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| CMS-PAS-BPH-24-005 | ||
| Simultaneous differential branching fraction and isospin asymmetry measurements of rare $ \mathrm{b \to s} \mu \mu $ decays with 2022--2024 data | ||
| CMS Collaboration | ||
| 2026-08-20 | ||
| Abstract: In the standard model (SM), flavor-changing neutral-current decays corresponding to b$ \to $s$ \mu\mu $ transitions are forbidden at tree level and proceed only through higher-order electroweak loop diagrams. These decays are therefore rare and sensitive probes of potential physics beyond the SM. This note reports the differential branching fractions, $ d\mathcal{B}/dq^{2} $, as a function of the squared dimuon invariant mass, $ q^{2} $, for six rare decays of b-flavored hadrons, $ \mathrm{B}^{+}\to \mathrm{K}^{+}\mu\mu $, $ \mathrm{B}^{+}\to \mathrm{K}^{*+}\mu\mu $, $ \mathrm{B}^{0}\to \mathrm{K}_{\mathrm{S}}^{0}\mu\mu $, $ \mathrm{B}^{0}\to \mathrm{K}^{*0}\mu\mu $, $ \mathrm{B}_{\mathrm{s}}^{0}\to\phi\mu\mu $, and $ \Lambda_{\mathrm{b}}^{0}\to\Lambda^{0}\mu\mu $. The isospin asymmetries of $ \mathrm{B}^{+} $ vs $ \mathrm{B}^{0} $ are also measured, for pseudoscalar and vector K final states, as function of $ q^2 $. The measured $ d\mathcal{B}/dq^{2} $ fractions are consistent with previous experimental results and remain below the SM predictions, while the measured isospin asymmetries are consistent with SM expectations. The results are obtained using proton-proton collisions recorded by the CMS detector during 2022-2024 at $ \sqrt{s}=13.6 \mathrm{TeV} $, corresponding to an integrated luminosity of 172 fb$ ^{-1} $. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Feynman diagrams for the decay of a b quark into a s quark and a lepton pair in the SM ("penguin" diagram - left and "box" diagram center) and in a NP scenario (right). |
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Figure 2:
Total efficiency as a function of the $ q^{2} $ normalized to the efficiency product of the $ \mathrm{J}/\psi $ mode. |
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Figure 3:
Simultaneous fit to the mass distributions for the six rare decays $ X_{\mathrm{b}}\to\Upsilon_{\mathrm{s}}\mu\mu $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{K^+}\mu\mu $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{K^0_S}\mu\mu $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in middle left; $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right; $ \mathrm{B}_{s}\to\phi\mu\mu $ in lower left; and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 3-a:
Simultaneous fit to the mass distributions for the six rare decays $ X_{\mathrm{b}}\to\Upsilon_{\mathrm{s}}\mu\mu $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{K^+}\mu\mu $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{K^0_S}\mu\mu $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in middle left; $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right; $ \mathrm{B}_{s}\to\phi\mu\mu $ in lower left; and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 3-b:
Simultaneous fit to the mass distributions for the six rare decays $ X_{\mathrm{b}}\to\Upsilon_{\mathrm{s}}\mu\mu $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{K^+}\mu\mu $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{K^0_S}\mu\mu $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in middle left; $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right; $ \mathrm{B}_{s}\to\phi\mu\mu $ in lower left; and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 3-c:
Simultaneous fit to the mass distributions for the six rare decays $ X_{\mathrm{b}}\to\Upsilon_{\mathrm{s}}\mu\mu $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{K^+}\mu\mu $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{K^0_S}\mu\mu $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in middle left; $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right; $ \mathrm{B}_{s}\to\phi\mu\mu $ in lower left; and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 3-d:
Simultaneous fit to the mass distributions for the six rare decays $ X_{\mathrm{b}}\to\Upsilon_{\mathrm{s}}\mu\mu $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{K^+}\mu\mu $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{K^0_S}\mu\mu $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in middle left; $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right; $ \mathrm{B}_{s}\to\phi\mu\mu $ in lower left; and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 3-e:
Simultaneous fit to the mass distributions for the six rare decays $ X_{\mathrm{b}}\to\Upsilon_{\mathrm{s}}\mu\mu $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{K^+}\mu\mu $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{K^0_S}\mu\mu $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in middle left; $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right; $ \mathrm{B}_{s}\to\phi\mu\mu $ in lower left; and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 3-f:
Simultaneous fit to the mass distributions for the six rare decays $ X_{\mathrm{b}}\to\Upsilon_{\mathrm{s}}\mu\mu $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{K^+}\mu\mu $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{K^0_S}\mu\mu $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in middle left; $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right; $ \mathrm{B}_{s}\to\phi\mu\mu $ in lower left; and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 4:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \mathrm{J}/\psi \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{J}/\psi\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\mathrm{J}/\psi{\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\mathrm{J}/\psi\phi $ in lower left; and $ \Lambda_{b}^{0}\to\mathrm{J}/\psi\Lambda $ in lower right. |
