CMS-PAS-BPH-24-007

CMS-PAS-BPH-24-007
Search for the rare $ \mathrm{B^0_s} (\mathrm{B}^0)\to \mu^+ \mu^- \mu^+ \mu^- $ decays in proton-proton collisions
CMS Collaboration
2026-03-24

Abstract: A search for the rare decays $ \mathrm{B^0_s}\to \mu^+ \mu^- \mu^+ \mu^- $ and $ \mathrm{B}^0 \to \mu^+ \mu^- \mu^+ \mu^- $ is performed with a sample of proton-proton collisions at $ \sqrt{s}= $ 13.6 TeV collected in 2022--2024 and corresponding to an integrated luminosity of 171 fb$ ^{-1} $. Signal candidates are reconstructed from four-muon final states and are normalized to the kinematically similar process $ \mathrm{B_s^0} \to \mathrm{J}\!/\!\psi(\mu^+ \mu^-) \phi(\mu^+ \mu^-) $, thus reducing systematic uncertainties. No significant excesses over the expected backgrounds are observed. Assuming only one signal process at a time, 95% confidence level upper limits are obtained on the branching fractions $ \mathcal{B}(\mathrm{B}^0 \to \mu^+ \mu^- \mu^+ \mu^-) < 1.3 (1.4) \times 10^{-10} $ and $ \mathcal{B}(\mathrm{B^0_s} \to \mu^+ \mu^- \mu^+ \mu^-) < 5.7 (6.0) \times 10^{-10} $, where the values in parentheses denote the expected limits. These results represent an improvement of about 30% with respect to the previous best bounds. For the first time, exclusion contours in the $ \mathcal{B}(\mathrm{B}^0 \to \mu^+ \mu^- \mu^+ \mu^-) $ vs. $ \mathcal{B}(\mathrm{B^0_s} \to \mu^+ \mu^- \mu^+ \mu^-) $ plane are also obtained from a scan over branching fraction pairs.
Links: CDS record (PDF) ; CADI line (restricted) ;

