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Using $448.0 \times 10^6$~$\psi(3686)$ events collected with the BESIIIdetector, an amplitude analysis is performed for$\psi(3686)\to\gamma\chi_{c1}$, $\chi_{c1}\to\eta\pi^+\pi^-$ decays. The mostdominant two-body structure observed is $a_0(980)^{\pm}\pi^{\mp}$;$a_0(980)^{\pm}\to\eta\pi^{\pm}$. The $a_0(980)$ line shape is modeled using adispersion relation, and a significant non-zero $a_0(980)$ coupling to the$\eta^{\prime}\pi$ channel is measured. We observe $\chi_{c1}\to a_2(1700)\pi$production for the first time, with a significance larger than 17$\sigma$. Theproduction of mesons with exotic quantum numbers, $J^{PC}=1^{-+}$, isinvestigated, and upper limits for the branching fractions $\chi_{c1}\to\pi_1(1400)^{\pm}\pi^{\mp}$, $\chi_{c1}\to \pi_1(1600)^{\pm}\pi^{\mp}$, and$\chi_{c1}\to\pi_1(2015)^{\pm}\pi^{\mp}$, with subsequent $\pi_1(X)^{\pm} \to\eta\pi^{\pm}$ decay, are determined.

Amplitude analysis of the $\chi_{c1} \to \eta\pi^+\pi^-$ decays