Isospin violation effect and three-body decays of the Tcc+ state

Abstract

In this work, we make a study of the Tcc+ state observed by the LHCb collaboration in 2021. In obtaining the effective potentials using the one-boson-exchange potential model we use an exponential form factor and find that, in the short and medium range, the contributions of the π, ρ, and ω exchanges are comparable while in the long range the pion-exchange contribution is dominant. Based on the assumption that Tcc+ is a loosely bound state of D*D, we focus on its three-body decay using the meson-exchange method. Considering that the difference between the thresholds of D*+D0 and D*0D+ is even larger than the binding energy of Tcc+, the isospin-breaking effect is amplified by the small binding energy of Tcc+. Explicitly including such an isospin-breaking effect we obtain, by solving the Schrödinger equation, that the probability of the isoscalar component is about 91% while that of the isovector component is around 9% for Tcc+. Using the experimental value of the mass of Tcc+ as an input, we obtain the wave function of Tcc+ and further obtain its width via the three-body hadronic as well as the radiative decays. The total width we obtain is in agreement with the experimental value of the LHCb measurement with a unitarized Breit-Wigner profile. Conversely, the current results support the conclusion that Tcc+ is a hadronic molecule of D*D. Published by the American Physical Society 2024