SANE long paper v2

\label{sec:main_intro} Introduction

\label{sec:exp_intro} Experiment

\label{sec:exp_beam} Beam

\label{sec:exp_daq} DAQ

\label{sec:exp_target} Polarized Target

\label{sec:beta} BETA

\label{sec:beta-bigcal} BigCal

\label{sec:beta-cer} Gas

\label{sec:beta-luc} Lucite

\label{sec:beta-tracker} Tracker

\label{sec:data-anal} Data analysis

\label{sec:data-anal-bc-calib} Bigcal calibration

\label{sec:data-anal-cer-pid} Cerenkov Electron Identification

\label{sec:data-anal-track} Tracking

\label{sec:data-anal-bin} Binning

\label{sec:meas-asym} Extraction of Asymmetry

\label{sec:meas-asym-charge} Charge Normalization

\label{sec:meas-asym-livet} Live time correction

\label{sec:meas-asym-bpol} Beam Polarization

\label{sec:meas-asym-tpol} Target Polarization

\label{sec:meas-asym-pf} Packing Fraction

\label{sec:meas-asym-df} Target Dilution Factor

\label{sec:meas-asym-results} Measured Asymmetries

\label{sec:rad-back-corr} Radiative and Background corrections

\label{sec:rad-back-corr-eltail} Radiative Elastic tail subtraction

\label{sec:rad-back-corr-pair} Pair-symmetric background subtraction

\label{sec:pion-asym} Pion asymmetry

\label{sec:rad-back-corr-inel} Inelastic radiative corrections

\label{sec:spin-asym} Spin Asymmetries

\label{sec:syste-err} Systematic errors

\label{sec:spin-struct} Spin structure functions

\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 \(g_{1T}(x,k^2_T)\)</