Search for hadronic transition<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>χ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mo>→</mml:mo><mml:msub><mml:mi>η</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>and observation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>χ</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>J</mml:mi></mml:mrow></mml:msub><mml:mo>→</mml:mo><mml:mi>K</mml:mi><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>π</mml:mi><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>

Hadronic transitions of chi(cJ) -&gt; eta(c)pi(+)pi(-) (J = 0, 1, 2) are searched for using a sample of 1.06 x 10(8) psi(3686) events collected with the BESIII detector at the BEPCII storage ring. The eta(c) is reconstructed with (KSK +/-)-K-0 pi(-/+) and K+K-pi(0) final states. No signals are observed in any of the three chi(cJ) states in either eta(c) decay mode. At the 90% confidence level, the upper limits are determined to be B(chi(c0) -&gt; eta(c)pi(+)pi(-)) &lt;0.07%, B(chi(c1) -&gt; eta(c)pi(+)pi(-)) &lt;0.32%, and B(chi(c2) -&gt; eta(c)pi(+)pi(-)) &lt;0.54%. The upper limit of B(chi(c1) -&gt; eta(c)pi(+)pi(-)) is lower than the existing theoretical prediction by almost an order of magnitude. The branching fractions of chi(cJ) -&gt; (KSK +/-)-K-0 pi(-/+)pi(+)pi(-), K+K-pi(+)pi(-)pi(0), omega K+K-, and phi pi(+)pi(-)pi(0) (J = 0, 1, 2) are measured for the first time. DOI: 10.1103/PhysRevD.87.012002