A search is made for the highlysuppressed B meson decays $B^{+}\rightarrow K^{+}K^{+}\pi^{}$ and $B^{+}\rightarrow \pi^{+}\pi^{+}K^{}$ using a data sample corresponding to an integrated luminosity of 3.0 $fb^{1}$ collected by the LHCb experiment in protonproton collisions at centreofmass energies of 7 and 8 TeV. No evidence is found for the decays, and upper limits at 90% confidence level are determined to be $\mathcal{B}(B^{+}\rightarrow K^{+}K^{+}\pi^{}) < 1.1\times 10^{8}$ and $\mathcal{B}(B^{+}\rightarrow \pi^{+}\pi^{+}K^{}) < 4.6\times 10^{8}$.
Main SM diagrams for the suppressed decays (left) $ B ^+ \rightarrow K ^+ K ^+ \pi ^ $ and (right) $ B ^+ \rightarrow \pi ^+ \pi ^+ K ^ $ . 
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Invariant mass spectra of (a) $ B ^+ \rightarrow K ^+ K ^+ \pi ^ $ and (b) $ B ^+ \rightarrow K ^+ K ^ \pi ^+ $ candidates, with the results of the unbinned extended maximum likelihood fits overlaid. The dashed (blue) line represents the partially reconstructed background, the dotted (green) line the combinatorial background, the long dashed (red) line is the signal, and the solid (magenta) line the total. Residual differences between data and the fits are shown below the mass plots in units of standard deviation. 
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KKPi_O[..].pdf [43 KiB] HiDef png [314 KiB] Thumbnail [272 KiB] *.C file 

Invariant mass spectra of (a) $ B ^+ \rightarrow \pi ^+ \pi ^+ K ^ $ and (b) $ B ^+ \rightarrow \pi ^+ \pi ^ K ^+ $ candidates, with the results of the unbinned extended maximum likelihood fits overlaid. The dashed (blue) line represents the partially reconstructed background, the dotted (green) line the combinatorial background, the long dashed (red) line is the signal, the dotdash (dark green) line the $ B ^0_ s $ fourbody backgrounds, and the solid (magenta) line the total. Residual differences between data and the fits are shown below the mass plots in units of standard deviation. 
KPiPi_[..].pdf [25 KiB] HiDef png [266 KiB] Thumbnail [234 KiB] *.C file 

KPiPi_[..].pdf [43 KiB] HiDef png [284 KiB] Thumbnail [247 KiB] *.C file 

FeldmanCousins 90% (green) and 95% (yellow) confidence level (CL) bands for (a) $ B ^+ \rightarrow K ^+ K ^+ \pi ^ $ and (b) $ B ^+ \rightarrow \pi ^+ \pi ^+ K ^ $ , including statistical and systematic uncertainties. The black solid line shows the expected central value of the true branching fraction as a function of the fitted number of signal events. The horizontal dotted lines show the 90% CL upper limits on the branching fractions prior to the present measurement. The dashed lines in the lower left corner of each figure show the equivalent 90% CL upper limits reported in this paper. 
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limits[..].pdf [25 KiB] HiDef png [185 KiB] Thumbnail [159 KiB] *.C file 

Animated gif made out of all figures. 
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Systematic uncertainties on the $ B ^+ \rightarrow K ^+ K ^+ \pi ^ $ and $ B ^+ \rightarrow \pi ^+ \pi ^+ K ^ $ branching fractions in units of $10^{8}$ and $10^{9}$, respectively. 
Table_1.pdf [48 KiB] HiDef png [64 KiB] Thumbnail [30 KiB] tex code 
Created on 20 February 2021.