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

[to restricted-access page]

## 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. datama[..].pdf [69 KiB] HiDef png [264 KiB] Thumbnail [217 KiB] *.C file 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. eff_fitted.pdf [70 KiB] HiDef png [196 KiB] Thumbnail [148 KiB] *.C file 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. finalp[..].pdf [28 KiB] HiDef png [464 KiB] Thumbnail [331 KiB] *.C file finalp[..].pdf [28 KiB] HiDef png [383 KiB] Thumbnail [263 KiB] *.C file finalp[..].pdf [28 KiB] HiDef png [433 KiB] Thumbnail [315 KiB] *.C file finalp[..].pdf [28 KiB] HiDef png [355 KiB] Thumbnail [247 KiB] *.C file 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. Wilson[..].pdf [17 KiB] HiDef png [170 KiB] Thumbnail [153 KiB] *.C file Animated gif made out of all figures. PAPER-2016-045.gif Thumbnail

## 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. Table_1.pdf [44 KiB] HiDef png [34 KiB] Thumbnail [16 KiB] tex code Parameters describing the efficiency to trigger, reconstruct and select simulated $B ^+ \rightarrow K ^+ \mu ^+\mu ^-$ decays as a function of $m_{\mu\mu}$. Table_2.pdf [37 KiB] HiDef png [76 KiB] Thumbnail [35 KiB] tex code 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. Table_3.pdf [46 KiB] HiDef png [259 KiB] Thumbnail [128 KiB] tex code Coefficients of the form factor $f_{+}( q^2 )$ as introduced in Eq. 8 with both prior (from Ref. [42]) and posterior values shown. Table_4.pdf [37 KiB] HiDef png [57 KiB] Thumbnail [28 KiB] tex code Summary of systematic uncertainties. The branching fraction refers to the short-distance SM contribution. A dash indicates that the uncertainty is negligible. Table_5.pdf [47 KiB] HiDef png [53 KiB] Thumbnail [25 KiB] tex code

## 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. Fig1-S.pdf [16 KiB] HiDef png [203 KiB] Thumbnail [181 KiB] *C file Fig2-S.pdf [75 KiB] HiDef png [186 KiB] Thumbnail [155 KiB] *C file Fig3a-S.pdf [29 KiB] HiDef png [490 KiB] Thumbnail [341 KiB] *C file Fig3b-S.pdf [29 KiB] HiDef png [408 KiB] Thumbnail [273 KiB] *C file Fig3c-S.pdf [29 KiB] HiDef png [461 KiB] Thumbnail [325 KiB] *C file Fig3d-S.pdf [29 KiB] HiDef png [380 KiB] Thumbnail [257 KiB] *C file Fig4a-S.pdf [26 KiB] HiDef png [471 KiB] Thumbnail [306 KiB] *C file Fig4b-S.pdf [27 KiB] HiDef png [411 KiB] Thumbnail [249 KiB] *C file Fig4c-S.pdf [26 KiB] HiDef png [459 KiB] Thumbnail [302 KiB] *C file Fig4d-S.pdf [27 KiB] HiDef png [397 KiB] Thumbnail [239 KiB] *C file Fig5-S.pdf [21 KiB] HiDef png [327 KiB] Thumbnail [244 KiB] *C file supp-app.pdf [419 KiB] HiDef png [413 KiB] Thumbnail [232 KiB] *C file

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