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Angular analysis of the rare decay $B_s^0\to\phi\mu^+\mu^-$

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Abstract

An angular analysis of the rare decay $B^0_s\rightarrow\phi\mu^+\mu^-$ is presented, using proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of $7$, $8$ and $13 \rm{TeV}$, corresponding to an integrated luminosity of $8.4 \rm{fb}^{-1}$. The observables describing the angular distributions of the decay $B^0_s\rightarrow\phi\mu^+\mu^-$ are determined in regions of $q^2$, the square of the dimuon invariant mass. The results are consistent with Standard Model predictions.

Figures and captions

The $m( K ^+ K ^- \mu ^+\mu ^- )$ distribution for $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates integrated over the $0.1 < q^2 <0.98\text{ Ge V} ^2 /c^4 $, $1.1 < q^2 <8\text{ Ge V} ^2 /c^4 $, $11.0 < q^2 < 12.5\text{ Ge V} ^2 /c^4 $ and $15.0 < q^2 <18.9\text{ Ge V} ^2 /c^4 $ regions for the data-taking periods 2011-2012 (top left), 2016 (top right), and 2017--2018 (bottom). The data are overlaid with the PDF used to describe the $m( K ^+ K ^- \mu ^+\mu ^- )$ spectrum, fitted separately for each data set.

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Angular projections in the region $1.1 < q^2 <6.0\text{ Ge V} ^2 /c^4 $ for the combined 2011--2012, 2016 and 2017--2018 data sets. The data are overlaid with the projection of the combined PDF. The red shaded area indicates the background component and the solid black line the total PDF. The angular projections are given for candidates in (left) the entire mass region used to determine the observables in this paper and (right) the signal mass window $\pm50\text{ Me V /}c^2 $ around the known $ B ^0_ s $ mass.

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$ C P$ -averaged angular observables $ F_{\mathrm{L}}$ and $S_{3,4,7}$ and $ C P$ -asymmetries $ A_{\mathrm{FB}}^{ C P }$ and $A_{5,8,9}$ shown by black crosses, overlaid with the SM prediction [23,24,25,26] as blue boxes, where available. The grey crosses indicate the results from Ref. [4]. The grey bands indicate the regions of the charmonium resonances and the $ B ^0_ s \rightarrow \phi\phi$ region.

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Mass distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the different $ q^2$ regions for the combined 2011--2012, 2016 and 2017--2018 data sets. The data are overlaid with the projection of the combined PDF. The red shaded area indicates the background component and the solid black line the total PDF.

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Projections in the region $0.1 < q^2 <0.98\text{ Ge V} ^2 /c^4 $ for the angular distributions of the combined 2011--2012, 2016 and 2017--2018 data sets. The data are overlaid with the projection of the combined PDF. The red shaded area indicates the background component and the solid black line the total PDF. The angular projections are given for candidates in (left) the entire mass region used to determine the observables in this paper and (right) the signal mass window $\pm50\text{ Me V /}c^2 $ around the known $ B ^0_ s $ mass.

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Projections in the region $1.1 < q^2 <4.0\text{ Ge V} ^2 /c^4 $ for the angular distributions of the combined 2011--2012, 2016 and 2017--2018 data set. The data are overlaid with the projection of the combined PDF. The red shaded area indicates the background component and the solid black line the total PDF. The angular projections are given for candidates in (left) the entire mass region used to determine the observables in this paper and (right) the signal mass window $\pm50\text{ Me V /}c^2 $ around the known $ B ^0_ s $ mass.

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Projections in the region $4.0 < q^2 <6.0\text{ Ge V} ^2 /c^4 $ for the angular distributions of the combined 2011--2012, 2016 and 2017--2018 data sets. The data are overlaid with the projection of the combined PDF. The red shaded area indicates the background component and the solid black line the total PDF. The angular projections are given for candidates in (left) the entire mass region used to determine the observables in this paper and (right) the signal mass window $\pm50\text{ Me V /}c^2 $ around the known $ B ^0_ s $ mass.

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Projections in the region $6.0 < q^2 <8.0\text{ Ge V} ^2 /c^4 $ for the angular distributions of the combined 2011--2012, 2016 and 2017--2018 data sets. The data are overlaid with the projection of the combined PDF. The red shaded area indicates the background component and the solid black line the total PDF. The angular projections are given for candidates in (left) the entire mass region used to determine the observables in this paper and (right) the signal mass window $\pm50\text{ Me V /}c^2 $ around the known $ B ^0_ s $ mass.

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Projections in the region $11.0 < q^2 <12.5\text{ Ge V} ^2 /c^4 $ for the angular distributions of the combined 2011--2012, 2016 and 2017--2018 data sets. The data are overlaid with the projection of the combined PDF. The red shaded area indicates the background component and the solid black line the total PDF. The angular projections are given for candidates in (left) the entire mass region used to determine the observables in this paper and (right) the signal mass window $\pm50\text{ Me V /}c^2 $ around the known $ B ^0_ s $ mass.

