On next to soft threshold corrections to DIS and SIA processes

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

Automated summary

This study investigates the perturbative structure of threshold enhanced logarithms in the coefficient functions of deep inelastic scattering and semi-inclusive e(+)e(-) annihilation processes, proposing a framework to sum them up to all orders in perturbation theory. Utilizing the Sudakov differential, renormalisation group equations, and factorisation properties of parton level cross sections, the resummed result predicts SV and next to SV contributions to all orders in the strong coupling constant. Large logarithms in the form of log(i)(N) are resummed in Mellin N space, with towers of logarithms for different values of alpha summed to all orders in a(s).