Abstract
We develop an approach to the solution of the spinless Bethe-Salpeter equation for the different-mass case. Although the calculations are developed for spinzero particles in any arbitratry spherically symmetric potential, the non-Coulombic effective power-law potential is used as a kernel to produce the spin-averaged bound states of the non-self-conjugate mesons. The analytical formulas are also applicable to the self-conjugate mesons in the equal-mass case. The flavor-independent case is investigated in this work. The calculations are carried out to the third-order correction of the energy series. Results are consistent with those obtained before.
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Ikhdair, S.M., Sever, R. Bethe-Salpeter equation for non-self conjugate mesons in a power-law potential. Z. Phys. C - Particles and Fields 58, 153–157 (1993). https://doi.org/10.1007/BF01554088
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DOI: https://doi.org/10.1007/BF01554088