Transverse momentum dependent parton distribution and fragmentation functions with QCD evolution

Evolution of the helicity and transversity. Transverse-momentum-dependent parton distributions

“…In conclusion, the results derived in Ref. [6,13] do not depend on the gamma matrix structure Γ used to define the specific polarized TMD, therefore they are universal for all polarization states and allow us to write down immediately the results for evolution of helicity and transversity TMD PDFs.…”

“…Being independent of the type of initial hadron, the computation of the hard coefficients can be performed for the parton-target case [6,13]. We can write perturbative results for the TMD distribution at small b T up the the first order of perturbation expansion as (removing for convenience the dependence on the scales)…”

“…(26,27) along with the soft subtraction factors (see Appendix A of Ref. [13]) for the TMD PDF for finding a quark of flavor j ′ in a quark of flavor j we find to order α s ,…”

“…For the TMD PDF of a quark in a quark we follow the steps of Refs. [6,13]. To deal with eikonal propagators, we use the Feynman rules from Refs.…”

“…[6] and applied in Refs. [13][14][15][16]. Another definition has been proposed in the context of Soft-Collinear Effective Theory by Echevarria, Idilbi, and Scimemi in Refs.…”