Complex Angular Momentum in Spinor BetheSalpeter Equation
Abstract
A model of fermionantifermion scattering, mediated by pseudoscalar neutral bosons, is described by the corresponding spinorial BetheSalpeter equation in the ladder approximation. The decomposition of the equation into partial waves by means of fusion amplitudes and conventional spherical harmonics is discussed in detail; various important symmetries of the resulting kernel and Born amplitudes are pointed out. The resulting set of coupled equations is continued into the complex angular momentum (J) plane, and it is shown that Fredholm theory is inapplicable for any J. The equations are solved in a weak coupling, lowenergy limit by an iterative scheme. The resulting solutions exhibit a cut of the squareroot type extending along the real axis to G2π (G=coupling constant) in the righthand plane; other cuts and poles prevent the extension of our solutions into the lefthand J plane. The dominance of the cut is used to extract the large momentum transfer limit and obtain certain results for the highenergy limit in the cross channel. The total cross section for fermionantifermion annihilation is extracted by means of the optical theorem and is found to exhibit an energy dependence of the form t^{(G2π)1}[lnt]^{32}, where t is the c.m. energy squared.
 Publication:

Physical Review
 Pub Date:
 August 1963
 DOI:
 10.1103/PhysRev.131.1857
 Bibcode:
 1963PhRv..131.1857S