# Search for the rare decay $D^0 \to \mu^+ \mu^-$

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## Abstract

A search for the rare decay $D^0 \to \mu^+ \mu^-$is performed using a data sample, corresponding to an integrated luminosity of 0.9 fb$^{-1}$, of $pp$ collisions collected at a centre-of-mass energy of 7 TeV by the LHCb experiment. The observed number of events is consistent with the background expectations and corresponds to an upper limit of ${\cal B}(D^0 \to \mu^+ \mu^-) < 6.2(7.6) \times 10^{-9}$ at 90% (95%) confidence level. This result represents an improvement of more than a factor twenty with respect to previous measurements.

## Figures and captions

 (a) Invariant mass difference $\Delta m_{\pi^{+}\pi^{-} }$ , with $m_{\pi^{+}\pi^{-}}$ in the range 1840$-$1885 ${\mathrm{\,Me V\!/}c^2}$ , and (b) invariant mass $m_{\pi^{+}\pi^{-}}$ , with $\Delta m_{\pi^{+}\pi^{-} }$ in the range 144$-$147 ${\mathrm{\,Me V\!/}c^2}$ , for $D^{\ast +}\rightarrow D^0 (\pi^{+}\pi^{-}) \pi^+$ candidates in data. The projections of the two-dimensional unbinned extended maximum likelihood fit are overlaid. The curves represent the total (solid black), $D^{\ast +}\rightarrow D^0 (\pi^{+}\pi^{-}) \pi^+$ (dashed red), the untagged $D^0 \rightarrow \pi^{+} \pi^{-}$ (dash-dotted cyan), the combinatorial background (dashed yellow) and the $D^{\ast +}\rightarrow D^0 (K^{-} \pi^{+}) \pi^+$ (dash-dotted blue) contributions. The $D^{\ast +}\rightarrow D^0 (\pi^{+}\pi^{-}) \pi^+$ candidates are prescaled at the software trigger stage by a factor 0.03. pipi_f[..].pdf [24 KiB] HiDef png [186 KiB] Thumbnail [60 KiB] *.C file pipi_f[..].pdf [24 KiB] HiDef png [180 KiB] Thumbnail [56 KiB] *.C file (a) Invariant mass difference $\Delta m_{K^{-}\pi^{+}}$ and (b) invariant mass $m_{K^{-}\pi^{+}}$ distributions in data for $D^{\ast +}\rightarrow D^0 (K^{-} \pi^{+}) \pi^+$ candidates, with muon identification applied to the pion. The events are triggered by spectator particles with respect to the $D^0$ daughter pion. The $D^{\ast +}\rightarrow D^0 (K^{-} \pi^{+}) \pi^+$ candidates are prescaled at the software trigger stage by a factor 0.15. DeltaM[..].pdf [16 KiB] HiDef png [114 KiB] Thumbnail [49 KiB] *.C file MKmu_a[..].pdf [18 KiB] HiDef png [114 KiB] Thumbnail [49 KiB] *.C file Invariant mass difference $\Delta m_{K^{-}\pi^{+}}$ for $D^{\ast +}\rightarrow D^0 (K^{-} \pi^{+}) \pi^+$ candidates, with both hadrons misidentified as muons, with $m_{\mu^{+}\mu^{-}}$ in the range 1720$-$1800 ${\mathrm{\,Me V\!/}c^2}$ . The two muons are reconstructed using the $K\pi$ and $\pi K$ mass hypotheses. The result of the unbinned extended maximum likelihood fit is overlaid. The curves represent the total distribution (solid black), the combinatorial background (dashed yellow) and the $D^{\ast +}\rightarrow D^0 (K^{-} \pi^{+}) \pi^+$ (dash-dotted blue) contribution. dmkpi1[..].pdf [18 KiB] HiDef png [185 KiB] Thumbnail [67 KiB] *.C file (a) Invariant mass difference $\Delta m_{\mu^{+}\mu^{-}}$ , with $m_{\mu^{+}\mu^{-}}$ in the range 1820$-$1885 ${\mathrm{\,Me V\!/}c^2}$ and (b) invariant mass $m_{\mu^{+}\mu^{-}}$ , with $\Delta m_{\mu^{+}\mu^{-}}$ in the range 144$-$147 ${\mathrm{\,Me V\!/}c^2}$ for $D^{\ast +}\rightarrow D^0 (\mu^{+} \mu^{-}) \pi^+$ candidates. The projections of the two-dimensional unbinned extended maximum likelihood fit are overlaid. The curves represent the total distribution (solid black), the $D^{\ast +}\rightarrow D^0 (\pi^{+}\pi^{-}) \pi^+$ (dashed red), the combinatorial background (dashed yellow), the $D^{\ast +}\rightarrow D^0 (K^{-} \pi^{+}) \pi^+$ (dash-dotted blue), the $D^{\ast +}\rightarrow D^0 (\pi^{-} \mu^{+} \nu_\mu)\pi^+$ (dash-dotted purple) and the signal $D^{\ast +}\rightarrow D^0 (\mu^{+} \mu^{-}) \pi^+$ (solid green) contribution. deltaM[..].pdf [20 KiB] HiDef png [185 KiB] Thumbnail [63 KiB] *.C file mumu_f[..].pdf [19 KiB] HiDef png [201 KiB] Thumbnail [74 KiB] *.C file CL$_{s}$ (solid line) as a function of the assumed $D^0 \rightarrow \mu^+ \mu^-$ branching fraction and median (dashed line), 1$\sigma$ and 2$\sigma$ bands of the expected CL$_{s}$, in the background-only hypothesis, obtained with the asymptotic CL$_{s}$ method. The horizontal line corresponding to CL$_{s}$=0.05 is also drawn. limit_2011.pdf [15 KiB] HiDef png [118 KiB] Thumbnail [41 KiB] *.C file Animated gif made out of all figures. PAPER-2013-013.gif Thumbnail

