NT/RIKEN Seminar

We present [hep-ph/2006.06726] a framework that resums threshold enhanced large logarithms to all orders in perturbation theory for inclusive processes such as the production of a pair of leptons in Drell-Yan process and of Higgs boson in gluon fusion as well as in bottom quark annihilation at the hadron colliders. In addition, we apply [hep-ph/2007.12214] this to Deep Inelastic Scattering (DIS) and hadron production in Semi-Inclusive Annihilation (SIA) of electron positron colliders. These logarithms include the distributions P(log?^i (1−z))/1−z)) resulting from soft plus virtual (SV) and the logarithms log?^i (1−z) from next to SV contributions. We use collinear factorisation and renormalisation group invariance to achieve this. We find that the resummed result is a solution to Sudakov type differential equation and hence it can predict soft plus virtual contributions as well as next to SV contributions to all orders in strong coupling constant to the partonic coefficient function in terms of infrared anomalous dimensions and process independent functions. The z space resummed result is shown to have integral representation which allows us to resum the large logarithms of the form log?i(N) retaining 1/N corrections resulting from next to SV terms. We show that in N space, tower of logarithms are summed to all orders in strong coupling constant.