Figures & Tables	Summary	Additional Figures	References	CMS Publications

Figures
png pdf	Figure 1: Two possible $ \mathrm{B}_{s}^{0}({\mathrm{B}^0}) \rightarrow 4 \mu $ Feynman diagrams foreseen in the SM, ``penguin" (upper) and ``box" (lower). The relevant CKM elements, $ V_{tb} $ and $ V_{ts}^,V_{td}^ $, are indicated. The photon emission can occur from any charged fermion line.
png pdf	Figure 1-a: Two possible $ \mathrm{B}_{s}^{0}({\mathrm{B}^0}) \rightarrow 4 \mu $ Feynman diagrams foreseen in the SM, ``penguin" (upper) and ``box" (lower). The relevant CKM elements, $ V_{tb} $ and $ V_{ts}^,V_{td}^ $, are indicated. The photon emission can occur from any charged fermion line.
png pdf	Figure 1-b: Two possible $ \mathrm{B}_{s}^{0}({\mathrm{B}^0}) \rightarrow 4 \mu $ Feynman diagrams foreseen in the SM, ``penguin" (upper) and ``box" (lower). The relevant CKM elements, $ V_{tb} $ and $ V_{ts}^,V_{td}^ $, are indicated. The photon emission can occur from any charged fermion line.
png pdf	Figure 2: Four-muon mass resolution in three different pseudorapidity regions, with edges at 0.8 and 1.2. The vertical dashed lines represent the boundaries of the A, B, and C categories reported in Table 1. Each histogram is normalized to unit area.
png pdf	Figure 3: Comparison of the BDT score distribution between the $ \mathrm{B}_{s}^{0} \to \mathrm{J}/\psi (\mu\mu) \phi (\mathrm{K}\mathrm{K}) $ simulation and background-subtracted data. The initial disagreement is corrected by the applied reweighting.
png pdf	Figure 4: Fit to data in the normalization channel $ \mathrm{B}_{s}^{0}\to\mathrm{J}/\psi(\mu\mu)\phi(\mu\mu) $
png pdf	Figure 5: Combined signal PDF in the A1 category, for $ \mathcal{B}(\mathrm{B}_{s}^{0}\to4\mu)=1.0\times 10^{-9} $ and $ \mathcal{B}({\mathrm{B}^0}\to4\mu) = 4\times 10^{-10} $.
png pdf	Figure 6: Four-muon mass distributions for the six event categories. The combined expected signal PDFs for branching ratios $ \mathcal{B}(\mathrm{B}_{s}^{0}\to 4\mu) = 3.2 \times 10^{-10} $ and $ \mathcal{B}({\mathrm{B}^0}\to 4\mu)= 5.2 \times 10^{-11} $ are also shown.
png pdf	Figure 6-a: Four-muon mass distributions for the six event categories. The combined expected signal PDFs for branching ratios $ \mathcal{B}(\mathrm{B}_{s}^{0}\to 4\mu) = 3.2 \times 10^{-10} $ and $ \mathcal{B}({\mathrm{B}^0}\to 4\mu)= 5.2 \times 10^{-11} $ are also shown.
png pdf	Figure 6-b: Four-muon mass distributions for the six event categories. The combined expected signal PDFs for branching ratios $ \mathcal{B}(\mathrm{B}_{s}^{0}\to 4\mu) = 3.2 \times 10^{-10} $ and $ \mathcal{B}({\mathrm{B}^0}\to 4\mu)= 5.2 \times 10^{-11} $ are also shown.
png pdf	Figure 6-c: Four-muon mass distributions for the six event categories. The combined expected signal PDFs for branching ratios $ \mathcal{B}(\mathrm{B}_{s}^{0}\to 4\mu) = 3.2 \times 10^{-10} $ and $ \mathcal{B}({\mathrm{B}^0}\to 4\mu)= 5.2 \times 10^{-11} $ are also shown.
png pdf	Figure 6-d: Four-muon mass distributions for the six event categories. The combined expected signal PDFs for branching ratios $ \mathcal{B}(\mathrm{B}_{s}^{0}\to 4\mu) = 3.2 \times 10^{-10} $ and $ \mathcal{B}({\mathrm{B}^0}\to 4\mu)= 5.2 \times 10^{-11} $ are also shown.
png pdf	Figure 6-e: Four-muon mass distributions for the six event categories. The combined expected signal PDFs for branching ratios $ \mathcal{B}(\mathrm{B}_{s}^{0}\to 4\mu) = 3.2 \times 10^{-10} $ and $ \mathcal{B}({\mathrm{B}^0}\to 4\mu)= 5.2 \times 10^{-11} $ are also shown.
png pdf	Figure 6-f: Four-muon mass distributions for the six event categories. The combined expected signal PDFs for branching ratios $ \mathcal{B}(\mathrm{B}_{s}^{0}\to 4\mu) = 3.2 \times 10^{-10} $ and $ \mathcal{B}({\mathrm{B}^0}\to 4\mu)= 5.2 \times 10^{-11} $ are also shown.
png pdf	Figure 7: Exclusion limits at 95% CL in the $ \mathcal{B}({\mathrm{B}^0} \rightarrow \mu^{+} \mu^{-} \mu^{+} \mu^{-}) $ vs.\ $ \mathcal{B}(\mathrm{B}_{s}^{0} \rightarrow \mu^{+} \mu^{-} \mu^{+} \mu^{-}) $ plane.

Tables
png pdf	Table 1: Mass resolution categories, with their corresponding signal region and veto definitions. The signal mass windows and the veto regions are defined to extend three standard deviations on either side of the $ {\mathrm{B}} $ mass values [44] (below the $ {\mathrm{B}^0} $ and above the $ \mathrm{B}_{s}^{0} $ mass) and $ \mathrm{J}/\psi $, \PGyP2S, $ \phi $, and $ \omega $ meson masses, respectively.
png pdf	Table 2: Event categories. The three mass resolution regions, defined in Table 1, are subdivided into six subcategories, based on the BDT score. The signal purity is higher for the higher-resolution and higher-score categories.
png pdf	Table 3: Summary of systematic uncertainties. The `norm` uncertainties directly affect the signal yield, while the `shape` uncertainties affect the shape of the signal or background PDFs. The symbol $ \oplus $ indicates the sum in quadrature, while the dash indicates that a range of systematic uncertainties is applied to different event categories. In the last column, `yes` indicates that the uncertainty is correlated across all six categories, whereas `anti` indicates that the uncertainty is anti-correlated between the subcategories 1 and 2 within the same mass resolution bin, while independent of the other ones.

