Relativistic Bethe–Salpeter Study of Bottomonium Mass Spectra and Annihilation Decays

This study presents a comprehensive analysis of the mass spectra and decay properties of bottomonium ([Formula: see text]) mesons in the framework of the Bethe–Salpeter equation (BSE) with the Covariant Instantaneous Ansatz(CIA). The interaction kernel contains a long-range linear confining term plus a short-range one-gluon-exchange term, and the corresponding relativistic wave functions are derived for scalar ([Formula: see text]), axial-vector ([Formula: see text]), pseudovector ([Formula: see text]), pseudoscalar ([Formula: see text]) and vector ([Formula: see text]) states, with relativistic corrections of order [Formula: see text] retained but those of order [Formula: see text] neglected. To establish the relativistic consistency of the approach, the kernel is expanded to order [Formula: see text] and matched term by term with the Breit Hamiltonian for the vector and scalar Lorentz structures: the vector one-gluon exchange reproduces the standard Breit spin-independent, spin–orbit, tensor and spin–spin terms, a vector confining interaction adds the corresponding [Formula: see text] contributions, whereas a scalar confining interaction reverses the sign of the Darwin and spin–orbit terms and removes the tensor and spin–spin terms at this order. The masses of the ground and excited states of [Formula: see text], [Formula: see text] and [Formula: see text] agree well with the latest experimental data from the Particle Data Group (PDG) [1], and the two-photon decay widths of [Formula: see text] and [Formula: see text] together with the two-gluon hadronic decay widths of [Formula: see text] and the [Formula: see text]-wave states are evaluated with the same wave functions. The results confirm that the [Formula: see text] relativistic effects are essential for describing heavy quarkonia, especially for the higher excited states, while the Breit matching serves as a consistency check of the kernel structure rather than a precision determination of fine-structure effects, and the first-order perturbative treatment of the Coulomb term and the harmonic-oscillator truncation remain explicit limitations of the present model.