Born-Oppenheimer Approximation for Double-Heavy Tetraquarks

A double-heavy tetraquark that can be identified with a bound state in a Born-Oppenheimer potential can decay into pairs of heavy hadrons through transitions to hadron-pair potentials with the same Born-Oppenheimer quantum numbers. The transitions are also constrained by conservation of angular momentum and by charge conjugation and parity symmetries. The transition rate can be expressed as the product of the transition rate between Born-Oppenheimer potentials and a constant factor determined by angular-momentum algebra. The Born-Oppenheimer potentials, the hadron-pair potentials, and the transition rates form the entries of a potential matrix from which the mass spectrum of double-heavy tetraquarks and their decays into hadron pairs can be calculated. This talk will focus on tetraquark Born-Oppenheimer potentials with isospin 0 and 1 which have direct implications to the study of X(3872) and Z_Q, respectively.