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Search for lepton-universality violation in $B^+\to K^+\ell^+\ell^-$ decays

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Abstract

A measurement of the ratio of branching fractions of the decays $B^+\to K^+\mu^+\mu^-$ and $B^+\to K^+e^+e^-$ is presented. The proton-proton collision data used correspond to an integrated luminosity of $5.0 $fb$^{-1}$ recorded with the LHCb experiment at centre-of-mass energies of $7$, $8$ and $13 $TeV. For the dilepton mass-squared range $1.1 < q^2 < 6.0 $GeV$^2 /c^4$ the ratio of branching fractions is measured to be $R_K = {0.846 ^{+ 0.060}_{- 0.054} ^{+ 0.016}_{- 0.014}}$, where the first uncertainty is statistical and the second systematic. This is the most precise measurement of $R_K$ to date and is compatible with the Standard Model at the level of 2.5 standard deviations.

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(Top) expected distributions of the opening angle between the two leptons, in the laboratory frame, for the four modes in the double ratio used to determine $ R_{ K }$ . (Bottom) the single ratio $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ relative to its average value $\left< r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } \right>$ as a function of the opening angle.

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Fits to the $ m_{( { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} )}{( K ^+ \ell^+ \ell^- )}$ invariant mass distribution for (left) electron and (right) muon candidates for (top) nonresonant and (bottom) resonant decays. For the electron (muon) nonresonant plots, the red-dotted line shows the distribution that would be expected from the observed number of $ B ^+ \rightarrow K ^+ \mu ^+\mu ^- $ ( $ B ^+ \rightarrow K ^+ e ^+ e ^- $ ) decays and $ R_{ K } =1$.

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Two-dimensional distributions of $[ m({ K ^+ \ell^+ \ell^- }) , q^2 ]$ for (left) muon and (right) electron candidates after the application of the pre-selection and trigger requirements but not the multivariate selection.

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Distributions of various reconstructed properties for simulated decays. The first row shows the angle between the two leptons, or one lepton and the kaon. The second row shows the rapidity distributions, and the third row the transverse momentum distributions of all the final-state particles. The bottom left plot shows the distribution for the quality of the $ B ^+ $ vertex fit and the bottom right plot shows the $\chi^2_{\text{IP}} ( B ^+ )$ variable, which quantifies the significance of the $ B ^+ $ impact parameter.

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Simulated $K^+e^-$ mass distributions for signal and various cascade background samples. The distributions are all normalised to unity. (Left) the bremsstrahlung correction to the momentum of the electron is taken into account, resulting in a tail to the right. (Right) the mass is computed only from the track information ($m^{\mathrm{track}}$). The notation $\pi_{[\rightarrow e]}$ ($e_{[\rightarrow \pi]}$) is used to denote an electron (pion) that is misidentified as a pion (electron).

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Fit to the $ m({ K ^+ \ell^+ \ell^- })$ invariant-mass distribution of nonresonant candidates in the (left) 7 and 8 $\text{ Te V}$ and (right) 13 $\text{ Te V}$ data samples. The top row shows the fit to the muon modes and the subsequent rows the fits to the electron modes triggered by (second row) one of the electrons, (third row) the kaon and (last row) by other particles in the event.

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Fit to the $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }{( K ^+ \ell^+ \ell^- )}$ invariant-mass distribution of resonant candidates in the (left) 7 and 8 $\text{ Te V}$ and (right) 13 $\text{ Te V}$ data samples. The top row shows the fit to the muon modes and the subsequent rows the fits to the electron modes triggered by (second row) one of the electrons, (third row) the kaon and (last row) by other particles in the event. Some large pulls are observed but have a negligible impact on the yields extracted.

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(Top) distributions of the spectra of (left) the $ B ^+ $ transverse momentum and (right) the minimum $ p_{\mathrm{T}}$ of the leptons. (Bottom) the single ratio $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ relative to its average value $\left< r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} } \right>$ as a function of these variables.

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(Left) the value of $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ , relative to the average value of $ r_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }$ , measured in two-dimensional bins of the maximum lepton momentum ($p(l)$) and the opening angle between the two leptons ($\alpha(l^+,l^-)$). (Right) the bin definition in this two-dimensional space together with the distribution for $ B ^+ \rightarrow K ^+ e ^+ e ^- $ ( $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow e ^+ e ^- ) K ^+ $ ) decays depicted as red (blue) contours.

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Likelihood function from the fit to the data profiled as a function of $ R_{ K }$ (solid line). The blue dashed line depicts the expected shape of the likelihood profile if the uncertainties were Gaussian.

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Tables and captions

Resonant and nonresonant mode $ q^2 $ and $ m({ K ^+ \ell^+ \ell^- })$ ranges. The variables $ m({ K ^+ \ell^+ \ell^- })$ and $ m_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} }{( K ^+ \ell^+ \ell^- )}$ are used for nonresonant and resonant decays, respectively.

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Total yields of the decay modes $ B ^+ \rightarrow K ^+ e ^+ e ^- $ , $ B ^+ \rightarrow K ^+ \mu ^+\mu ^- $ , $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow e ^+ e ^- ) K ^+ $ and $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow \mu ^+\mu ^- ) K ^+ $ obtained from the fits to the data.

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Supplementary Material [file]

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Created on 17 August 2019.Citation count from INSPIRE on 20 August 2019.