Double-logarithmic asymptotics of the quark scattering amplitudes with nonvacuum exchange in the t channel

Nonlinear differential equations of the Riccati type for the t-channel partial waves fsub(j)(t) describing the scattering of quarks on the mass shell are derived by employing the dispersion relations. The derivation applied to high energies ssup(1/2) in the range of αsub(s)nsup(2)(s/μsup(2)) approximately 1, where μ is the/nl/nfrared cut-off parameter with respect to the transverse momenta of the virtual particles and αsub(s) is the effective coupling constant for strong interaction. For colorless channels the solutions are found in explicit form. It is shown that the singularities of the partial waves with a negative signature are in all cases located to the right of the singularities of partial waves with a positive signature, i. e. the negative signature dominates in the asymptotic αsub(s)lnsup(2)(s/μsup(2)) >> 1