# Observation of the decay $\overline{B}_s^0 \rightarrow \psi(2S) K^+ \pi^-$

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## Abstract

The decay $\overline{B}_s^0 \rightarrow \psi(2S) K^+ \pi^-$ is observed using a data set corresponding to an integrated luminosity of $3.0fb^{-1}$ collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV. The branching fraction relative to the $B^0\rightarrow \psi(2S) K^+ \pi^-$ decay mode is measured to be $$\frac{{\cal B}(\overline{B}^0_s \rightarrow \psi(2S) K^+ \pi^-)}{{\cal B}(B^0 \rightarrow \psi(2S) K^+ \pi^-)} = 5.38 \pm 0.36 (stat) \pm 0.22 (syst) \pm 0.31 (f_s/f_d) \%,\nonumber$$ where $f_s/f_d$ indicates the uncertainty due to the ratio of probabilities for a $b$ quark to hadronise into a $B_s^0$ or $B^0$ meson. Using an amplitude analysis, the fraction of decays proceeding via an intermediate $K^*(892)^0$ meson is measured to be $0.645 \pm 0.049 (stat) \pm 0.049 (syst)$ and its longitudinal polarisation fraction is $0.524 \pm 0.056 (stat) \pm 0.029 (syst)$. The relative branching fraction for this component is determined to be $$\frac{{\cal B}(\overline{B}^0_s \rightarrow \psi(2S) K^*(892)^0)}{{\cal B}(B^0 \rightarrow \psi(2S) K^*(892)^0)} = 5.58 \pm 0.57 (stat) \pm 0.40 (syst) \pm 0.32 (f_s/f_d) \%. \nonumber$$ In addition, the mass splitting between the $B_s^0$ and $B^0$ mesons is measured as $$M(B^0_s) - M(B^0) = 87.45 \pm 0.44 (stat) \pm 0.07 (syst) MeV/c^2. \nonumber$$

## Figures and captions

 Tree (left) and penguin (right) topologies contributing to the $B ^0_{( s )} \rightarrow \psi V$ decays where $\psi = J/\psi, \psi(2S)$ and $V = \phi, K^*(892)^0$. Fig1a.pdf [9 KiB] HiDef png [114 KiB] Thumbnail [65 KiB] *.C file Fig1b.pdf [10 KiB] HiDef png [147 KiB] Thumbnail [84 KiB] *.C file Invariant mass distribution for selected $\psi(2S)K^+ \pi^-$ candidates in the data. A fit to the model described in the text is superimposed. The full fit model is shown by the solid (red) line, the combinatorial background by the solid (yellow) and the sum of background from the exclusive $b \rightarrow \psi(2S)X$ modes considered in the text by the shaded (blue) area. The maximum of the $y$-scale is restricted so as to be able to see more clearly the $\overline{ B }{} {}^0_ s \rightarrow \psi(2S)K^+ \pi^-$ signal. The lower plot shows the differences between the fit and measured values divided by the corresponding uncertainty of the measured value, the so-called pull distribution. Fig2.pdf [16 KiB] HiDef png [252 KiB] Thumbnail [188 KiB] *.C file Dalitz plot for the selected $\overline{ B }{} {}^0_ s \rightarrow \psi(2S) K ^+ \pi^-$ candidates in the signal window $m(\psi(2S) K ^+ \pi^-) \in [5350, 5380] {\mathrm{ Me V /}c^2}$. Fig3.pdf [27 KiB] HiDef png [207 KiB] Thumbnail [231 KiB] *.C file Definition of the helicity angles. Fig4.png [85 KiB] HiDef png [20 KiB] Thumbnail [9 KiB] *.C file Distributions of (a) $\cos\theta_\mu$, (b) $\phi$, (c) $\cos\theta_K$ and (d) $m( K ^+ \pi^-)$ of simulated $B^0_s\rightarrow \psi(2S) K ^+ \pi^-$ decays in a phase space configuration (black points) with the parameterisation of the efficiency overlaid (blue lines). Fig5.pdf [38 KiB] HiDef png [239 KiB] Thumbnail [213 KiB] *.C file Distributions of (a) $\cos\theta_\mu$, (b) $\phi$, (c) $\cos\theta_K$ and (d) $m( K ^+ \pi^-)$ of $B^0_{(s)}\rightarrow \psi(2S) K ^+ \pi^-$ candidates with $m(\psi(2S) K ^+ \pi^-) > 5390 {\mathrm{ Me V /}c^2}$ (black points), with the parameterisation of the background distribution overlaid (blue lines). Fig6.pdf [26 KiB] HiDef png [206 KiB] Thumbnail [208 KiB] *.C file Distributions of (a) $\cos\theta_\mu$, (b) $\phi$, (c) $\cos\theta_K$ and (d) $m( K ^+ \pi^-)$ for selected $\overline{ B }{} {}^0_ s \rightarrow \psi(2S) K ^+ \pi^-$ candidates (black points) with the projections of the fitted amplitude model overlaid. The following components are included in the model: $K^*(892)^0$ (red dashed), LASS S-wave (green dotted), and background (grey dashed-dotted). The residual pulls are shown below each distribution. Fig7a.pdf [21 KiB] HiDef png [464 KiB] Thumbnail [179 KiB] *.C file Fig7b.pdf [20 KiB] HiDef png [420 KiB] Thumbnail [158 KiB] *.C file Fig7c.pdf [20 KiB] HiDef png [444 KiB] Thumbnail [170 KiB] *.C file Fig7d.pdf [23 KiB] HiDef png [495 KiB] Thumbnail [183 KiB] *.C file Animated gif made out of all figures. PAPER-2015-010.gif Thumbnail

## Tables and captions

 Summary of systematic uncertainties on the $K^*(892)^0$ fit fraction and $f_{\rm L}$. Rows marked with (*) refer to uncorrelated sources of uncertainty between the $B ^0_ s$ and $B ^0$ modes for the computation of the ratio of branching fractions. Table_1.pdf [50 KiB] HiDef png [114 KiB] Thumbnail [50 KiB] tex code Systematic uncertainties on the ratio of branching fractions. Table_2.pdf [38 KiB] HiDef png [95 KiB] Thumbnail [44 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [123 KiB] Fig8.pdf [3 KiB] HiDef png [174 KiB] Thumbnail [143 KiB] *C file Fig9.pdf [14 KiB] HiDef png [154 KiB] Thumbnail [132 KiB] *C file

Created on 17 August 2019.Citation count from INSPIRE on 23 August 2019.