Speaker: Shaoyang Jia (Argonne National Laboratory)

Title: Solving the Bethe-Salpeter Equations for Pion, Rho Meson, Kaon, and the Quark-Photon Vertex.

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Abstract:
 We solve for the structure of pseudoscalar mesons with light and strange quarks from the homogeneous Bethe—Salpeter equation (BSE) in the Euclidean space within the rainbow-ladder truncation, applying the Maris—Tandy modeling of quark-gluon interaction. In order to compute the electromagnetic form factors (EMFFs) of the pion and the kaon, we solve for their Bethe—Salpeter amplitudes (BSAs) in the reference frame where the spatial momentum of the bound states is nonzero. Another input to the EMFF is the quark-photon vertex for the light and for the strange quarks, which is determined from the inhomogeneous BSE within the same truncation. Because the Ball—Chiu vertex specifies the components of this vertex longitudinal to the photon momentum, we formulate this inhomogeneous BSE in terms of transverse vectors orthogonal with respect to trace operations in the Dirac space. As a byproduct of such a formulation, we also solve for the BSA of the rho meson in the rest frame from its homogeneous BSE. We illustrate the BSAs of the pion, the kaon, and the rho meson in the Euclidean space. We also present the EMFFs of the pion and of the kaon when the photon momentum is spacelike.