Next-to-Next-to-Leading Electroweak Logarithms for W-Pair Production at LHC

We derive the high energy asymptotic of one- and two-loop corrections in the next-to-next-to-leading logarithmic approximation to the differential cross section of $W$-pair production at the LHC. For large invariant mass of the W-pair the (negative) one-loop terms can reach more than 40%, which are partially compensated by the (positive) two-loop terms of up to 10%.