cern.ch

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 [255 KiB]
Thumbnail [80 KiB]
*.C file
datamass_fullmodel_kmm.pdf

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.

[Failure to get the plot]

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.

[Failure to get the plot]
[Failure to get the plot]
[Failure to get the plot]
[Failure to get the plot]

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 [161 KiB]
Thumbnail [59 KiB]
*.C file
WilsonProfile.pdf

Animated gif made out of all figures.

PAPER-2016-045.gif
Thumbnail
thumbnail_PAPER-2016-045.gif

Tables and captions

Resolution parameters of the different convolution regions in units of $ {\mathrm{\,MeV\!/}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 [28 KiB]
Thumbnail [4 KiB]
tex code
Table_1.pdf

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 [61 KiB]
Thumbnail [9 KiB]
tex code
Table_2.pdf

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 [216 KiB]
Thumbnail [32 KiB]
tex code
Table_3.pdf

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 [45 KiB]
Thumbnail [7 KiB]
tex code
Table_4.pdf

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 [42 KiB]
Thumbnail [6 KiB]
tex code
Table_5.pdf

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 [198 KiB]
Thumbnail [73 KiB]
*C file
Fig1-S.pdf
Fig2-S.pdf [75 KiB]
HiDef png [176 KiB]
Thumbnail [60 KiB]
*C file
Fig2-S.pdf
Fig3a-S.pdf [29 KiB]
HiDef png [450 KiB]
Thumbnail [130 KiB]
*C file
Fig3a-S.pdf
Fig3b-S.pdf [29 KiB]
HiDef png [375 KiB]
Thumbnail [104 KiB]
*C file
Fig3b-S.pdf
Fig3c-S.pdf [29 KiB]
HiDef png [421 KiB]
Thumbnail [125 KiB]
*C file
Fig3c-S.pdf
Fig3d-S.pdf [29 KiB]
HiDef png [347 KiB]
Thumbnail [100 KiB]
*C file
Fig3d-S.pdf
Fig4a-S.pdf [26 KiB]
HiDef png [380 KiB]
Thumbnail [116 KiB]
*C file
Fig4a-S.pdf
Fig4b-S.pdf [27 KiB]
HiDef png [316 KiB]
Thumbnail [93 KiB]
*C file
Fig4b-S.pdf
Fig4c-S.pdf [26 KiB]
HiDef png [368 KiB]
Thumbnail [114 KiB]
*C file
Fig4c-S.pdf
Fig4d-S.pdf [27 KiB]
HiDef png [303 KiB]
Thumbnail [91 KiB]
*C file
Fig4d-S.pdf
Fig5-S.pdf [21 KiB]
HiDef png [291 KiB]
Thumbnail [95 KiB]
*C file
Fig5-S.pdf
supp-app.pdf [419 KiB]
HiDef png [407 KiB]
Thumbnail [87 KiB]
*C file
supp-app.pdf

Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.