Light-cone behavior of the pion Bethe-Salpeter wave function in the ladder model

The Bethe-Salpeter wave function χ(q^ν+P^ν, q^ν) for two spin-{} quarks bound by the exchange of a scalar meson is examined in the ladder model. We seek the behavior of χ as the squared momentum, (q+P)², on one leg becomes infinite while the squared momentum, q², on the other leg remains fixed. This behavior is investigated by making a Wick rotation, expanding χ in partial-wave amplitudes χJⁱ(q²) of the group O(4), and then looking for the rightmost poles of χJⁱ(q²) in the complex J plane. Our results verify (in the ladder model) the useful hypothesis that the locations of these poles are independent of q² and can thus be computed in the q²→∞ limit by using conformal invariance.