Tcc+ and χc1(3872) with the complex scaling method and DD(D¯)π three-body effect

Abstract

We use the leading-order contact interactions and one-pion-exchange potentials to investigate the newly observed double-charm state Tcc+. We employ the complex scaling method to search for the poles on the first Riemann sheet with respect to the DD* threshold and the second Riemann sheet with respect to the DDπ threshold. The DDπ three-body effect is important in this system since the intermediate states can go on shell. We involve the three-body effect through an energy-dependent one-pion-exchange potential, which results in a unitary cut at the DDπ three-body threshold. We find a pole corresponding to the Tcc+ on the physical Riemann sheet. Its width is around 80 keV and nearly independent of the choice of the cutoff. Assuming the DD¯π and DD¯* channels as the main decay channels, we apply the similar calculations to the χc1(3872), and find its width is even smaller. The isospin breaking effect is so significant for the χc1(3872) that it is mainly a molecular state of D0D¯*0. Furthermore, we introduce a revised Schrödinger equation for unstable particles to include the contribution of the D* width, which is also revised by the three-body effect. Published by the American Physical Society 2024