Solving the Homogeneous Bethe-Salpeter Equation

Physics – High Energy Physics – High Energy Physics - Phenomenology

Scientific paper

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26 pages (LaTeX), 6 PostScript figures are included as uuencoded-compressed-tar file at the end

Scientific paper

10.1103/PhysRevD.53.1482

We study a method for solving the homogeneous Bethe-Salpeter equation. By introducing a `fictitious' eigenvalue $\lambda$ the homogeneous Bethe-Salpeter equation is interpreted as a linear eigenvalue equation, where the bound state mass is treated as an input parameter. Using the improved ladder approximation with the constant fermion mass, we extensively study the spectrum of the fictitious eigenvalue $\lambda$ for the vector bound states and find the discrete spectrum for vanishing bound state mass. We also evaluate the bound state masses by tuning appropriate eigenvalues $\lambda$ to be unity, and find massless vector bound states for specific values of the constant fermion masses.

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