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Figure 4-a:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \mathrm{J}/\psi \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{J}/\psi\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\mathrm{J}/\psi{\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\mathrm{J}/\psi\phi $ in lower left; and $ \Lambda_{b}^{0}\to\mathrm{J}/\psi\Lambda $ in lower right. |
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Figure 4-b:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \mathrm{J}/\psi \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{J}/\psi\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\mathrm{J}/\psi{\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\mathrm{J}/\psi\phi $ in lower left; and $ \Lambda_{b}^{0}\to\mathrm{J}/\psi\Lambda $ in lower right. |
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Figure 4-c:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \mathrm{J}/\psi \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{J}/\psi\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\mathrm{J}/\psi{\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\mathrm{J}/\psi\phi $ in lower left; and $ \Lambda_{b}^{0}\to\mathrm{J}/\psi\Lambda $ in lower right. |
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Figure 4-d:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \mathrm{J}/\psi \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{J}/\psi\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\mathrm{J}/\psi{\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\mathrm{J}/\psi\phi $ in lower left; and $ \Lambda_{b}^{0}\to\mathrm{J}/\psi\Lambda $ in lower right. |
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Figure 4-e:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \mathrm{J}/\psi \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{J}/\psi\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\mathrm{J}/\psi{\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\mathrm{J}/\psi\phi $ in lower left; and $ \Lambda_{b}^{0}\to\mathrm{J}/\psi\Lambda $ in lower right. |
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Figure 4-f:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \mathrm{J}/\psi \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\mathrm{J}/\psi\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\mathrm{J}/\psi\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\mathrm{J}/\psi{\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\mathrm{J}/\psi\phi $ in lower left; and $ \Lambda_{b}^{0}\to\mathrm{J}/\psi\Lambda $ in lower right. |
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Figure 5:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \psi(2S) \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\psi(2S)\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\psi(2S){\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\psi(2S)\phi $ in lower left; and $ \Lambda_{b}^{0}\to\psi(2S)\Lambda^{0} $ in lower right. |
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Figure 5-a:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \psi(2S) \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\psi(2S)\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\psi(2S){\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\psi(2S)\phi $ in lower left; and $ \Lambda_{b}^{0}\to\psi(2S)\Lambda^{0} $ in lower right. |
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Figure 5-b:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \psi(2S) \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\psi(2S)\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\psi(2S){\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\psi(2S)\phi $ in lower left; and $ \Lambda_{b}^{0}\to\psi(2S)\Lambda^{0} $ in lower right. |
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Figure 5-c:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \psi(2S) \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\psi(2S)\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\psi(2S){\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\psi(2S)\phi $ in lower left; and $ \Lambda_{b}^{0}\to\psi(2S)\Lambda^{0} $ in lower right. |
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Figure 5-d:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \psi(2S) \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\psi(2S)\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\psi(2S){\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\psi(2S)\phi $ in lower left; and $ \Lambda_{b}^{0}\to\psi(2S)\Lambda^{0} $ in lower right. |
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Figure 5-e:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \psi(2S) \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\psi(2S)\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\psi(2S){\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\psi(2S)\phi $ in lower left; and $ \Lambda_{b}^{0}\to\psi(2S)\Lambda^{0} $ in lower right. |
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Figure 5-f:
Simultaneous fit to the mass distributions for the six resonant decays $ X_{\mathrm{b}}\to \psi(2S) \Upsilon_{\mathrm{s}} $ decays, using the full 2022--2024 data. The $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K^+} $ channel is displayed in upper left figure; $ {\mathrm{B}^0}\to\psi(2S)\mathrm{K^0_S} $ in upper right; $ {\mathrm{B}^{+}}\to\psi(2S)\mathrm{K}^{*+} $ in middle left; $ {\mathrm{B}^0}\to\psi(2S){\mathrm{K}}{\ast0} $ in middle right; $ \mathrm{B}_{s}\to\psi(2S)\phi $ in lower left; and $ \Lambda_{b}^{0}\to\psi(2S)\Lambda^{0} $ in lower right. |
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Figure 6:
