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Measurement of the phase difference between short- and long-distance amplitudes in the $B^{+}\to K^{+}\mu^{+}\mu^{-}$ decay

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Abstract

A measurement of the phase difference between the short- and long-distance contributions to the $B^{+}\to K^{+}\mu^{+}\mu^{-}$ decay is performed by analysing the dimuon mass distribution. The analysis is based on $pp$ collision data corresponding to an integrated luminosity of 3 $\rm fb^{-1}$ collected by the LHCb experiment in 2011 and 2012. The long-distance contribution to the $B^{+}\to K^{+}\mu^{+}\mu^{-}$ decay is modelled as a sum of relativistic Breit--Wigner amplitudes representing different vector meson resonances decaying to muon pairs, each with their own magnitude and phase. The measured phases of the $J/\psi$ and $\psi(2S)$ resonances are such that the interference with the short-distance component in dimuon mass regions far from their pole masses is small. In addition, constraints are placed on the Wilson coefficients, $\mathcal{C}_{9}$ and $\mathcal{C}_{10}$, and the branching fraction of the short-distance component is measured.

Figures and captions

Reconstructed $ K ^+ \mu ^+\mu ^- $ mass of the selected $ B ^+ \rightarrow K ^+ \mu ^+\mu ^- $ candidates. The fit to the data is described in the text.

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Efficiency to reconstruct, trigger and select simulated $ B ^+ \rightarrow K ^+ \mu ^+ \mu ^- $ decays as a function of the true dimuon mass. The efficiency is normalised to the efficiency at the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ meson mass. The band indicates the efficiency parameterisation used in this analysis and its statistical uncertainty.

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Fits to the dimuon mass distribution for the four different phase combinations that describe the data equally well. The plots show cases where the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and $\psi {(2S)}$ phases are both negative (top left); the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ phase is positive and the $\psi {(2S)}$ phase is negative (top right); the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ phase is negative and the $\psi {(2S)}$ phase is positive (bottom left); and both phases are positive (bottom right). The component labelled interference refers to the interference between the short- and long-distance contributions to the decay. The $\chi^2$ value of the four solutions is almost identical, with a value of 110 for 78 degrees of freedom.

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Two-dimensional likelihood profile for the Wilson coefficients $\mathcal{C}_{9}$ and $\mathcal{C}_{10}$. The SM point is indicated by the blue marker. The intervals correspond to $\chi^2$ probabilities with two degrees of freedom.

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Animated gif made out of all figures.

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Tables and captions

Resolution parameters of the different convolution regions in units of $ {\mathrm{ Me V /}c^2}$ . The $\alpha_{\rm l}$ and $\alpha_{\rm u}$ parameters are shared between the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and $\psi {(2S)}$ regions. The parameters without uncertainties are fixed from fits to the simulated events.

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Parameters describing the efficiency to trigger, reconstruct and select simulated $ B ^+ \rightarrow K ^+ \mu ^+\mu ^- $ decays as a function of $m_{\mu\mu}$.

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Branching fractions and phases for each resonance in the fit for the four solutions of the $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ and $\psi {(2S)}$ phases. Both statistical and systematic contributions are included in the uncertainties. There is a common systematic uncertainty of 4.5%, dominated by the uncertainty on the $ B ^+ \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ branching fraction, which provides the normalisation for all measurements.

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Coefficients of the form factor $f_{+}( q^2 )$ as introduced in Eq. 8 with both prior (from Ref. [42]) and posterior values shown.

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Summary of systematic uncertainties. The branching fraction refers to the short-distance SM contribution. A dash indicates that the uncertainty is negligible.

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Supplementary Material [file]

This ZIP file contains supplementary material for the publication LHCb-PAPER-2016-045. The files are: Supplementary.pdf: An overview of the extra figure *.pdf, *.png, *.eps, *.C: The figures in various formats. The *.C files contain the data on the figures.

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