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Projections in the region $1.1 < q^2 <6.0\text{ Ge V} ^2 /c^4 $ for the angular distributions of the combined 2011--2012, 2016 and 2017--2018 data sets. The data are overlaid with the projection of the combined PDF. The red shaded area indicates the background component and the solid black line the total PDF. The angular projections are given for candidates in (left) the entire mass region used to determine the observables in this paper and (right) the signal mass window $\pm50\text{ Me V /}c^2 $ around the known $ B ^0_ s $ mass.

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Projections in the region $15.0 < q^2 <18.9\text{ Ge V} ^2 /c^4 $ for the angular distributions of the combined 2011--2012, 2016 and 2017--2018 data sets. The data are overlaid with the projection of the combined PDF. The red shaded area indicates the background component and the solid black line the total PDF. The angular projections are given for candidates in (left) the entire mass region used to determine the observables in this paper and (right) the signal mass window $\pm50\text{ Me V /}c^2 $ around the known $ B ^0_ s $ mass.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $0.1< q^2 <0.98\text{ Ge V} ^2 /c^4 $ for data taken in 2011--2012. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $0.1< q^2 <0.98\text{ Ge V} ^2 /c^4 $ for data taken in 2016. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $0.1< q^2 <0.98\text{ Ge V} ^2 /c^4 $ for data taken in 2017--2018. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $1.1< q^2 <4.0\text{ Ge V} ^2 /c^4 $ for data taken in 2011--2012. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $1.1< q^2 <4.0\text{ Ge V} ^2 /c^4 $ for data taken in 2016. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $1.1< q^2 <4.0\text{ Ge V} ^2 /c^4 $ for data taken in 2017--2018. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $4.0< q^2 <6.0\text{ Ge V} ^2 /c^4 $ for data taken in 2011--2012. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $4.0< q^2 <6.0\text{ Ge V} ^2 /c^4 $ for data taken in 2016. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $4.0< q^2 <6.0\text{ Ge V} ^2 /c^4 $ for data taken in 2017--2018. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $6.0< q^2 <8.0\text{ Ge V} ^2 /c^4 $ for data taken in 2011--2012. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $6.0< q^2 <8.0\text{ Ge V} ^2 /c^4 $ for data taken in 2016. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $6.0< q^2 <8.0\text{ Ge V} ^2 /c^4 $ for data taken in 2017--2018. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $11.0< q^2 <12.5\text{ Ge V} ^2 /c^4 $ for data taken in 2011--2012. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $11.0< q^2 <12.5\text{ Ge V} ^2 /c^4 $ for data taken in 2016. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $11.0< q^2 <12.5\text{ Ge V} ^2 /c^4 $ for data taken in 2017--2018. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $1.1< q^2 <6.0\text{ Ge V} ^2 /c^4 $ for data taken in 2011--2012. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $1.1< q^2 <6.0\text{ Ge V} ^2 /c^4 $ for data taken in 2016. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $1.1< q^2 <6.0\text{ Ge V} ^2 /c^4 $ for data taken in 2017--2018. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $15.0< q^2 <18.9\text{ Ge V} ^2 /c^4 $ for data taken in 2011--2012. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $15.0< q^2 <18.9\text{ Ge V} ^2 /c^4 $ for data taken in 2016. The data are overlaid with the projections of the fitted PDF.

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Mass and angular distributions of $ B ^0_ s \rightarrow \phi\mu ^+ \mu ^- $ candidates in the region $15.0< q^2 <18.9\text{ Ge V} ^2 /c^4 $ for data taken in 2017--2018. The data are overlaid with the projections of the fitted PDF.

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Animated gif made out of all figures.

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Tables and captions

$ C P$ averages $ F_{\mathrm{L}}$ and $S_{3,4,7}$ and $ C P$ asymmetries $ A_{\mathrm{FB}}^{ C P }$ and $A_{5,8,9}$ obtained from the maximum likelihood fit. The first uncertainty is statistical and the second is the total systematic uncertainty, as described in Sec. 6.

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Sources of the systematic uncertainties associated with the angular observables. As the size of a systematic effect can vary strongly depending on the observable and $ q^2$ region in question, only the magnitude of the largest systematic uncertainty across all regions, rounded up to the next multiple of 0.005, is indicated.

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Correlation matrix for the $ q^2$ regions $0.1 < q^2 < 0.98 \text{ Ge V} ^2 /c^4 $ and $1.1 < q^2 <4.0 \text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ q^2$ regions $4.0< q^2 < 6.0\text{ Ge V} ^2 /c^4 $, $6.0 < q^2 < 8.0 \text{ Ge V} ^2 /c^4 $ and $11.0 < q^2 < 12.5 \text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ q^2$ region $1.1 < q^2 < 6.0 \text{ Ge V} ^2 /c^4 $ and $15.0 < q^2 < 18.9 \text{ Ge V} ^2 /c^4 $.

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Supplementary Material [file]

Supplementary material full pdf

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This ZIP file contains supplemetary material for the publication LHCb-PAPER-2021-021. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png : The figures in variuous formats

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Created on 21 December 2024.