“…In this kinematic regime where Q 2 P 2 h T 1/fm 2 , similar to the inclusive DIS, SIDIS cross section can be factorized into a product of perturbatively calculable lepton-parton scattering at the hard scale Q, corresponding transverse momentum dependent (TMD) parton distribution functions (or simply, TMDs), φ i/P (x, k T , µ 2 ) with k T being the active parton's transverse momentum perpendicular to the direction of the colliding hadron of momentum P , and TMD fragmentation functions (FFs), D j→h (z, p T , µ 2 ) with the emergent hadron-type h carrying momentum fraction between z and z + dz of the fragmenting parton of momentum p and p T being the parton's transverse momentum off the direction of the observed final-state hadron of momentum P h , where i, j = {q,q, g} represent the active parton flavors [9,10]. In terms of this TMD factorization formalism, with the corrections of O(P h T /Q), lepton-hadron SIDIS is an excellent process to probe three-dimensional (3D) confined motion of quarks and gluons inside a bound proton, and has been actively pursued by experimental programs at all lepton-hadron scattering facilities, such as COMPASS at CERN [11] and various experiments at Jefferson Lab [12], as well as the future Electron-Ion Collider (EIC) [13].…”