Abstract
Using soft collinear effective field theory, we derive the factorization theorem for the quasi-transverse-momentum-dependent (quasi-TMD) operator. We check the factorization theorem at one-loop level and compute the corresponding coefficient function and anomalous dimensions. The factorized expression is built from the physical TMD distribution, and a nonperturbative lattice related factor. We demonstrate that lattice related functions cancel in appropriately constructed ratios. These ratios could be used to explore various properties of TMD distributions, for instance, the nonperturbative evolution kernel. A discussion of such ratios and the related continuum properties of TMDs is presented.
Highlights
Over the last years, continuous progress in theory and phenomenology of a transverse-momentum-dependent (TMD) factorization theorem made it a valuable tool for analysis and prediction of many observables
The prospects for obtaining complementary information from QCD lattice simulations look extremely promising, in particular, due to the possibility of measuring correlators directly in coordinate space. The latter point is advantageous because the TMD factorization theorem we discuss and TMD distributions are naturally formulated in coordinate space, despite the fact that their interpretation is usually given in momentum space
We present a different analysis of the same operator within the TMD factorization approach, based on the qT-dependent soft-collinear effective field theory (SCET II)
Summary
Continuous progress in theory and phenomenology of a transverse-momentum-dependent (TMD) factorization theorem made it a valuable tool for analysis and prediction of many observables (for a review see [1]). The prospects for obtaining complementary information from QCD lattice simulations look extremely promising, in particular, due to the possibility of measuring correlators directly in coordinate space The latter point is advantageous because the TMD factorization theorem we discuss and TMD distributions are naturally formulated in coordinate space, despite the fact that their interpretation is usually given in momentum space. We present a different analysis of the same operator within the TMD factorization approach, based on the qT-dependent soft-collinear effective field theory (SCET II). Each order term has a stronger small-x singularity than the preceding ones Such a problem is quite common for factorization theorems for lattice observables. The situation is different for physical kinematics where the scattering plane is formed by two timelike vectors and the vector bμ is restricted to a plane
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