# Measurement of $CP$ asymmetries and polarisation fractions in $B_s^0 \rightarrow K^{*0}\overline{K}{}^{*0}$ decays

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## Abstract

An angular analysis of the decay $B_s^0 \rightarrow K^{*0}\bar{K}{}^{*0}$ is performed using $pp$ collisions corresponding to an integrated luminosity of $1.0$ ${fb}^{-1}$ collected by the LHCb experiment at a centre-of-mass energy $\sqrt{s} = 7$ TeV. A combined angular and mass analysis separates six helicity amplitudes and allows the measurement of the longitudinal polarisation fraction $f_L = 0.201 \pm 0.057 {(stat.)} \pm 0.040{(syst.)}$ for the $B_s^0 \rightarrow K^*(892)^0 \bar{K}{}^*(892)^0$ decay. A large scalar contribution from the $K^{*}_{0}(1430)$ and $K^{*}_{0}(800)$ resonances is found, allowing the determination of additional $CP$ asymmetries. Triple product and direct $CP$ asymmetries are determined to be compatible with the Standard Model expectations. The branching fraction $\mathcal{B}(B_s^0 \rightarrow K^*(892)^0 \bar{K}{}^*(892)^0)$ is measured to be $(10.8 \pm 2.1 {\ \rm (stat.)} \pm 1.4 {\ \rm (syst.)} \pm 0.6 \ (f_d/f_s) ) \times 10^{-6}$.

## Figures and captions

 Definition of the angles involved in the analysis of $B ^0_ s \rightarrow K ^{*0} \overline{ K }{} {}^{*0}$ decays. Fig1.pdf [8 KiB] HiDef png [88 KiB] Thumbnail [45 KiB] *.C file Invariant mass distribution for selected $K^+\pi^- K^- \pi^+$ candidates. The (blue) solid line is the result of the fit explained in the text. The $B ^0_ s$ and $B ^0$ signal peaks are shown as as dashed-dotted lines (pink and dark green, respectively). The various peaking background components are represented as dotted lines: (red) $B ^0 \rightarrow \phi K ^{*0}$ , (green) $\Lambda^0_b \rightarrow p\pi^- K^- \pi^+$ and (light blue) partially reconstructed decays. The (grey) dotted line is the combinatorial background component. The normalised residual (pull) is shown below. Fig2.pdf [25 KiB] HiDef png [269 KiB] Thumbnail [200 KiB] *.C file Results of the simultaneous fit to $B ^0_ s \rightarrow K^+\pi^-K^-\pi^+$ candidates (blue solid line) in the three helicity angles. The dots represent the data after background subtraction and acceptance correction. The red dashed line is the {P--wave} component, the green dashed line is the {S--wave} component and the light-blue dashed line represents the $\mathcal{A}^+_s \mathcal{A}_0$ interference term. Fig3a.pdf [16 KiB] HiDef png [166 KiB] Thumbnail [140 KiB] *.C file Fig3b.pdf [16 KiB] HiDef png [165 KiB] Thumbnail [139 KiB] *.C file Fig3c.pdf [16 KiB] HiDef png [171 KiB] Thumbnail [145 KiB] *.C file Projections of the model fitted to $B ^0_ s \rightarrow K^+\pi^-K^-\pi^+$ candidates (blue solid line) in the (top) invariant mass of $K\pi$ pairs and (bottom) $\cos\theta$ asymmetries as functions of $K\pi$ mass ($m_1$, $m_2$). The dots represent the data after background subtraction and acceptance correction. The red dashed line is the {P--wave} component, the green dashed line is the {S--wave} component and the light-blue dashed line represents the ${A}^+_s {A}_0$ interference term. Fig4a.pdf [17 KiB] HiDef png [216 KiB] Thumbnail [185 KiB] *.C file Fig4b.pdf [17 KiB] HiDef png [216 KiB] Thumbnail [184 KiB] *.C file Fig4c.pdf [15 KiB] HiDef png [160 KiB] Thumbnail [141 KiB] *.C file Fig4d.pdf [15 KiB] HiDef png [161 KiB] Thumbnail [141 KiB] *.C file (Left) Profile likelihood for the parameter $f_L$. (Right) Regions corresponding to $\Delta\ln\mathcal{L} =$ 0.5, 2 and 4.5 (39%, 87% and 99% confidence level) in the $|A_s^-|^2$ -- $f_L$ plane. Fig5a.pdf [13 KiB] HiDef png [104 KiB] Thumbnail [80 KiB] *.C file Fig5b.pdf [15 KiB] HiDef png [164 KiB] Thumbnail [142 KiB] *.C file Invariant mass of the selected $K^+K^-K^{\pm}\pi^{\mp}$ combinations and result of the fit to the data. The points represent the data and the (blue) solid line is the fit model. The $B ^0_ s$ and $B ^0$ signal peaks are shown as as dashed-dotted lines (pink and dark green, respectively). The contribution from partially reconstructed decays is represented as a (light blue) dashed line. The (grey) dotted line is the combinatorial background component. The normalised residual (pull) is shown below. Fig6.pdf [21 KiB] HiDef png [247 KiB] Thumbnail [199 KiB] *.C file Animated gif made out of all figures. PAPER-2014-068.gif Thumbnail

## Tables and captions

 Untagged time-integrated terms used in the analysis, under the assumption of no $C P$ violation. Table_1.pdf [79 KiB] HiDef png [205 KiB] Thumbnail [95 KiB] tex code Parameters of the mass propagators used in the fit. Table_2.pdf [51 KiB] HiDef png [67 KiB] Thumbnail [34 KiB] tex code Triple product and direct $C P$ asymmetries measured in this analysis. The first uncertainties are statistical and the second systematic. Table_3.pdf [43 KiB] HiDef png [123 KiB] Thumbnail [58 KiB] tex code Results of the simultaneous fit to $B ^0_ s \rightarrow K^+\pi^-K^-\pi^+$ TOS and non-TOS candidates with $|M(K^+, \pi^-, K^-, \pi^+) - m_{ B ^0_ s }| < 30 {\mathrm{ Me V /}c^2}$ (phases are measured in radians). The first uncertainties are statistical and the second systematic. Table_4.pdf [50 KiB] HiDef png [144 KiB] Thumbnail [65 KiB] tex code Systematic uncertainties in the measurement of the magnitude and phase of the different amplitudes contributing to the $B ^0_ s \rightarrow K^+\pi^-K^-\pi^+$ decay. Table_5.pdf [52 KiB] HiDef png [121 KiB] Thumbnail [48 KiB] tex code Summary of relevant quantities in the ${\cal B}( B ^0_ s \rightarrow K ^{*0} \overline{ K }{} {}^{*0} )$ calculation. The factor $\kappa( B ^0_ s \rightarrow K ^{*0} \overline{ K }{} {}^{*0} )$ is defined as $\lambda_{f_L}( B ^0_ s \rightarrow K ^{*0} \overline{ K }{} {}^{*0} )/f_{ B ^0_ s \rightarrow K ^{*0} \overline{ K }{} {}^{*0} }$, and equivalently for the $B ^0 \rightarrow \phi K ^{*0}$ decay. The first uncertainty is statistical, the second systematic. Table_6.pdf [63 KiB] HiDef png [48 KiB] Thumbnail [23 KiB] tex code

Created on 20 February 2021.