TMD-like functions through the twisted quark states

We investigate a new class of transverse momentum dependent functions (TMDs), as known as align-spin (AS) functions. In the paper, we propose the most suitable proof of the AS-function existence together with the demonstration of the preponderances if the framework of twisted quark states has been employed. The twisted state corresponds to the elementary particle (quark) which possesses the nontrivial intrinsic orbital angular momentum owing to the swirling trajectory of motion. In its turn, it leads to the cylindric system applied for the consideration. In this connection, we reveal that the twisted (vortex) quark states serve as effective tools for the study of TMDs, thereby facilitating a comprehensive analysis of AS-functions. In contrast to the previous studies, where the existence of new TMDs is related to the the corresponding interactions encoded in the correlators, we now focus on the leading order of interactions providing a simplified and robust method. This has been ensured by the twisted quark in the corresponding correlator because the essential transverse momentum dependence of quarks generated by interactions in the correlators can be alternatively described by the twisted states. Using a cylindrical formulation for twisted states, we can combine the properties of plane-wave particles with a description stemmed from spherical harmonics, resulting in well-defined propagation directions accompanied by essential OAM projections. In particular, this innovative framework opens a new window for the direct investigations of AS-functions, generating the unique angular $\phi$-dependence of differential cross sections. It also points towards promising applications in experimental particle physics.