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= The CLAS12 Polarized Structure Function Program =


;2007 NSAC long range plan has a Delta-d/d graph in Fig 2.3 on pg 23.

\paragraph{The CLAS12 Polarized Structure Function Program}

Nucleon spin structure functions have been measured using deep inelastic lepton scattering (DIS) for over 20 years since the first experiments at SLAC. Interest increased substantially in the 1980s when the EMC collaboration reported that quarks make a small contribution to the overall spin of the proton. This ``spin puzzle" led to a vigorous theoretical and experimental effort that continues to this day.  Although substantial, the world data set is more accurate in a kinematic range that is sensitive to both valence quarks and quark-antiquark pairs.  Despite these efforts, research on the quark contribution to a nucleon's structure continues unabated.  

The 2007 NSAC long range plan ~\cite{NSACLRP_2007} identified the fractional polarization of down quarks in the nucleon ($\frac{\Delta d}{d}$) as providing the insight that down quarks prefer to be oriented with their spins opposite to the spin of a nucleon.  Fig.~\ref{deltadJLab} illustrates the data used to support this conclusion.  HERMES and JLab measured $\frac{\Delta d}{d}$ in a kinematic range where the down quark carried a fraction of the nucleon's momentum ($x_B$) that was less than 0.7.  The HERMES measurement used Semi-Inclusive Deep Inelastic (SIDIS) scattering where the quark flavor is tagged by identifying a meson in the final state along with an electron.  The JLab measurements used fits to Inclusive electron scattering measurements of g/F  using polarized proton, deuteron, and He-3 and the ratio of up and down quark distributions from proton and deuteron data.

While the constituent quark model (CQM) predicts that  $\frac{\Delta d}{d}$ remains negative as $x_B$ approaches unity, perturbative quantum chromodynamics (pQCD) predicts that it will become positive, as shown in a Fig.~\ref{deltadJLab}.  This large difference between the two predictions presents experiments with an opportunity to resolve the disagreement.  The current measurements shown in Fig.~\ref{deltadJLab} have not shown a clear indication of this predicted sign change as there is a sparsity of data beyond $x_B > 0.5$.  There is a clear need to perform measurements above $x_B$ of 0.5 in order to evaluate the veracity of the pQCD and CQM predictions.

One of the goals of experiment PR12-06-109 is to measure $\frac{\Delta d}{d}$ above $x_B$ of 0.5.  Fig.~\ref{deltadJLab} illustrates the precision that may be achieved using the CLAS12 apparatus.  In particular, the measurement at $x_B$ of 0.7 should distinguish between the two prediction at the 2$\sigma$ level.

The comprehensive data set to be collected by experiment PR12-06-109 (Co-PI Forest) will contribute substantially to our knowledge of polarized parton distribution functions for all quark flavors and even the polarized gluon distribution $\Delta g$. Through Next-to-Leading Order (NLO) analysis of the world data on inclusive DIS (using the DGLAP evolution equations), one can constrain these distribution functions and their integrals. Existing CLAS data from 6 GeV have already made an impact on these fits. The expected data from the proposed experiment at 11~GeV will further reduce the uncertainties of these distributions. Semi-inclusive DIS (SIDIS) data will also be collected, where, in addition to the scattered electron,  hadrons produced after the struck quark hadronizes are also detected. These data will further constrain the NLO fits and improve the separation of the various quark flavors' contribution to nucleon observables. 

At large Bjorken $x$, new data from JLab address for the first time the question of the helicity structure of the nucleon in a kinematic realm where sea quark and gluon contributions are minimal thereby making one mostly sensitive to valence quarks. An example of these results is shown in Fig.~\ref{deltadJLab}. To extend this region to higher $x$ and moderate $Q^2$, one needs higher beam energies than presently available at JLab. In particular, to test various models of the asymptotic value of the virtual photon asymmetry $A_1(x)$ as $x \rightarrow 1$, one needs the upgraded CEBAF with 12~GeV beam energy.


\singlespace
\begin{figure} [t]
\begin{center}
{ 
\scalebox{0.4} [0.5]{\includegraphics[height=5in]{figs/DeltaDoverD_CLAS12.eps}}
} 
\caption{The expected statistical uncertainty of a $\Delta d/d$ measurement from CLAS12.  The dashed line represents a pQCD prediction while the solid line represents the prediction from a hyperfine perturbed constituent quark model. The solid triangles are measurements from X.~Zheng {\it et al.}~\cite{Zhang}, and the diamonds are from A.~Airapetian {\it et al.}~\cite{AirapetianHERMES}. The squares represent a prediction of the precision obtained by a SIDIS measurement performed using the energy upgraded CEBAF and the upgraded CLAS. The risers represent systematic uncertainty and the error bar lines are statistical uncertainties.}
\label{deltadJLab}
\end{center}
\end{figure}
\doublespace




{| border="1"  |cellpadding="20" cellspacing="0 
|-
| [[File:DeltaDoverD_CLAS12.png | 200 px]]
|-
| The dashed line represents a pQCD prediction while the solid line represents the prediction from a hyperfine perturbed constituent quark model.  The solid triangles are measurements from X.~Zheng {\it et al.}, Phys.~Rev.~Lett.~92 (2004) 012004 and the diamonds are from A. Airapetian {\it et al}, Phys.~Rev~D~71 (2005) 012003.  The squares represent a prediction of the precision obtained by a SIDIS measurement performed using an energy upgrade CEBAF and the upgraded CLAS.  The risers represent systematic uncertainty and the error bar lines are statistical uncertainties.
|}<br>

[[File:DeltaDoverD.eps]]

[[File:DeltaDoverD.xmgrace.txt]]

[[2012_NSF_Proposal]]