Searches for the lepton flavour violating decay $\tau^\rightarrow \mu^\mu^+\mu^$ and the lepton flavour and baryon number violating decays $\tau^\rightarrow \bar{p}\mu^+\mu^$ and $\tau^\rightarrow p\mu^\mu^$ have been carried out using protonproton collision data, corresponding to an integrated luminosity of 1.0 fb$^{1}$, taken by the LHCb experiment at $\sqrt{s} = 7$ TeV. No evidence has been found for any signal, and limits have been set at 90% confidence level on the branching fractions: $\cal B(\tau^\rightarrow \mu^\mu^+\mu^) < 8.0 \times 10^{8}$, $\cal B(\tau^\rightarrow \bar{p}\mu^+\mu^) < 3.3 \times 10^{7}$ and $\cal B(\tau^\rightarrow p\mu^\mu^) < 4.4 \times 10^{7}$. The results for the $\tau^\rightarrow \bar{p}\mu^+\mu^$ and $\tau^\rightarrow p\mu^\mu^$ decay modes represent the first direct experimental limits on these channels.
Distribution of (a) $ {\rm \mathcal{M}_{3body}}$ and (b) $ {\rm \mathcal{M}_{PID}}$ for $\tau^\rightarrow \mu^\mu^+\mu^$ where the binning corresponds to that used in the limit calculation. The short dashed (red) lines show the response of the data sidebands, whilst the long dashed (blue) and solid (black) lines show the response of simulated signal events before and after calibration. Note that in both cases the lowest likelihood bin is later excluded from the analysis. 
4a_new.pdf [14 KiB] HiDef png [142 KiB] Thumbnail [59 KiB] *.C file 

4b_new.pdf [14 KiB] HiDef png [147 KiB] Thumbnail [55 KiB] *.C file 

Invariant mass distribution of $\phi(\mu^+\mu^)\pi^$ after (a) the $\tau^\rightarrow \mu^\mu^+\mu^$ selection and (b) the $\tau\rightarrow p\mu\mu$ selection and PID cuts. The solid (blue) lines show the overall fits, the long dashed (green) and short dashed (red) lines show the two Gaussian components of the signal and the dot dashed (black) lines show the backgrounds. 
1a.pdf [26 KiB] HiDef png [233 KiB] Thumbnail [74 KiB] *.C file 

1b.pdf [26 KiB] HiDef png [251 KiB] Thumbnail [81 KiB] *.C file 

Invariant mass distributions and fits to the mass sidebands in data for (a) $\mu^+\mu^\mu^$ candidates in the four merged bins that contain the highest signal probabilities, (b) ${\bar p}\mu^+\mu^$ candidates in the two merged bins with the highest signal probabilities, and (c) $p\mu^\mu^$ candidates in the two merged bins with the highest signal probabilities. 
2a.pdf [17 KiB] HiDef png [146 KiB] Thumbnail [57 KiB] *.C file 

2b.pdf [16 KiB] HiDef png [154 KiB] Thumbnail [59 KiB] *.C file 

2c.pdf [16 KiB] HiDef png [144 KiB] Thumbnail [53 KiB] *.C file 

Distribution of $\textrm{CL}_{\textrm{s}}$ values as functions of the assumed branching fractions, under the hypothesis to observe background events only, for (a) $\tau^\rightarrow \mu^\mu^+\mu^$ , (b) $\tau^\rightarrow \bar{p}\mu^+\mu^$ and (c) $\tau^\rightarrow p\mu^\mu^$ . The dashed lines indicate the expected curves and the solid lines the observed ones. The light (yellow) and dark (green) bands cover the regions of 68% and 95% confidence for the expected limits. 
3a.pdf [17 KiB] HiDef png [156 KiB] Thumbnail [52 KiB] *.C file 

3b.pdf [15 KiB] HiDef png [166 KiB] Thumbnail [54 KiB] *.C file 

3c.pdf [15 KiB] HiDef png [174 KiB] Thumbnail [56 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2013014.gif Thumbnail 
Terms entering in the normalisation factor $\alpha$ for $\tau^\rightarrow \mu^\mu^+\mu^$ , $\tau^\rightarrow \bar{p}\mu^+\mu^$ and $\tau^\rightarrow p\mu^\mu^$ , and their combined statistical and systematic uncertainties. 
Table_1.pdf [63 KiB] HiDef png [70 KiB] Thumbnail [12 KiB] tex code 

Expected background candidate yields, with their systematic uncertainties, and observed candidate yields within the $\tau$ signal window in the different likelihood bins for the $\tau^\rightarrow \mu^\mu^+\mu^$ analysis. The likelihood values for $ {\rm \mathcal{M}_{PID}}$ range from $0$ (most backgroundlike) to $+1$ (most signallike), while those for $ {\rm \mathcal{M}_{3body}}$ range from $1$ (most backgroundlike) to $+1$ (most signallike). The lowest likelihood bins have been excluded from the analysis. 
Table_2.pdf [30 KiB] HiDef png [250 KiB] Thumbnail [42 KiB] tex code 

Expected background candidate yields, with their systematic uncertainties, and observed candidate yields within the $\tau$ mass window in the different likelihood bins for the $\tau\rightarrow p\mu\mu$ analysis. The likelihood values for $ {\rm \mathcal{M}_{3body}}$ range from $1$ (most backgroundlike) to $+1$ (most signallike). The lowest likelihood bin has been excluded from the analysis. 
Table_3.pdf [44 KiB] HiDef png [62 KiB] Thumbnail [11 KiB] tex code 
Supplementary material full pdf 
supple[..].pdf [224 KiB] 

This zip file contains supplementary material for the publication LHCbPAPER2013014. The files included are: Supplementary.pdf: The appendix from the paper, including the figures with captions and some brief explanation. *pdf, *eps, *png: The figures 
Fig4a.pdf [14 KiB] HiDef png [155 KiB] Thumbnail [61 KiB] *C file 

Fig4b.pdf [14 KiB] HiDef png [180 KiB] Thumbnail [66 KiB] *C file 

Fig5a.pdf [14 KiB] HiDef png [165 KiB] Thumbnail [63 KiB] *C file 

Fig5b.pdf [14 KiB] HiDef png [153 KiB] Thumbnail [61 KiB] *C file 

Fig6.pdf [13 KiB] HiDef png [192 KiB] Thumbnail [63 KiB] *C file 

Fig7.pdf [16 KiB] HiDef png [138 KiB] Thumbnail [56 KiB] *C file 

Fig8a.pdf [22 KiB] HiDef png [274 KiB] Thumbnail [80 KiB] *C file 

Fig8b.pdf [25 KiB] HiDef png [253 KiB] Thumbnail [85 KiB] *C file 
Created on 16 February 2019.Citation count from INSPIRE on 16 February 2019.