Comparison of measured differential Branching Fraction with the theoretical prediction taken from the Flavio package for (a) $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $, (c) $ {\mathrm{B}^0}\to \mathrm{K^0_S}\mu\mu $, (d) $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $, (e) $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $, and (f) $ \Lambda_{b}^{0}\to\Lambda\mu\mu $. |
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Figure 6-a:
Comparison of measured differential Branching Fraction with the theoretical prediction taken from the Flavio package for (a) $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $, (c) $ {\mathrm{B}^0}\to \mathrm{K^0_S}\mu\mu $, (d) $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $, (e) $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $, and (f) $ \Lambda_{b}^{0}\to\Lambda\mu\mu $. |
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Figure 6-b:
Comparison of measured differential Branching Fraction with the theoretical prediction taken from the Flavio package for (a) $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $, (c) $ {\mathrm{B}^0}\to \mathrm{K^0_S}\mu\mu $, (d) $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $, (e) $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $, and (f) $ \Lambda_{b}^{0}\to\Lambda\mu\mu $. |
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Figure 6-c:
Comparison of measured differential Branching Fraction with the theoretical prediction taken from the Flavio package for (a) $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $, (c) $ {\mathrm{B}^0}\to \mathrm{K^0_S}\mu\mu $, (d) $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $, (e) $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $, and (f) $ \Lambda_{b}^{0}\to\Lambda\mu\mu $. |
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Figure 6-d:
Comparison of measured differential Branching Fraction with the theoretical prediction taken from the Flavio package for (a) $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $, (c) $ {\mathrm{B}^0}\to \mathrm{K^0_S}\mu\mu $, (d) $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $, (e) $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $, and (f) $ \Lambda_{b}^{0}\to\Lambda\mu\mu $. |
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Figure 6-e:
Comparison of measured differential Branching Fraction with the theoretical prediction taken from the Flavio package for (a) $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $, (c) $ {\mathrm{B}^0}\to \mathrm{K^0_S}\mu\mu $, (d) $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $, (e) $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $, and (f) $ \Lambda_{b}^{0}\to\Lambda\mu\mu $. |
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Figure 6-f:
Comparison of measured differential Branching Fraction with the theoretical prediction taken from the Flavio package for (a) $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $, (c) $ {\mathrm{B}^0}\to \mathrm{K^0_S}\mu\mu $, (d) $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $, (e) $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $, and (f) $ \Lambda_{b}^{0}\to\Lambda\mu\mu $. |
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Figure 7:
CP-averaged isospin asymmetries measured as functions of $ q^{2} $ for $ {\mathrm{B}}\to\mathrm{K}\mu\mu $ (left) and $ {\mathrm{B}}\to\mathrm{K}^{*}\mu\mu $ (right) decays modes. |
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Figure 7-a:
CP-averaged isospin asymmetries measured as functions of $ q^{2} $ for $ {\mathrm{B}}\to\mathrm{K}\mu\mu $ (left) and $ {\mathrm{B}}\to\mathrm{K}^{*}\mu\mu $ (right) decays modes. |
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Figure 7-b:
CP-averaged isospin asymmetries measured as functions of $ q^{2} $ for $ {\mathrm{B}}\to\mathrm{K}\mu\mu $ (left) and $ {\mathrm{B}}\to\mathrm{K}^{*}\mu\mu $ (right) decays modes. |
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Figure 8:
The $ R_{\Upsilon_{\mathrm{s}}}(\psi(2S)) $ ratios. |
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Figure 9:
Breakdown of uncertainties using the COMBINE package for $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $ in upper left figure, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in upper right, $ {\mathrm{B}^0}\to \mathrm{K^0}\mu\mu $ in middle left, $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right, $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $ in lower left and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 9-a:
Breakdown of uncertainties using the COMBINE package for $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $ in upper left figure, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in upper right, $ {\mathrm{B}^0}\to \mathrm{K^0}\mu\mu $ in middle left, $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right, $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $ in lower left and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 9-b:
Breakdown of uncertainties using the COMBINE package for $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $ in upper left figure, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in upper right, $ {\mathrm{B}^0}\to \mathrm{K^0}\mu\mu $ in middle left, $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right, $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $ in lower left and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 9-c:
Breakdown of uncertainties using the COMBINE package for $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $ in upper left figure, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in upper right, $ {\mathrm{B}^0}\to \mathrm{K^0}\mu\mu $ in middle left, $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right, $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $ in lower left and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 9-d:
