A Master Formula for Nnlo Soft and Virtual Qcd Corrections

with σ the physical cross section, σ̂ the perturbatively calculable hard scattering factor, and φf/hi the parton distribution for parton f in hadron hi. The partonic hard-scattering factors σ̂ include soft and virtual corrections, arising from soft-gluon emission and loop diagrams, which manifest themselves as plus distributions and delta functions with respect to a kinematical variable xth that measures distance from threshold. In single-particle-inclusive (1PI) kinematics, xth is often called s4 = s+ t+u− ∑ m, and the plus distributions are Dl(s4) ≡ [ln (s4/M )/s4]+, with l ≤ 2n− 1 at nth order in αs beyond the leading order. In pair-inclusive (PIM) kinematics, the relevant distributions are Dl(z) ≡ [ln (1 − z)/(1 − z)]+ with z = Q /s (Q is of the pair). These