# Amplitude analysis of the decay $\overline{B}^0 \to K_{S}^0 \pi^+ \pi^-$ and first observation of the CP asymmetry in $\overline{B}^0 \to K^{*}(892)^- \pi^+$

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## Abstract

The time-integrated Dalitz plot of the three-body hadronic charmless decay ${{\overline{B}}^0 \to K_{\mathrm{\scriptscriptstyle S}}^0 \pi^+ \pi^-}$ is studied using a $pp$ collision data sample recorded with the LHCb detector, corresponding to an integrated luminosity of $3.0\;\mathrm{fb}^{-1}$. The decay amplitude is described with an isobar model. Relative contributions of the isobar amplitudes to the ${\overline{B}^0 \to K_{\mathrm{\scriptscriptstyle S}}^0 \pi^+ \pi^-}$ decay branching fraction and CP asymmetries of the flavour-specific amplitudes are measured. The CP asymmetry between the conjugate ${\overline{B}^0 \to K^{*}(892)^{-}\pi^+}$ and ${\overline{B}^0 \to K^{*}(892)^{+}\pi^-}$ decay rates is determined to be $-0.308 \pm 0.062$.

## Figures and captions

 Invariant mass distributions of $K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^-$ candidates, summing the two years of data taking and the two $K ^0_{\mathrm{ \scriptscriptstyle S}}$ reconstruction categories. The sum of the partially reconstructed contributions from $B$ to open charm decays, charmless hadronic decays, $\overline{ B }{} {}^0 \!\rightarrow \eta ^{\prime} K ^0_{\mathrm{ \scriptscriptstyle S}}$ and charmless radiative decays are denoted $\overline{ B }{} ^0_{(s)} \!\rightarrow K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- (X)$. FusedC[..].pdf [15 KiB] HiDef png [254 KiB] Thumbnail [79 KiB] Projections of the sum of all data categories (black points) and the nominal fit function onto the DP variables (left) $m_{K_{\rm S}^0\pi^+}^2$, (right) $m_{K_{\rm S}^0\pi^-}^2$ and (bottom) $m_{\pi^+\pi^-}^2$, restricted to the two-body low invariant-mass regions. The full fit is shown by the solid blue line and the signal model by the dashed red line. The observed difference is due to the (green) combinatorial and (light red) cross-feed background contributions, barely visible in these projections. DalPro[..].pdf [20 KiB] HiDef png [278 KiB] Thumbnail [91 KiB] DalPro[..].pdf [20 KiB] HiDef png [264 KiB] Thumbnail [89 KiB] DalPro[..].pdf [20 KiB] HiDef png [267 KiB] Thumbnail [88 KiB] Animated gif made out of all figures. PAPER-2017-033.gif Thumbnail

## Tables and captions

 Components of the DP model used in the fit. The individual amplitudes are referred to by the resonance they contain. The parameter values are given in ${\mathrm{\,Me V\!/}c^2}$ for the masses and $\mathrm{\,Me V}$ for the widths, except for $f_0(980)$ resonance. The parameter $m_0$ is the pole mass of the resonance and $\Gamma_0$ its natural width. The mass-dependent lineshapes employed to model the resonances are indicated in the third column. Relativistic Breit-Wigner and Gounaris-Sakurai lineshapes are denoted RBW and GS, respectively. EFKLLM is a parameterisation of the $K ^0_{\mathrm{ \scriptscriptstyle S}} \pi^{-}$ S-wave lineshape, $(K\pi)^{-}_0$. Table_1.pdf [58 KiB] HiDef png [144 KiB] Thumbnail [24 KiB] tex code

Created on 20 April 2019.Citation count from INSPIRE on 25 April 2019.