Pion Electromagnetic Form Factor from Bethe-Salpeter Amplitudes with Appropriate Kinematics
arxiv(2024)
摘要
Within the framework provided by quantum chromodynamics's Schwinger-Dyson
equations (SDEs), the pion's electromagnetic form factor is computed using
solutions of the Bethe-Salpeter equation (BSE) that have finite spacial
momentum, and therefore allow the appropriate kinematics for a given momentum
transfer. This removes, for the first time, a limiting approximation in
previous SDE calculations where rest-frame solutions to the BSE are used for
both the initial and final pion states. In performing these calculations, the
rainbow-ladder truncation to the SDEs in the Landau gauge is used, with the
quark-gluon interaction given by the Maris-Tandy model. Using Bethe-Salpeter
amplitudes (BSAs) that have the correct spacial momentum for a given momentum
transfer, Q^2, has a dramatic impact on results for the pion's
electromagnetic form factor. The difference between results that use rest-frame
BSAs and those with correct kinematics is less that 10% for 0 ⩽ Q^2
≲ 1GeV^2, however, these corrections grow with increasing momentum
transfer and approach 100% for Q^2 ≃ 3GeV^2.
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