Decoding Z c ( 4430 ) and Z c ( 4200 ) : The role of P -wave charmed mesons

In this work, we perform a systematic investigation of the hidden-charm tetraquark states with I G ( J P C ) = 1 + ( 1 + − ) within the hadronic molecular picture, placing particular emphasis on systems composed of an S -wave ( D , D * ) meson and a P -wave [ D 0 * ( 2300 ) , D 1 ( 2430 ) , D 1 ( 2420 ) , D 2 * ( 2460 ) ] meson. Adopting the one-boson exchange potential, we solve the Schrödinger equation in momentum space via the complex scaling method. A crucial feature of our approach is the rigorous treatment of the unstable nature of the P -wave constituents by incorporating three-body decay effects arising from self-energy corrections and the static limit approximation. Our results demonstrate that these three-body dynamics play a crucial role in determining the pole positions, specifically in reproducing the large decay widths observed experimentally. We identify several broad resonances in the D * D ¯ 1 ( 2420 ) and D * D ¯ 2 * ( 2460 ) systems as candidates for the Z c ( 4430 ) , while the significantly broader resonances in the D D ¯ 0 * ( 2300 ) and D D ¯ 1 ( 2430 ) sectors are suggested as candidates for the Z c ( 4200 ) . Focusing on the D * D ¯ 2 * (