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Angular Analysis of the $B^{+}\rightarrow K^{\ast+}\mu^{+}\mu^{-}$ Decay

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Abstract

We present an angular analysis of the $B^{+}\rightarrow K^{\ast+}(\rightarrow K_{S}^{0}\pi^{+})\mu^{+}\mu^{-}$ decay using 9$ fb^{-1}$ of $pp$ collision data collected with the LHCb experiment. For the first time, the full set of CP-averaged angular observables is measured in intervals of the dimuon invariant mass squared. Local deviations from Standard Model predictions are observed, similar to those in previous LHCb analyses of the isospin-partner $B^{0}\rightarrow K^{\ast0}\mu^{+}\mu^{-}$ decay. The global tension is dependent on which effective couplings are considered and on the choice of theory nuisance parameters.

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Distribution of the $ K ^0_{\mathrm{S}} \pi ^+ \mu ^+\mu ^- $ invariant mass. The black points represent the full data set, while the solid curve shows the fit result. The background component is represented by the orange shaded area.

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The $ C P$ -averaged observables (left) $P_2$ and (right) $P^\prime_5$ in intervals of $ q^2$ . The first (second) error bars represent the statistical (total) uncertainties. The theoretical predictions in blue are based on Ref. [78] with hadronic form factors taken from Refs. [79,80,81] and are obtained with the Flavio software package [85] (version 2.0.0). The theoretical predictions in orange are based on Refs. [82,83] with hadronic form factors from Ref. [84]. The grey bands indicate the regions of excluded $\phi(1020)$, $ { J \mskip -3mu/\mskip -2mu\psi }$ and $\psi {(2S)}$ resonances.

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The $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ versus $ q^2$ . The first (second) error bars represent the statistical (total) uncertainties. The theoretical predictions are based on Refs. [78,79,80,81]. The grey bands indicate regions of excluded resonances.

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The optimised observables $P_1$ to $P^{\prime}_8$ versus $ q^2$ . The first (second) error bars represent the statistical (total) uncertainties. The theoretical predictions are based on Refs. [82,83,84] (orange) and on Refs. [78,79,80,81] (blue). The grey bands indicate regions of excluded resonances.

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Projections for the invariant mass $m( K ^0_{\mathrm{S}} \pi ^+ \mu ^+\mu ^- )$ in the ten $ q^2$ intervals. The black points represent the data, while the solid curve shows the fit result. The background component is represented by the orange shaded area.

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Projections for the angle $\cos{\theta_K}$ in the ten $ q^2$ intervals. The black points represent the data, while the solid curve shows the fit result. The background component is represented by the orange shaded area. The invariant mass $m( K ^0_{\mathrm{S}} \pi ^+ \mu ^+\mu ^- )$ is required to be within $50\text{ Me V /}c^2 $ of the measured $ B ^+$ meson mass.

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Projections for the angle $\cos{\theta_\ell}$ in the ten $ q^2$ intervals. The black points represent the data, while the solid curve shows the fit result. The background component is represented by the orange shaded area. The invariant mass $m( K ^0_{\mathrm{S}} \pi ^+ \mu ^+\mu ^- )$ is required to be within $50\text{ Me V /}c^2 $ of the measured $ B ^+$ meson mass.

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Projections for the angle $\phi$ in the ten $ q^2$ intervals. The black points represent the data, while the solid curve shows the fit result. The background component is represented by the orange shaded area. The invariant mass $m( K ^0_{\mathrm{S}} \pi ^+ \mu ^+\mu ^- )$ is required to be within $50\text{ Me V /}c^2 $ of the measured $ B ^+$ meson mass.

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Tables and captions

Results for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$. The first uncertainties are statistical and the second systematic.

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Results for the optimised observables $ F_{\rm L}$ and $P_1\text{--}P_8^{\prime}$. The first uncertainties are statistical and the second systematic.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $0.10< q^2 <0.98\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $1.1< q^2 <2.5\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $2.5< q^2 <4.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $4.0< q^2 <6.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $6.0< q^2 <8.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $11.0< q^2 <12.5\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $15.0< q^2 <17.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $17.0< q^2 <19.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $1.1< q^2 <6.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ , $ A_{\rm FB}$ and $S_{3} \text{--} S_{9}$ from the maximum-likelihood fit in the interval $15.0< q^2 <19.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $0.10< q^2 <0.98\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $1.1< q^2 <2.5\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $2.5< q^2 <4.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $4.0< q^2 <6.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $6.0< q^2 <8.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $11.0< q^2 <12.5\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $15.0< q^2 <17.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $17.0< q^2 <19.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $1.1< q^2 <6.0\text{ Ge V} ^2 /c^4 $.

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Correlation matrix for the $ C P$ -averaged observables $ F_{\rm L}$ and $P_{i}^{(\prime)}$ from the maximum-likelihood fit in the interval $15.0< q^2 <19.0\text{ Ge V} ^2 /c^4 $.

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Maximum values for each source of systematic uncertainty.

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Yields of signal candidates in the ten $ q^2$ intervals. They are obtained from extended maximum-likelihood fits to the $m( K ^0_{\mathrm{S}} \pi ^+ \mu ^+\mu ^- )$ distribution. The total number corresponds to the sum of the eight nominal $ q^2$ intervals.

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Supplementary Material [file]

Supplementary material full pdf

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This ZIP file contains supplementary material for the publication LHCb-PAPER-2020-041. The files are: Supplementary.pdf : An overview of the extra figures Supplementary.tex : the LaTeX code of the supplementary material Fig9.pdf, Fig9.png, Fig9.eps : Figure 9 in various graphic formats Fig9.py, Fig9.csv : Figure 9 as python macro plus data values

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Created on 20 April 2024.