科研之友
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摘要
In this Letter, we investigate the under-structures of the pi and B mesons in the framework of the Bethe-Salpeter equation with the confining effective potential (infrared modified flat bottom potential). In bare quark-gluon vertex approximation, we obtain the algebraic expressions for the solutions of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation. Firstly, we neglect the rainbow Schwinger-Dyson equation, take the bare quark propagator and solve the Bethe-Salpeter equation numerically alone. Although the bare quark propagator cannot embody dynamical chiral symmetry breaking and has a mass pole in the time-like region, it can give reasonable results for the values of decay constants f(pi) and f(B) compared with the values of experimental data and other theoretical calculations, such as lattice simulations and QCD sum rules. Secondly, we explore those mesons within the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation. The Schwinger-Dyson functions for the u and d quarks are greatly renorinalized at small momentum region and the curves are steep at about q(2) = 1 GeV2 which indicates an explicitly dynamical symmetry breaking. The Euclidean time Fourier-transformed quark propagator has no mass poles in the time-like region which naturally implements confinement. As for the b quark, the current mass is very large, the renormalization is more tender, however, mass pole in the time-like region is also absent. The Bethe-Salpeter wavefunctions for both the pi and B mesons have the same type (Gaussian type) momentum dependence as the corresponding wavefunctions with the bare quark propagator, however, the quantitative values are changed and the values for the decay constants f(pi) and f(B) are changed correspondingly.
- 出版日期2004-3-25
- 单位华北电力大学
