# \label{sec:conclusion} Conclusion

After more than 30 years of experimental and theoretical work, the study of the nucleon spin structure has entered a mature stage, extending beyond the exploration of the properties of the polarized structure functions in the scaling regime into the region of the Bjorken scaling variable $$x$$ near its unity upper limit. Moreover, the experimental techniques have expanded from the original simple approach of measuring double spin asymmetries in inclusive deep inelastic scattering - DIS (citation not found: E80) (citation not found: E130) (citation not found: EMC) (citation not found: E142) (citation not found: E154) (citation not found: HERMESa) for parallel beam and target spins, or even for parallel and orthogonal configurations (citation not found: E143) (citation not found: SMC) (citation not found: E155D) (citation not found: E155) (citation not found: E155x), to semi-inclusive measurements with detection of a $$\pi$$ or $$K$$ meson in coincidence with the scattered electron (citation not found: hermessidis) (citation not found: smcsidis) and the investigation of the gluon polarization (citation not found: compassg) (citation not found: hermesg). From the inclusive measurements in DIS it has been established that the quarks carry only about 25% of the nucleon spin, and from the inclusive and semi-inclusive measurements, the quark polarization by flavor has been determined (citation not found: hermessidis) (citation not found: clas) (citation not found: halla).

The modern description of nucleon structure is done in terms of transverse momentum dependent quark distributions functions (citation not found: Mulders:1995dh) defined in terms of quark-quark ($$qq$$) and quark-gluon-quark($$qgq$$) correlations in the nucleon. Two of the leading twist distributions from $$qq$$ correlations translate, after integration over the transverse momentum $$\vec k_\perp$$, into the more familiar structure functions (SF) measured in DIS. The longitudinal momentum distribution $$q(x,k^2_T)$$ (also known as $$f_1$$) leads to the unpolarized SF $$F_1(x,Q^2)$$, which is a function of the Bjorken scaling variable $$x$$ and the four-momentum transfer squared $$Q^2=-q_\mu^2$$. The quark helicity distribution $$\Delta q(x)$$ (or $$g_{1L}$$) is related to the spin SF $$g_1(x,Q^2)$$. These distributions have quark flavor indices associated with them and the nucleon structure functions are linear combinations of all active flavors, weighted by their charges squared.

At subleading twist-3, there are two $$k_T$$-integrated distributions related to $$qq$$ correlations, namely $$g_{T}(x)$$ and $$h_{L}(x)$$. In addition, at the same twist-3 $${\cal O} (1/Q)$$, three-particle $$qgq$$ correlations lead to the corresponding distributions $$\tilde g_{T}(x)$$ and $$\tilde h_{L}(x)$$.

The transverse distribution $$g_{T}(x)$$ is of particular interest, because it can be measured in inclusive double polarized DIS with target polarization transverse to the beam helicity. In terms of the $$k_T$$ dependent distribution $$g_{1T}(x,k^2_T)$$</