CMS-BPH-15-009

CMS-BPH-15-009 ; CERN-EP-2020-188
Angular analysis of the decay $\mathrm{B^{+}}\to {\mathrm{K}^{\ast}(892)^{+}} \mu^{+} \mu^{-}$ in proton-proton collisions at $\sqrt{s} =$ 8 TeV
CMS Collaboration
27 October 2020
JHEP 04 (2021) 124
Abstract: Angular distributions of the decay $\mathrm{B^{+}}\to {\mathrm{K}^{\ast}(892)^{+}} \mu^{+} \mu^{-}$ are studied using events collected with the CMS detector in $\sqrt{s} =$ 8 TeV proton-proton collisions at the LHC, corresponding to an integrated luminosity of 20.0 fb $^{-1}$ . The forward-backward asymmetry of the muons and the longitudinal polarization of the ${\mathrm{K}^{\ast}(892)^{+}}$ meson are determined as a function of the square of the dimuon invariant mass. These are the first results from this exclusive decay mode and are in agreement with a standard model prediction.
Links: e-print arXiv:2010.13968 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Definition of the angular observables $\theta _{\mathrm{K}}$ (left), $\theta _{\ell}$ (middle), and $\phi$ (right) for the decay ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} \mu^{+} \mu^{-}}$ .
png pdf	Figure 2: The signal efficiency as a function of $\cos\theta _\mathrm{K}$ (upper row) and $\cos\theta _\ell$ (lower row) from simulation for the ${q^2}$ ranges indicated. The vertical bars indicate the statistical uncertainty. The curves show the projection of the fitted result obtained from the two-dimensional fit, as described in the text.
png pdf	Figure 2-a: The signal efficiency as a function of $\cos\theta _\mathrm{K}$ from simulation for the ${q^2}$ range indicated. The vertical bars indicate the statistical uncertainty. The curve shows the projection of the fitted result obtained from the two-dimensional fit, as described in the text.
png pdf	Figure 2-b: The signal efficiency as a function of $\cos\theta _\mathrm{K}$ from simulation for the ${q^2}$ range indicated. The vertical bars indicate the statistical uncertainty. The curve shows the projection of the fitted result obtained from the two-dimensional fit, as described in the text.
png pdf	Figure 2-c: The signal efficiency as a function of $\cos\theta _\mathrm{K}$ from simulation for the ${q^2}$ range indicated. The vertical bars indicate the statistical uncertainty. The curve shows the projection of the fitted result obtained from the two-dimensional fit, as described in the text.
png pdf	Figure 2-d: The signal efficiency as a function of $\cos\theta _\ell$ from simulation for the ${q^2}$ range indicated. The vertical bars indicate the statistical uncertainty. The curve shows the projection of the fitted result obtained from the two-dimensional fit, as described in the text.
png pdf	Figure 2-e: The signal efficiency as a function of $\cos\theta _\ell$ from simulation for the ${q^2}$ range indicated. The vertical bars indicate the statistical uncertainty. The curve shows the projection of the fitted result obtained from the two-dimensional fit, as described in the text.
png pdf	Figure 2-f: The signal efficiency as a function of $\cos\theta _\ell$ from simulation for the ${q^2}$ range indicated. The vertical bars indicate the statistical uncertainty. The curve shows the projection of the fitted result obtained from the two-dimensional fit, as described in the text.
png pdf	Figure 3: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ invariant mass (upper row), $\cos\theta _\mathrm{K}$ (middle row), and $\cos\theta _\ell$ (lower row) distributions for each ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled areas, dashed lines, and solid lines represent the signal, background, and total contributions, respectively.
png pdf	Figure 3-a: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ invariant mass distribution for the indeicated ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 3-b: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ invariant mass distribution for the indeicated ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 3-c: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ invariant mass distribution for the indeicated ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 3-d: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ $\cos\theta _\mathrm{K}$ distribution for the indeicated ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 3-e: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ $\cos\theta _\mathrm{K}$ distribution for the indeicated ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 3-f: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ $\cos\theta _\mathrm{K}$ distribution for the indeicated ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 3-g: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ $\cos\theta _\ell$ distribution for the indeicated ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 3-h: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ $\cos\theta _\ell$ distribution for the indeicated ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 3-i: The ${\mathrm{K^0_S}} \pi^{+} \mu^{+} \mu^{-}$ $\cos\theta _\ell$ distribution for the indeicated ${q^2}$ range is shown for data, along with the fit projections. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 4: The $\cos\theta _\mathrm{K}$ (upper row) and $\cos\theta _\ell$ (lower row) distributions for each ${q^2}$ range is shown for data in the invariant mass region 5.18 $< m <$ 5.38 GeV, along with the fit projections for the same region. The vertical bars on the data points indicate the statistical uncertainty. The filled areas, dashed lines, and solid lines represent the signal, background, and total contributions, respectively.
png pdf	Figure 4-a: The $\cos\theta _\mathrm{K}$ distribution for the indicated ${q^2}$ range is shown for data in the invariant mass region 5.18 $< m <$ 5.38 GeV, along with the fit projections for the same region. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 4-b: The $\cos\theta _\mathrm{K}$ distribution for the indicated ${q^2}$ range is shown for data in the invariant mass region 5.18 $< m <$ 5.38 GeV, along with the fit projections for the same region. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 4-c: The $\cos\theta _\mathrm{K}$ distribution for the indicated ${q^2}$ range is shown for data in the invariant mass region 5.18 $< m <$ 5.38 GeV, along with the fit projections for the same region. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 4-d: The $\cos\theta _\ell$ distribution for the indicated ${q^2}$ range is shown for data in the invariant mass region 5.18 $< m <$ 5.38 GeV, along with the fit projections for the same region. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 4-e: The $\cos\theta _\ell$ distribution for the indicated ${q^2}$ range is shown for data in the invariant mass region 5.18 $< m <$ 5.38 GeV, along with the fit projections for the same region. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 4-f: The $\cos\theta _\ell$ distribution for the indicated ${q^2}$ range is shown for data in the invariant mass region 5.18 $< m <$ 5.38 GeV, along with the fit projections for the same region. The vertical bars on the data points indicate the statistical uncertainty. The filled area, dashed line, and solid line represent the signal, background, and total contributions, respectively.
png pdf	Figure 5: The measured values of ${A_\mathrm {FB}}$ (left) and ${F_\mathrm {L}}$ (right) versus ${q^2}$ for ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} \mu^{+} \mu^{-}}$ decays are shown with filled squares, centered on the ${q^2}$ bin. The statistical (total) uncertainty is shown by inner (outer) vertical bars. The vertical shaded regions correspond to the regions dominated by ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} {\mathrm{J}/\psi}}$ and ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} \psi(\text{2S}})$ decays. The SM predictions and associated uncertainties are shown by the filled circles and vertical bars, with the points slightly offset from the center of the ${q^2}$ bin for clarity.
png pdf	Figure 5-a: The measured values of ${A_\mathrm {FB}}$ versus ${q^2}$ for ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} \mu^{+} \mu^{-}}$ decays are shown with filled squares, centered on the ${q^2}$ bin. The statistical (total) uncertainty is shown by inner (outer) vertical bars. The vertical shaded regions correspond to the regions dominated by ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} {\mathrm{J}/\psi}}$ and ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} \psi(\text{2S}})$ decays. The SM predictions and associated uncertainties are shown by the filled circles and vertical bars, with the points slightly offset from the center of the ${q^2}$ bin for clarity.
png pdf	Figure 5-b: The measured values of ${F_\mathrm {L}}$ versus ${q^2}$ for ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} \mu^{+} \mu^{-}}$ decays are shown with filled squares, centered on the ${q^2}$ bin. The statistical (total) uncertainty is shown by inner (outer) vertical bars. The vertical shaded regions correspond to the regions dominated by ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} {\mathrm{J}/\psi}}$ and ${\mathrm{B^{+}} \to {\mathrm{K} ^{\ast +}} \psi(\text{2S}})$ decays. The SM predictions and associated uncertainties are shown by the filled circles and vertical bars, with the points slightly offset from the center of the ${q^2}$ bin for clarity.

