On next to soft threshold corrections to DIS and SIA processes

A bstract We study the perturbative structure of threshold enhanced logarithms in coefficient functions deep inelastic scattering (DIS) and semi-inclusive e + ? annihilation (SIA) processes setup a framework to sum them up all orders perturbation theory. Threshold show as distributions ((1 ?z ) 1 log i (1 )) from soft plus virtual (SV) next SV (NSV) contributions. use Sudakov differential renormalisation group equations along with factorisation properties parton level cross sections obtain resummed result which predicts well contributions strong coupling constant. In Mellin N space, we resum large form ( keeping /N corrections. particular, towers logarithms, each $$ {a}_s^n/{N}^{\alpha }{\log}^{2n-\alpha }(N),{a}_s^n/{N}^{\alpha }{\log}^{2n-1-\alpha }(N)\cdots a s n / N ? log 2 ? , 1 ? etc for ? = 0 , 1, are summed s .