Next-to-next-to-leading logarithms in four-fermion electroweak processes at high energy

We sum up the next-to-next-to-leading logarithmic virtual electroweak corre ctions to the high energy asymptotics of the neutral current four-fermion p rocesses for light fermions to all orders in the coupling constants using t he evolution equation approach, From this all order result we derive finite order expressions through next-to-next-to leading order for the total cros s section and various asymmetries. We observe an amazing cancellation betwe en the sizable leading, next-to-leading and next-to-next-to-leading logarit hmic contributions at TeV energies. (C) 2001 Elsevier Science B.V. All righ ts reserved.