# Search for the $C P$-violating strong decays $\eta \to \pi^+\pi^-$ and $\eta^\prime(958) \to \pi^+\pi^-$

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## Abstract

A search for the $C P$-violating strong decays $\eta \to \pi^+\pi^-$ and $\eta^\prime(958) \to \pi^+\pi^-$ has been performed using approximately $2.5 \times 10^{7}$ events of each of the decays $D^+ \to \pi^+\pi^+\pi^-$ and $D_s^+ \to \pi^+\pi^+\pi^-$, recorded by the LHCb experiment. The data set corresponds to an integrated luminosity of 3.0 fb$^{-1}$ of $pp$ collision data recorded during LHC Run 1 and 0.3 fb$^{-1}$ recorded in Run 2. No evidence is seen for $D^+_{(s)} \to \pi^+ \eta^{(\prime)}$ with $\eta^{(\prime)} \to \pi^+\pi^-$, and upper limits at 90% confidence level are set on the branching fractions, $\mathcal{B}(\eta \to \pi^+\pi^-) < 1.6 \times 10^{-5}$ and $\mathcal{B}(\eta^\prime \to \pi^+\pi^-) < 1.8 \times 10^{-5}$. The limit for the $\eta$ decay is comparable with the existing one, while that for the $\eta^\prime$ is a factor of three smaller than the previous limit.

## Figures and captions

 Mass spectra of selected $D_{(s)}^+\rightarrow \pi^+\pi^+\pi^-$ candidates, after the BDT selections, for (top) Run 1 and (bottom) Run 2 data, with the results from the fits superimposed. The dot-dashed lines show the total fitted backgrounds, and the vertical lines indicate the optimised $D^+_{(s)}$ signal regions. The discontinuity in the Run 2 spectrum comes from the fact that the trigger has two separate output streams and there are different BDT selections for $D ^+$ and $D ^+_ s$ . Fig1a.pdf [36 KiB] HiDef png [168 KiB] Thumbnail [129 KiB] *.C file Fig1b.pdf [36 KiB] HiDef png [179 KiB] Thumbnail [145 KiB] *.C file The $\pi^+\pi^-$ invariant mass distribution in the $\eta$ mass fitting region from the sum of the four samples, showing also the sum of the fitted curves and the pulls. The vertical dashed lines indicate the $\eta$ signal region. Fig2.pdf [35 KiB] HiDef png [249 KiB] Thumbnail [248 KiB] *.C file The $\pi^+\pi^-$ invariant mass distribution in the $\eta^\prime$ mass fitting region from the sum of the four samples, showing also the sum of the fitted curves and the pulls. The vertical dashed lines indicate the $\eta^\prime$ signal region. Fig3.pdf [25 KiB] HiDef png [223 KiB] Thumbnail [215 KiB] *.C file Values of $\textrm{CL}_{\textrm{s}}$ as a function of ${\cal B}\left(\eta\rightarrow \pi^+\pi^- \right)$ . The expected variation is shown by the dashed line, with the $\pm 1\sigma$ and $\pm 2\sigma$ regions shaded. The observed variation is shown by the solid line, while the horizontal line indicates the $90\%$ confidence level. Fig4.pdf [246 KiB] HiDef png [210 KiB] Thumbnail [144 KiB] *.C file Values of $\textrm{CL}_{\textrm{s}}$ as a function of ${\cal B}\left(\eta^\prime\rightarrow \pi^+\pi^- \right)$ . The expected variation is shown by the dashed line, with the $\pm 1\sigma$ and $\pm 2\sigma$ regions shaded. The observed variation is shown by the solid line, which almost overlays the dashed line, while the horizontal line indicates the $90\%$ confidence level. Fig5.pdf [239 KiB] HiDef png [195 KiB] Thumbnail [135 KiB] *.C file Animated gif made out of all figures. PAPER-2016-046.gif Thumbnail

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [137 KiB] This ZIP file contains supplemetary material for the publication LHCb-PAPER-2016-046. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in variuous formats Fig6.pdf [17 KiB] HiDef png [172 KiB] Thumbnail [137 KiB] *C file Fig7.pdf [17 KiB] HiDef png [152 KiB] Thumbnail [126 KiB] *C file Fig8.pdf [20 KiB] HiDef png [159 KiB] Thumbnail [135 KiB] *C file Fig9.pdf [22 KiB] HiDef png [165 KiB] Thumbnail [139 KiB] *C file

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