Measurement of the $B_s^0\to {\mu }^{+}{\mu }^{-}$ decay properties and search for the $B^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$ decays

An improved measurement of the decay $B_s^0\to {\mu }^{+}{\mu }^{-}$ and searches for the decays $B^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$ are performed at the LHCb experiment using data collected in proton-proton collisions at $\sqrt{s}=7$, 8 and 13 TeV, corresponding to integrated luminosities of 1, 2 and $6{\mathrm{fb}}^{-1}$, respectively. The $B_s^0\to {\mu }^{+}{\mu }^{-}$ branching fraction and effective lifetime are measured to be $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-})=(3.09_{-0.43-0.11}^{+0.46+0.15})\times {10}^{-9}$ and $\tau (B_s^0\to {\mu }^{+}{\mu }^{-})=(2.07\pm 0.29\pm 0.03)\mathrm{ps}$, respectively, where the uncertainties include both statistical and systematic contributions. No significant signal for $B^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$ decays is found and the upper limits $\mathcal{B}(B^0\to {\mu }^{+}{\mu }^{-})<2.6\times {10}^{-10}$ and $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma )<2.0\times {10}^{-9}$ at 95% confidence level are determined, where the latter is limited to the range $m_{\mu \mu }>4.9\mathrm{GeV}/c^2$. Additionally, the ratio between the $B^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to {\mu }^{+}{\mu }^{-}$ branching fractions is measured to be ${\mathcal{R}}_{{\mu }^{+}{\mu }^{-}}<0.095$ at 95% confidence level. The results are in agreement with the Standard Model predictions.

Figure 1

SM Feynman diagrams mediating (top) the $B_s^0\to {\mu }^{+}{\mu }^{-}$ and (bottom) the $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$ processes. Subpanels show (a) the so-called “penguin” diagram and (b) the “box” diagram for $B_s^0\to {\mu }^{+}{\mu }^{-}$, and (c) an ISR contribution and (d) an FSR contribution to $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$.

Figure 2

BDT distribution calibrated using corrected simulated $B_s^0\to {\mu }^{+}{\mu }^{-}$ decays (black circles) and combinatorial background from high dimuon-mass data sidebands (blue filled circles) in (left) Run 1 and (right) Run 2 data. Blue error bands represent the statistical uncertainty.

Figure 3

Mass distributions of selected (top) $B^0\to K^{+}{\pi }^{-}$ and (bottom) $B_s^0\to K^{+}{K}^{-}$ candidates in (left) Run 1 and (right) Run 2 data. The results of the fits used to determine the means of the $B_{(s)}^0\to {\mu }^{+}{\mu }^{-}$ mass distributions are overlaid and the different components are detailed in the legends.

Figure 4

Mass distributions of (top) $J/\psi \to {\mu }^{+}{\mu }^{-}$, (center) $\psi (2S)\to {\mu }^{+}{\mu }^{-}$, (bottom) $\mathrm{\Upsilon }(1S,2S,3S)\to {\mu }^{+}{\mu }^{-}$ candidates in (left) Run 1 and (right) Run 2 data. The result from the fit to determine the mass resolutions to each sample is overlaid, and the components are detailed in the legend.

Figure 5

Fit to the measured mass resolutions of quarkonia resonances (blue dots) with a power-law function to obtain the mass resolution at the $B^0$ and $B_s^0$ masses as indicated by the two dashed lines in (left) Run 1 and (right) Run 2 data.

Figure 6

The calibrated BDT distribution for $B_s^0\to {\mu }^{+}{\mu }^{-}$ decays with $A_{\mathrm{\Delta }{\mathrm{\Gamma }}_s}^{\mu \mu }=1$ (black) and $B^0\to {\mu }^{+}{\mu }^{-}$ decays (red) for (left) Run 1 and (right) Run 2, including the total uncertainty on the fraction per BDT region. The $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B^0\to {\mu }^{+}{\mu }^{-}$ distributions are determined on corrected simulated samples, as described in the text.

