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Angular analysis and differential branching fraction of the decay $B^0_s\to\phi\mu^+\mu^-$

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Abstract

An angular analysis and a measurement of the differential branching fraction of the decay $B^0_s\to\phi\mu^+\mu^-$ are presented, using data corresponding to an integrated luminosity of $3.0 {\rm fb^{-1}}$ of $pp$ collisions recorded by the LHCb experiment at $\sqrt{s} = 7$ and $8 {\rm TeV}$. Measurements are reported as a function of $q^{2}$, the square of the dimuon invariant mass and results of the angular analysis are found to be consistent with the Standard Model. In the range $1<q^2<6 {\rm GeV}^{2}/c^{4}$, where precise theoretical calculations are available, the differential branching fraction is found to be more than $3 \sigma$ below the Standard Model predictions.

Figures and captions

Examples of $b\rightarrow s$ loop diagrams contributing to the decay $ B ^0_ s \rightarrow \phi\mu ^+\mu ^- $ in the SM.

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Two-dimensional distribution of $ q^2$ versus the invariant mass of the $ K ^+ K ^- \mu ^+\mu ^- $ system. The signal decay $ B ^0_ s \rightarrow \phi\mu ^+\mu ^- $ is clearly visible within the $\pm50 {\mathrm{ Me V /}c^2} $ interval around the $ B ^0_ s $ mass, indicated by the dashed vertical lines. The horizontal lines denote the charmonium regions, where the tree-level decays $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi $ and $ B ^0_ s \rightarrow \psi {(2S)} \phi $ dominate.

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Invariant mass distribution for (left) $ B ^0_ s \rightarrow \phi\mu ^+\mu ^- $ signal decays, integrated over the $q^2$ bins used, and for (right) the control mode $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi $ in the $ K ^+ K ^- \mu ^+\mu ^- $ final state. The signal component is given by the solid blue area, the background component by the shaded red area.

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Differential branching fraction of the decay $ B ^0_ s \rightarrow \phi\mu ^+\mu ^- $, overlaid with SM predictions [4,5] indicated by blue shaded boxes. The vetoes excluding the charmonium resonances are indicated by grey areas.

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$ C P$ -averaged angular observables $F_{\rm L}$ and $S_{3,4,7}$ and $ C P$ asymmetries $A_{5,6,8,9}$ shown by black dots, overlaid with SM predictions [4,5], where available, indicated as blue shaded boxes. The vetoes excluding the charmonium resonances are indicated by grey areas.

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Invariant mass distributions for $ B ^0_ s \rightarrow \phi\mu ^+\mu ^- $ signal decays in bins of $q^2$. The signal component is shown by the solid blue area, the background component by the shaded red area.

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One-dimensional projections of the fit to the angles $\cos\theta_l$, $\cos\theta_K$, $\Phi$ in bins of $q^2$. The signal component is shown by the solid blue area, the background component by the shaded red area.

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One-dimensional projections of the fit to the angles $\cos\theta_l$, $\cos\theta_K$, $\Phi$ in bins of $q^2$. The signal component is shown by the solid blue area, the background component by the shaded red area.

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Confidence level obtained from a likelihood scan (shaded blue) and from the Feldman-Cousins method (solid black). The shaded blue and solid red vertical lines indicate the corresponding $68\%$ CL intervals obtained from the likelihood scan and the Feldman-Cousins method, respectively.

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Confidence level obtained from a likelihood scan (shaded blue) and from a Feldman-Cousins method (solid black). The shaded blue and solid red vertical lines indicate the corresponding $68\%$ CL intervals obtained from the likelihood scan and the Feldman-Cousins method, respectively.

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Confidence level obtained from a likelihood scan (shaded blue) and from a Feldman-Cousins method (solid black). The shaded blue and solid red vertical lines indicate the corresponding $68\%$ CL intervals obtained from the likelihood scan and the Feldman-Cousins method, respectively.

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Confidence level obtained from a likelihood scan (shaded blue) and from a Feldman-Cousins method (solid black). The shaded blue and solid red vertical lines indicate the corresponding $68\%$ CL intervals obtained from the likelihood scan and the Feldman-Cousins method, respectively.

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Confidence level obtained from a likelihood scan (shaded blue) and from a Feldman-Cousins method (solid black). The shaded blue and solid red vertical lines indicate the corresponding $68\%$ CL intervals obtained from the likelihood scan and the Feldman-Cousins method, respectively.

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Confidence level obtained from a likelihood scan (shaded blue) and from a Feldman-Cousins method (solid black). The shaded blue and solid red vertical lines indicate the corresponding $68\%$ CL intervals obtained from the likelihood scan and the Feldman-Cousins method, respectively.

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Confidence level obtained from a likelihood scan (shaded blue) and from a Feldman-Cousins method (solid black). The shaded blue and solid red vertical lines indicate the corresponding $68\%$ CL intervals obtained from the likelihood scan and the Feldman-Cousins method, respectively.

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Confidence level obtained from a likelihood scan (shaded blue) and from a Feldman-Cousins method (solid black). The shaded blue and solid red vertical lines indicate the corresponding $68\%$ CL intervals obtained from the likelihood scan and the Feldman-Cousins method, respectively.

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Tables and captions

The signal yields for $ B ^0_ s \rightarrow \phi\mu ^+\mu ^- $ decays, as well as the differential branching fraction relative to the normalisation mode and the absolute differential branching fraction, in bins of $q^2$. The given uncertainties are (from left to right) statistical, systematic, and the uncertainty on the branching fraction of the normalisation mode.

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Systematic uncertainties $[10^{-5}\mathrm{ Ge V} ^{-2}c^{4}]$ on the branching fraction ratio ${\rm d}\cal B ( B ^0_ s \rightarrow \phi\mu ^+\mu ^- )/\cal B ( B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi){\rm d} q^2 $ per bin of $ q^2$ $[ {\mathrm{ Ge V^2 /}c^4} ]$.

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(Top) $ C P$ -averaged angular observables $F_{\rm L}$ and $S_{3,4,7}$ and (bottom) $ C P$ asymmetries $A_{5,6,8,9}$ obtained from the unbinned maximum likelihood fit, where the first uncertainty is statistical and the second is systematic.

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Correlation matrices for the $q^2$ bins $0.1<q^2<2.0 {\mathrm{ Ge V^2 /}c^4} $, $2.0<q^2<5.0 {\mathrm{ Ge V^2 /}c^4} $ and $5.0<q^2<8.0 {\mathrm{ Ge V^2 /}c^4} $.

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Correlation matrices for the $q^2$ bins $11.0<q^2<12.5 {\mathrm{ Ge V^2 /}c^4} $, $15.0<q^2<17.0 {\mathrm{ Ge V^2 /}c^4} $ and $17.0<q^2<19.0 {\mathrm{ Ge V^2 /}c^4} $.

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Correlation matrices for the $q^2$ bins $1.0<q^2<6.0 {\mathrm{ Ge V^2 /}c^4} $ and $15.0<q^2<19.0 {\mathrm{ Ge V^2 /}c^4} $.

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Supplementary Material [file]

Supplementary material full pdf

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This ZIP file contains supplementary material for the publication of LHCb-PAPER-2015-023. The files are: supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps, *.C : The figures in various formats

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Created on 20 February 2021.