Breakdown of uncertainties using the COMBINE package for $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $ in upper left figure, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in upper right, $ {\mathrm{B}^0}\to \mathrm{K^0}\mu\mu $ in middle left, $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right, $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $ in lower left and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 9-e:
Breakdown of uncertainties using the COMBINE package for $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $ in upper left figure, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in upper right, $ {\mathrm{B}^0}\to \mathrm{K^0}\mu\mu $ in middle left, $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right, $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $ in lower left and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 9-f:
Breakdown of uncertainties using the COMBINE package for $ {\mathrm{B}^{+}}\to \mathrm{K^+}\mu\mu $ in upper left figure, $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ in upper right, $ {\mathrm{B}^0}\to \mathrm{K^0}\mu\mu $ in middle left, $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ in middle right, $ \mathrm{B}_{s}^{0}\to\phi\mu\mu $ in lower left and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ in lower right. |
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Figure 10:
Breakdown of uncertainties using the COMBINE package for the $ R_{\Upsilon_{\mathrm{s}}}(\psi(2S)) $ ratios. |
| Tables | |
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Table 1:
Preselection |
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Table 2:
List of BDT training variables. The training variables are listed according to their importance on the BDT output. |
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Table 3:
Systematic uncertainties of branching ratios. The "Range" column corresponds to the minimum and maximum value of the uncertainty across the $ q^{2} $ bins and decay modes. |
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Table 4:
$ \Delta m $ values. |
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Table 5:
Differential branching fraction results $ [ \text{GeV}^{-2}] $ along with the total uncertainties at 68% CL intervals. The values shown are multiplied by a factor of $ 10^{9} $. |
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Table 6:
Isospin asymmetry results along with the total uncertainties at 68% CL intervals. The values shown are multiplied by a factor of 10. |
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Table 7:
$ R_{\Upsilon_{\mathrm{s}}}(\psi(2S)) $ measurements along with the total uncertainties. The values shown are multiplied by a factor of $ \times 10^{3} $. |
| Summary |
| This note presents measurements of the differential branching fraction measurements as a function of the squared dimuon invariant mass $ d\mathcal{B}/dq^{2} $, for six rare decays of b-flavored hadrons, described at quark level by flavor-changing neutral-currents $ \mathrm{b}\to\mathrm{s}\mu\mu $: $ {\mathrm{B}^{+}}\to\mathrm{K^+}\mu\mu $, $ {\mathrm{B}^{+}}\to K^{*+}\mu\mu $, $ {\mathrm{B}^0}\to\mathrm{K^0_S}\mu\mu $, $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $, $ \mathrm{B}_{s}\to\phi\mu\mu $, and $ \Lambda_{b}^{0}\to\Lambda\mu\mu $. All differential branching fractions are measured with respect to the corresponding resonant decay with a $ \mathrm{J}/\psi $, to limit the systematic uncertainties. The results are obtained using proton-proton collisions recorded by the CMS detector at CERN LHC during 2022--2024 at $ \sqrt{s}= $ 13.6 TeV, corresponding to an integrated luminosity of 172 fb$ ^{-1} $. The results, along with the 68% CL statistical and systematic uncertainties, are obtained by fitting simultaneously the mass distributions of these decay modes and $ q^{2} $ bins using the CMS statistical analysis tool. The results are compared with the SM theoretical predictions calculated with various software packages. The pseudoscalar $ {\mathrm{B}^{+}}\to\mathrm{K^+}\mu\mu $ and $ {\mathrm{B}^0}\to\mathrm{K^0_S}\mu\mu $ modes are at the edges of the theory bands, while the vector $ {\mathrm{B}^{+}}\to\mathrm{K}^{*+}\mu\mu $ and $ {\mathrm{B}^0}\to{\mathrm{K}}^{\ast0} \mu\mu $ modes are closer to the predictions. The $ \mathrm{B}_{s}\to\phi\mu\mu $ mode is lower than all the theory predictions, as already seen by LHCb and previous CMS measurement, but with smaller uncertainties. The $ \Lambda_{b}^{0}\to\Lambda\mu\mu $ mode is dominated by the statistical uncertainty. In all cases, the tendencies that have been reported for the $ d\mathcal{B}/dq^{2} $ observables with respect to the theoretical predictions from other analyses and other experiments are verified from the current work. The statistical uncertainty is significantly reduced with respect to previous CMS and LHCb and results and are now comparable with the external systematic uncertainties arising from the normalization $ X_{\mathrm{b}}\to \mathrm{J}/\psi \Upsilon_{\mathrm{s}} $ modes. The isospin asymmetries for the pseudoscalar $ {\mathrm{B}}\to\mathrm{K}\mu\mu $ and vector $ {\mathrm{B}}\to\mathrm{K^{\ast}(892)}\mu\mu $ modes are measured, as a function of $ q^{2} $, and the results are compatible with zero, i.e.,, with the SM prediction, with significant uncertainty reduction, and more $ q^{2} $ bins due to larger sample. In addition, all the $ R_{\Upsilon_{\mathrm{s}}}(\psi(2S)) $ ratios are consistent with the corresponding world-average values, with uncertainties that are more than an order of magnitude smaller. For all the results, the compatibility with data from 2022, 2023, and 2024 is observed. |
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