Summary

A search for the rare decays $ \mathrm{B}_{s}^{0} \to \mu^{+} \mu^{-} \mu^{+} \mu^{-} $ and $ {\mathrm{B}^0} \to \mu^{+} \mu^{-} \mu^{+} \mu^{-} $ has been conducted using a data sample of proton-proton collisions at $ \sqrt{s} = $ 13.6 TeV, corresponding to an integrated luminosity of 171 fb$^{-1}$ and collected between 2022 and 2024. The signals are normalized to the process $ \mathrm{B}_{s}^{0} \rightarrow \mathrm{J}/\psi(\mu \mu) \phi( \mu \mu) $, which has the same final-state particles and similar kinematic properties, thus reducing systematic uncertainties. The only relevant residual background consists of combinatorial four-muon events, which are suppressed by means of a multivariate discriminator. Events are categorized by mass resolution and signal purity, and the four-muon invariant mass distributions are simultaneously fitted using an unbinned maximum likelihood fit. No significant excess over background expectations is observed and upper limits at 95% confidence level are obtained, $ \mathcal{B}({\mathrm{B}^0}\to 4\mu) < 1.3 (1.4) \times 10^{-10} $ and $ \mathcal{B}(\mathrm{B}_{s}^{0}\to 4\mu) < 5.7 (6.0) \times 10^{-10} $. These results represent an improvement of approximately 30% over previous best exclusions. The $ \mathrm{B}_{s}^{0} $ upper limit is a factor of six above the SM prediction of $ \mathcal{B}(\mathrm{B}_{s}^{0} \to 4\mu) = (0.9-1.0) \times 10^{-10} $. Since the analysis is close to a background-free regime, its sensitivity is expected to improve faster than the square root of the integrated luminosity. With the full Run 2 and Run 3 data set combined, the sensitivity of this search is expected to approach the SM prediction. On the other hand, the SM prediction of $ \mathcal{B}({\mathrm{B}^0} \to 4\mu) = (0.4-4.0) \times 10^{-12} $ lies about two orders of magnitude below the current exclusion limit. Therefore, the $ {\mathrm{B}^0} $ channel constitutes a probe of BSM contributions in the near future. In this work, exclusion contours in the $ \mathcal{B}({\mathrm{B}^0} \rightarrow \mu^{+} \mu^{-} \mu^{+} \mu^{-}) $ vs.\ $ \mathcal{B}(\mathrm{B}_{s}^{0} \rightarrow \mu^{+} \mu^{-} \mu^{+} \mu^{-}) $ plane are reported for the first time. This approach removes the implicit assumption that only one of the two decays occurs and offers a more complete characterization of possible BSM contributions, as they would affect both decay channels through the same Wilson coefficients.

Additional Figures
png pdf	Additional Figure 1: Fit to the $\mu\mu KK$ invariant mass distribution. The two kaon candidate tracks are assigned the K mass. The dimuon (dikaon) mass is forced to the $\mathrm{J}\!/\!\psi$ ($\phi$) mass to improve the resolution.
png pdf	Additional Figure 2-a: $L_{xy}^{sig}$ and Vertex probability distributions in signal MC and data sidebands.
png pdf	Additional Figure 2-b: $L_{xy}^{sig}$ and Vertex probability distributions in signal MC and data sidebands.
png pdf	Additional Figure 3-a: Combined signal PDF in the B1 and C1 categories, for $\mathcal{B}(\mathrm{B}^0_s \to 4\mu)=1.0\times 10^{-9}$ and $\mathcal{B}(\mathrm{B}^0 \to 4\mu) = 4\times 10^{-10}$.
png pdf	Additional Figure 3-b: Combined signal PDF in the B1 and C1 categories, for $\mathcal{B}(\mathrm{B}^0_s \to 4\mu)=1.0\times 10^{-9}$ and $\mathcal{B}(\mathrm{B}^0 \to 4\mu) = 4\times 10^{-10}$.
png pdf	Additional Figure 4: Signal strength multiplier $r$ as a function of BDT cuts category C.
png pdf	Additional Figure 5: Observed signal strength multiplier $r$ as a function of different branching ratio combinations for $ \mathrm{B}^0 \to \mu^+ \mu^- \mu^+ \mu^- $ and $ \mathrm{B}^0_s \to \mu^+ \mu^- \mu^+ \mu^- $.

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