Factorization connecting continuum and lattice TMDs

Understand

Transverse-momentum-dependent parton distribution functions (TMDs) can be studied from first principles by a perturbative matching onto lattice-calculable quantities: so-called lattice TMDs, which are a class of equal-time correlators that includes quasi-TMDs and TMDs in the Lorentz-invariant approach.

• We introduce a general correlator that includes as special cases these two Lattice TMDs and continuum TMDs, like the Collins scheme.
• Then, to facilitate the derivation of a factorization relation between lattice and continuum TMDs, we construct a new scheme, the Large Rapidity (LR) scheme, intermediate between the Collins and quasi-TMDs.
• The LR and Collins schemes differ only by an order of limits, and can be matched onto one another by a multiplicative kernel.