Speaker
Description
In this work, we extend the semiclassical WKB (Wentzel–Kramers–Brillouin) approximation method, previously applied with success to heavy quark–antiquark (meson) systems, to the more challenging and less understood domain of tetraquark states. Tetraquarks, exotic states composed of two quarks and two antiquarks, provide a unique window into the dynamics of multiquark interactions and the non-perturbative regime of Quantum Chromodynamics (QCD). Understanding their mass spectrum is crucial for both theoretical hadron spectroscopy and experimental searches for new states observed at facilities such as LHCb, Belle II, and BESIII. To make the problem tractable, we adopt the diquark–antidiquark picture. In this framework, the tetraquark is treated as two clusters—a diquark and an antidiquark bound together by an effective potential. This reduction simplifies the four-body system into a quasi-two-body problem, allowing us to apply powerful semiclassical techniques while still retaining essential features of multiquark dynamics. The interaction is described by a generalized Cornell potential that combines short-range coulombic and long-range confining terms. Applying the leading order WKB quantization condition to the effective radial Schrödinger equation yields approximate analytic expressions for ground and excited state masses. Near the classical turning points, we expand the potential around a suitable equilibrium point r0 using Taylor series expansion. This approximation makes it possible to reduce the radial Schrödinger equation into a form suitable for the application of the WKB quantization condition. By imposing the standard WKB quantization integral, we derive analytic expressions for the energy eigenvalues that correspond to the tetraquark mass spectrum. This work demonstrates that the WKB approach provides a practical semi-analytic framework for exploring exotic tetraquarks and guiding experimental searches
