# First observations of the rare decays $B^+\!\rightarrow K^+\pi^+\pi^-\mu^+\mu^-$ and $B^+\!\rightarrow\phi K^+\mu^+\mu^-$

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## Abstract

First observations of the rare decays $B^+\rightarrow K^+\pi^+\pi^-\mu^+\mu^-$ and $B^+\rightarrow \phi K^+\mu^+\mu^-$ are presented using data corresponding to an integrated luminosity of $3.0\,{fb}^{-1}$, collected by the LHCb experiment at centre-of-mass energies of $7$ and $8\mathrm{\,TeV}$. The branching fractions of the decays are \begin{eqnarray*} \mathcal{B}(B^+\rightarrow K^+\pi^+\pi^-\mu^+\mu^-) &=& (4.36\,^{+0.29}_{-0.27}\,\mathrm{(stat)}\pm 0.21\,\mathrm{(syst)}\pm0.18\,\mathrm{(norm)})\times10^{-7},\\ \mathcal{B}(B^+\rightarrow\phi K^+\mu^+\mu^-) &=& (0.82 \,^{+0.19}_{-0.17}\,\mathrm{(stat)}\,^{+0.10}_{-0.04}\,\mathrm{(syst)}\pm0.27\,\mathrm{(norm)}) \times10^{-7},\end{eqnarray*} where the uncertainties are statistical, systematic, and due to the uncertainty on the branching fractions of the normalisation modes. A measurement of the differential branching fraction in bins of the invariant mass squared of the dimuon system is also presented for the decay $B^+\rightarrow K^+\pi^+\pi^-\mu^{+}\mu^{-}$.

## Figures and captions

 Invariant mass of $B ^+ \!\rightarrow K ^+ \pi ^+ \pi ^- \mu ^+\mu ^-$ candidates in bins of $q^2$ with fit projections overlaid. The signal component (shaded light blue) is modelled by the sum of two Gaussian functions, each with a power-law tail at low mass. The background component (shaded dark blue) is modelled by an exponential function. In the $q^2$ ranges $4.30< q^2 <8.68$ ${\mathrm{\,Ge V^2\!/}c^4}$ , $10.09< q^2 <12.86$ ${\mathrm{\,Ge V^2\!/}c^4}$ , and $14.18< q^2 <19.00$ ${\mathrm{\,Ge V^2\!/}c^4}$ , scaling factors are applied to account for the vetoes of the radiative tails of the charmonium resonances, resulting in steps in the background mass shape. The lower right plot shows a separate fit to the signal decay integrated over all $q^2$ bins. Fig1a.pdf [17 KiB] HiDef png [224 KiB] Thumbnail [70 KiB] *.C file Fig1b.pdf [18 KiB] HiDef png [238 KiB] Thumbnail [76 KiB] *.C file Fig1c.pdf [19 KiB] HiDef png [275 KiB] Thumbnail [82 KiB] *.C file Fig1d.pdf [18 KiB] HiDef png [250 KiB] Thumbnail [78 KiB] *.C file Fig1e.pdf [15 KiB] HiDef png [155 KiB] Thumbnail [58 KiB] *.C file Fig1f.pdf [20 KiB] HiDef png [260 KiB] Thumbnail [79 KiB] *.C file Invariant mass distribution of (a) the control decay $B ^+ \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ \pi ^+ \pi ^-$ and (b) the normalisation mode $B ^+ \!\rightarrow \psi {(2S)} K ^+$ with fit projections overlaid. Fig2a.pdf [21 KiB] HiDef png [235 KiB] Thumbnail [79 KiB] *.C file Fig2b.pdf [20 KiB] HiDef png [214 KiB] Thumbnail [73 KiB] *.C file Differential branching fraction ${\rm d}\cal B ( B ^+ \!\rightarrow K ^+ \pi ^+ \pi ^- \mu ^+\mu ^- )/ {\rm d} q^2$. Errors shown include both statistical and systematic uncertainties. Shaded regions indicate the vetoed charmonium resonances. Fig3.pdf [14 KiB] HiDef png [96 KiB] Thumbnail [40 KiB] *.C file Background-subtracted $m( K ^+ \pi ^+ \pi ^- )$ distributions for (a) the signal decay $B ^+ \!\rightarrow K ^+ \pi ^+ \pi ^- \mu ^+\mu ^-$ and (b) the control channel $B ^+ \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ \pi ^+ \pi ^-$. The vertical lines indicate the masses of the $K_1(1270)^+$ and $K_1(1400)^+$ resonances. Fig4a.pdf [19 KiB] HiDef png [174 KiB] Thumbnail [71 KiB] *.C file Fig4b.pdf [24 KiB] HiDef png [177 KiB] Thumbnail [68 KiB] *.C file Invariant $m(\phi K ^+ \mu ^+\mu ^- )$ distributions for (a) $B ^+ \!\rightarrow \phi K ^+ \mu ^+\mu ^-$ and (b) $B ^+ \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi K ^+$ decays with fit projections overlaid. Fig5a.pdf [18 KiB] HiDef png [215 KiB] Thumbnail [74 KiB] *.C file Fig5b.pdf [20 KiB] HiDef png [227 KiB] Thumbnail [73 KiB] *.C file Animated gif made out of all figures. PAPER-2014-030.gif Thumbnail

## Tables and captions

 Signal yields for the decay $B ^+ \!\rightarrow K ^+ \pi ^+ \pi ^- \mu ^+\mu ^-$ and resulting differential branching fractions in bins of $q^2$ . The first contribution to the uncertainty is statistical, the second systematic, where the uncertainty due to the branching fraction of the normalisation channel is included. The $q^2$ binning used corresponds to the binning used in previous analyses of $b\rightarrow s\mu ^+ \mu ^-$ decays [1,2,3]. Results are also presented for the $q^2$ range from $1$ to $6 {\mathrm{\,Ge V^2\!/}c^4}$, where theory predictions are expected to be most reliable. Table_1.pdf [60 KiB] HiDef png [122 KiB] Thumbnail [22 KiB] tex code

Created on 20 April 2019.Citation count from INSPIRE on 25 April 2019.