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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.
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Using a sample of $1.3times 10^9$ $J/psi$ events collected with the BESIII detector, we report the first observation of $eta^{prime}topi^{+}pi^{-}pi^{+}pi^{-}$ and $eta^{prime}topi^{+}pi^{-}pi^{0}pi^{0}$. The measured branching fractions are $mathcal{B}$($eta^{prime}topi^{+}pi^{-}pi^{+}pi^{-}$) = $(8.53pm0.69({rm stat.})pm0.64({rm syst.}))times10^{-5}$ and $mathcal{B}$($eta^{prime}topi^{+}pi^{-}pi^{0}pi^{0}$) = $(1.82pm0.35({rm stat.})pm0.18({rm syst.}))times10^{-4}$, which are consistent with theoretical predictions based on a combination of chiral perturbation theory and vector-meson dominance.
Based on a sample of $1.31 times 10^9$ $J/psi$ events collected with the BESIII detector, an amplitude analysis of the isospin-violating decays $eta^prime rightarrow pi^+pi^-pi^0$ and $eta^prime rightarrow pi^0pi^0pi^0$ is performed. A significant $P$-wave contribution from $eta^prime rightarrow rho^{pm} pi^{mp}$ is observed for the first time in $eta^prime rightarrow pi^+pi^-pi^0$. The branching fraction is determined to be ${mathcal B}(eta^prime rightarrow rho^{pm}pi^{mp})=(7.44pm0.60pm1.26pm1.84)times 10^{-4}$, where the first uncertainty is statistical, the second systematic, and the third model dependent. In addition to the nonresonant $S$-wave component, there is a significant $sigma$ meson component. The branching fractions of the combined $S$-wave components are determined to be ${mathcal B}(eta^prime rightarrow pi^+pi^-pi^0)_S=(37.63pm0.77pm2.22pm4.48)times 10^{-4}$ and ${mathcal B}(eta^prime rightarrow pi^0pi^0pi^0)=(35.22pm0.82pm2.54)times 10^{-4}$, respectively. The latter one is consistent with previous BESIII measurements.
Using a data sample of 2.59 x 10^7 psi(2S) decays obtained with the CLEO-c detector, we perform amplitude analyses of the complementary decay chains chi_c1 -> eta pi+ pi- and chi_c1 -> eta pi+ pi-. We find evidence for a P-wave eta pi scattering amplitude, which, if interpreted as a resonance, would have exotic J^PC = 1^-+ and parameters consistent with the pi_1(1600) state reported in other production mechanisms. We also make the first observation of the decay a_0(980) -> eta pi and measure the ratio of branching fractions B(a_0(980) -> eta pi)/B(a_0(980) -> eta pi) = 0.064 +- 0.014 +- 0.014. The pi pi spectrum produced with a recoiling eta is compared to that with eta recoil.
Using the data samples of $1.31times 10^9$ $J/psi$ events and $4.48times 10^8$ $psi(3686)$ events collected with the BESIII detector, partial wave analyses on the decays $J/psi$ and $psi(3686) to pi^+pi^-eta^prime$ are performed with a relativistic covariant tensor amplitude approach. The dominant contribution is found to be $J/psi$ and $psi(3686)$ decays to $rhoeta^prime$. In the $J/psi$ decay, the branching fraction ${cal B}(J/psito rhoeta^prime)$ is determined to be $(7.90pm0.19(mathrm{stat})pm0.49(mathrm{sys}))times 10^{-5}$. Two solutions are found in the $psi(3686)$ decay, and the corresponding branching fraction ${cal B}(psi(3686)to rhoeta^prime)$ is $(1.02pm0.11(mathrm{stat})pm0.24(mathrm{sys}))times 10^{-5}$ for the case of constructive interference, and $(5.69pm1.28(mathrm{stat})pm2.36(mathrm{sys}))times 10^{-6}$ for destructive interference. As a consequence, the ratios of branching fractions between $psi(3686)$ and $J/psi$ decays to $rhoeta^prime$ are calculated to be $(12.9pm1.4(mathrm{stat})pm3.1(mathrm{sys}))$% and $(7.2pm1.6(mathrm{stat})pm3.0(mathrm{sys}))$%, respectively. We also determine the inclusive branching fractions of $J/psi$ and $psi(3686)$ decays to $pi^+pi^-eta^prime$ to be $(1.36pm0.02(mathrm{stat})pm0.08(mathrm{sys}))times 10^{-4}$ and $(1.51pm0.14(mathrm{stat})pm 0.23(mathrm{sys}))times 10^{-5}$, respectively.
Based on a sample of $1.31 times 10^9$ $J/psi$ events collected with the BESIII detector at the BEPCII collider, Dalitz plot analyses of selected 79,625 $etarightarrowpi^{+}pi^{-}pi^0$ events, 33,908 $etarightarrowpi^0pi^0pi^0$ events and 1,888 $eta^{prime}rightarrowpi^0pi^0pi^0$ events are performed. The measured matrix elements of $etarightarrowpi^+pi^-pi^0$ are in reasonable agreement with previous measurements. The Dalitz plot slope parameters of $etarightarrowpi^0pi^0pi^0$ and $eta^{prime}rightarrowpi^0pi^0pi^0$ are determined to be $-0.055 pm 0.014 pm 0.004$ and $-0.640 pm 0.046 pm 0.047$, respectively, where the first uncertainties are statistical and the second systematic. Both values are consistent with previous measurements, while the precision of the latter one is improved by a factor of three. Final state interactions are found to have an important role in those decays.
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