Miguel G. Echevarria, Ahmad Idilbi, Ignazio Scimemi
We consider the factorization of hadronic physical observables with transverse momentum dependence when two collinear sectors are involved and which interact through emission of soft gluons. By proving a novel property of the relevant soft function as a geometric mean of two "hemisphere" soft functions, one can combine those functions with the two collinear ones to obtain a modified factorization theorem in which all quantities are well-defined and each "generalized" collinear quantity belongs to distinct region in rapidity space. Those quantities will be identified as the "transverse momentum dependent parton distribution functions". They are free from all rapidity divergences, including the mixed ultraviolet/non-ultraviolet ones, their evolution is governed by a homogeneous differential equation and no auxiliary parameters are needed to resum large logarithms.
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http://arxiv.org/abs/1211.1947
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