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Equality of two definitions for transverse momentum dependent parton distribution functions

Equality of two definitions for transverse momentum dependent parton distribution functions

We compare recent, seemingly different, approaches to transverse momentum dependent factorization (due to Echevarria, Idilbi, and Scimemi and to Collins), and show that they are the same, apart from an apparent difference in their definition of the $\overline{\mathrm{MS}}$ renormalization scheme.