Tables
png pdf	Table 1: Sources of systematic uncertainties and the effect on ${A_\mathrm {FB}}$ and ${F_\mathrm {L}}$ . The values given are absolute and the ranges indicate the variation over the ${q^2}$ bins.
png pdf	Table 2: The $Y_S$ , ${A_\mathrm {FB}}$ , and ${F_\mathrm {L}}$ values from the fit for each ${q^2}$ range. The first uncertainty is statistical and the second is systematic.

Summary

The first angular analysis of the exclusive decay

$\mathrm{B^{+}}\to {\mathrm{K}^{\ast}(892)^{+}} \mu^{+} \mu^{-}$ , including the charge-conjugate state, has been performed using a sample of proton-proton collisions at a center-of-mass energy of 8 TeV. The data were collected with the CMS detector in 2012 at the LHC, and correspond to an integrated luminosity of 20.0 fb

$^{-1}$ . For each bin of the dimuon invariant mass squared (

${q^2}$ ), a three-dimensional unbinned maximum likelihood fit is performed on the distributions of the

${\mathrm{K^{\ast}(892)}}(892)^{+}\mu^{+}\mu^{-}$ invariant mass and two decay angles. The muon forward-backward asymmetry,

${A_\mathrm{FB}}$ , and the

${\mathrm{K}^{\ast}(892)^{+}}$ longitudinal polarization fraction,

${F_\mathrm{L}}$ , are extracted from the fit in bins of

${q^2}$ and found to be consistent with a standard model prediction.

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