Figure 7

The BDT distributions of (top) $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to K^{+}{K}^{-}$ decays and (bottom) $B^0\to {\mu }^{+}{\mu }^{-}$ and $B^0\to K^{+}{\pi }^{-}$ decays in (left) Run 1 and (right) Run 2 data, including the total uncertainty on the fraction per BDT region. For $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B^0\to {\mu }^{+}{\mu }^{-}$ decays, the distributions are determined on corrected simulated samples, as described in the text, and are shown in black. The $B_s^0\to K^{+}{K}^{-}$ and $B^0\to K^{+}{\pi }^{-}$ distributions are determined using fits to data as described in the text and are shown in red.

Figure 8

Mass distribution of $B^{+}\to J/\psi K^{+}$ candidates in data for different data-taking years. Superimposed is a fit to the distribution: the blue line shows the total fit, the red dashed line is the $B^{+}\to J/\psi K^{+}$ component, the green dash-dotted line is the combinatorial background, the purple dash-three-dotted line is the $B^{+}\to J/\psi {\pi }^{+}$ misidentified background.

Figure 9

Mass distribution of $B^0\to K^{+}{\pi }^{-}$ candidates in data for different data-taking years, triggered independently of the signal. Superimposed is a fit to the distribution: the blue line shows the total fit, the red dashed line is the $B^0\to K^{+}{\pi }^{-}$ component, the magenta dashed line is the ${\overline{B}}_s^0\to K^{+}{\pi }^{-}$ component, the green dashed line is the combinatorial background, and the brown dashed line is the partially reconstructed background component.

Figure 10

Mass distribution of signal candidates (black dots) for (left) Run 1 and (right) Run 2 samples in regions of BDT. The result of the fit is overlaid (blue line) and the different components detailed in the legend. The solid bands represent the variation of the signal branching fractions within their total uncertainty.

Figure 11

Two-dimensional representations of the branching fraction measurements for the decays (top) $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B^0\to {\mu }^{+}{\mu }^{-}$, (bottom left) $B^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$ and (bottom right) $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$. The $B_s^0\to {\mu }^{+}{\mu }^{-}\gamma$ branching fraction is limited to the range $m_{\mu \mu }>4.9\mathrm{GeV}/c^2$. The measured central values of the branching fractions are indicated with a blue dot. The profile likelihood contours for 68%, 95% and 99% CL regions of the result presented in this paper are shown as blue contours, while in the top plot the brown contours indicate the previous measurement [32] and the red cross shows the SM prediction. Figure reproduced from Ref. [37].

Figure 12

Results from the ${\mathrm{CL}}_{\mathrm{s}}$ scan used to obtain the limit on (left) $\mathcal{B}(B^0\to {\mu }^{+}{\mu }^{-})$ and (right) $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma )$. The background-only expectation is shown by the red line and the $1\sigma$ and $2\sigma$ bands are shown as light blue and blue bands respectively. The observation is shown as the solid black line. The two dashed lines intersecting with the observation indicate the limits at 90% and 95% CL for the upper and lower line, respectively.

Figure 13

Dimuon mass distributions of $B_s^0\to {\mu }^{+}{\mu }^{-}$ candidates with the fit model used to perform the background subtraction for the measurement of the $B_s^0\to {\mu }^{+}{\mu }^{-}$ effective lifetime superimposed in the (left) low and (right) high BDT regions.

Figure 14

The functions used to model the decay-time efficiency in the (left) low and (right) high BDT regions in the fit for the $B_s^0\to {\mu }^{+}{\mu }^{-}$ effective lifetime.

Figure 15

Top: distribution of $K^{+}{K}^{-}$ mass with the fit models used to perform the background subtraction superimposed and bottom: the background-subtracted decay-time distributions with the fit model used to determine the $B_s^0\to K^{+}{K}^{-}$ effective lifetime superimposed (bottom row). The distributions in the low and high BDT regions are shown in the left and right columns, respectively.

Figure 16

Top: distribution of $K^{+}{\pi }^{-}$ mass with the fit models used to perform the background subtraction superimposed and bottom: the background-subtracted decay-time distributions with the fit model used to determine the $B^0\to K^{+}{\pi }^{-}$ lifetime superimposed. The distributions in the low and high BDT regions are shown in the left and right columns, respectively.

Figure 17

Background-subtracted decay-time distributions with the fit model used to extract the $B_s^0\to {\mu }^{+}{\mu }^{-}$ effective lifetime superimposed in the (left) low and (right) high BDT regions.