B^+ \to K^+ {\mu}^{\pm} e^{\mp})$

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## Abstract

A search for the lepton-flavour violating decays $B^+ \to K^+ {\mu}^{\pm} e^{\mp}$ is performed using a sample of proton-proton collision data, collected with the LHCb experiment at centre-of-mass energies of $7$ and $8 {\rm TeV}$ and corresponding to an integrated luminosity of 3$\rm fb^{-1}$. No significant signal is observed, and upper limits on the branching fractions are set as $\mathcal{B}(B^+ \to K^+ {\mu}^- e^+) < 7.0 (9.5) \times 10^{-9}$ and $\mathcal{B}(B^+ \to K^+ {\mu}^+ e^-) < 6.4 (8.8) \times 10^{-9}$ at 90 (95) % confidence level. The results improve the current best limits on these decays by more than one order of magnitude.

## Figures and captions

 Efficiency of (left) $B ^+ \rightarrow K ^+ \mu ^- e ^+$ and (right) $B ^+ \rightarrow K ^+ \mu ^+ e ^-$ as function of the squared invariant masses $m^2_{K^+e^\pm}$ and $m^2_{K^+\mu^\mp}$. The variation of efficiency across the Dalitz plane is due to applied vetoes. The efficiencies are given in per mille. Fig1a.pdf [14 KiB] HiDef png [143 KiB] Thumbnail [131 KiB] Fig1b.pdf [14 KiB] HiDef png [140 KiB] Thumbnail [129 KiB] Invariant-mass distributions of the (left) $B ^+ \rightarrow K ^+ \mu ^- e ^+$ and (right) $B ^+ \rightarrow K ^+ \mu ^+ e ^-$ candidates obtained on the combined data sets recorded in 2011 and 2012 with background only fit functions (blue continuous line) and the signal model normalised to 10 candidates (red dashed line) superimposed. The signal window is indicated with grey dotted lines. Difference between the two distributions arises from the effect of the $m(K^+\ell^-)$ requirement. Fig2a.pdf [21 KiB] HiDef png [202 KiB] Thumbnail [165 KiB] Fig2b.pdf [22 KiB] HiDef png [231 KiB] Thumbnail [183 KiB] Upper limits on the branching fractions of (left) $B ^+ \rightarrow K ^+ \mu ^- e ^+$ and (right) $B ^+ \rightarrow K ^+ \mu ^+ e ^-$ decays obtained on the combined data sets recorded in 2011 and 2012. The red solid line (black solid line with data points) corresponds to the distribution of the expected (observed) upper limits, and the light blue (dark blue) band contains the $1\sigma$ ($2\sigma$) uncertainties. Fig3a.pdf [28 KiB] HiDef png [297 KiB] Thumbnail [200 KiB] Fig3b.pdf [27 KiB] HiDef png [298 KiB] Thumbnail [205 KiB] Invariant-mass distributions of the $B ^+ \rightarrow K ^+ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} ( \rightarrow \mu ^+ \mu ^- )$ normalisation channel for (left) 2011 data and (right) 2012 data. Fig4a.pdf [22 KiB] HiDef png [209 KiB] Thumbnail [178 KiB] Fig4b.pdf [23 KiB] HiDef png [219 KiB] Thumbnail [186 KiB] Animated gif made out of all figures. PAPER-2019-022.gif Thumbnail

## Tables and captions

 Normalisation factor $\alpha$ for $B ^+ \rightarrow K ^+ \mu ^- e ^+$ and $B ^+ \rightarrow K ^+ \mu ^+ e ^-$ final states. The ratio $\alpha/\mathcal{B}( B ^+ \rightarrow K ^+ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} ( \rightarrow \mu ^+ \mu ^- ) )$ is independent of external inputs. Table_1.pdf [43 KiB] HiDef png [32 KiB] Thumbnail [16 KiB] tex code Upper limit on the branching fraction of $B ^+ \rightarrow K ^+ \mu ^- e ^+$ and $B ^+ \rightarrow K ^+ \mu ^+ e ^-$ decays obtained on the combined data sets recorded in 2011 and 2012 for confidence levels of $90\%$ and $95\%$. Table_2.pdf [42 KiB] HiDef png [35 KiB] Thumbnail [17 KiB] tex code Summary of systematic uncertainties. Table_3.pdf [46 KiB] HiDef png [77 KiB] Thumbnail [37 KiB] tex code

Created on 12 October 2019.