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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{\,GeV^2\!/}c^4}$ , $10.09< q^2 <12.86$ $ {\mathrm{\,GeV^2\!/}c^4}$ , and $14.18< q^2 <19.00$ $ {\mathrm{\,GeV^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.

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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.

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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.

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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.

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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.

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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{\,GeV^2\!/}c^4} $, where theory predictions are expected to be most reliable.

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