Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice

Understand

Transverse momentum dependent parton distributions (TMDPDFs) which appear in factorized cross sections involve infinite Wilson lines with edges on or close to the light-cone.

• Since these TMDPDFs are not directly calculable with a Euclidean path integral in lattice QCD, we study the construction of quasi-TMDPDFs with finite-length spacelike Wilson lines that are amenable to such calculations.
• We define an infrared consistency test to determine which quasi-TMDPDF definitions are related to the TMDPDF, by carrying out a one-loop study of infrared logarithms of transverse position $b_T\sim \Lambda_{\rm QCD}^{-1}$, which must agree between them.
• This agreement is a necessary condition for the two quantities to be related by perturbative matching.