## Tables and captions

 Contributions to the systematic uncertainty of the single event sensitivity $\alpha$. Table_1.pdf [46 KiB] HiDef png [76 KiB] Thumbnail [12 KiB] tex code PDF components describing $m_{\mu^{+}\mu^{-}}$ and $\Delta m_{\mu^{+}\mu^{-}}$ distributions in the signal and corresponding freely varying and Gaussian constrained fit parameters. The coefficients of the exponential (EXP) function used to describe both the $D^{\ast +}\rightarrow D^0 (K^{-} \pi^{+}) \pi^+$ and $D^{\ast +}\rightarrow D^0 (\pi^{-} \mu^{+} \nu_\mu)\pi^+$ backgrounds are $\gamma_{K\pi}$ and $\gamma_{\pi\mu\nu}$ while $f_{K\pi}$ and $f_{\pi\mu\nu}$ are the normalisation factors to the $D^{\ast +}\rightarrow D^0 (\pi^{+}\pi^{-}) \pi^+$ events. The symbols ${\langle\Delta m_{\mu^{+}\mu^{-}} \rangle}_{\eta}$, $\eta=i, j$ and $k$ represent the mean values and $(\sigma^{\Delta}_1)_{\eta}$ the narrower width of the double Gaussian (DG) PDF describing $D^{\ast +}\rightarrow D^0 (\pi^{+}\pi^{-}) \pi^+$ , $D^{\ast +}\rightarrow D^0 (K^{-} \pi^{+}) \pi^+$ and $D^{\ast +}\rightarrow D^0 (K^{-} \mu^{+} \nu_\mu)\pi^+$ distributions (for $D^{\ast +}\rightarrow D^0 (K^{-} \pi^{+}) \pi^+$ a single Gaussian (SG) PDF is used). The normalisation for the $D^{\ast +}\rightarrow D^0 (\pi^{+}\pi^{-}) \pi^+$ event yield is obtained from the procedure described in Section 5. The function $f_m$ is a constant. The parameters $\omega$, $\mu$ and $\sigma$ of the Crystal Ball function describing the $D^{\ast +}\rightarrow D^0 (\pi^{+}\pi^{-}) \pi^+$ events are described in Section 4. Table_2.pdf [71 KiB] HiDef png [54 KiB] Thumbnail [9 KiB] tex code

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