# 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 the SLAC National Accelerator Laboratory. 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 having a large world data set in a kinematic range that is sensitive to both valence quarks and quark-antiquark pairs, there is a limited amount of data in a region dominated by valence quarks. As a result, research on the quark contribution to a nucleon's structure continues unabated.

The 2007 NSAC long range plan identified measurements of 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{fig:DeltaDoverD} 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 the lepton probe. The JLab measurements used fits to inclusive electron scattering measurements of polarized structure functions ($g$) and unpolarized structure function ($F$) of the proton, deuteron, and He-3 as well as 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{fig:DeltaDoverD}. This large difference between the two predictions now relies on experiment to resolve the disagreement. The current measurements shown in Fig.~\ref{fig:DeltaDoverD} 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, in JLab's Hall B, is to measure $\frac{\Delta d}{d}$ above $x_B$ of 0.5. Fig~\ref{deltadJLab}b shows a measurement of the $\pi^+$ asymmetry from graduate student Tamar Didberidze's Ph.D thesis performing an SIDIS analysis of the data set used for the inclusive measurement shown in Fig~\ref{deltadJLab}a. The analysis has developed the infrastructure to use for an extraction of $\frac{\Delta d}{d}$ in experiment PR12-06-109 using an 11 GeV electron beam in Hall B. Fig.~\ref{fig:DeltaDoverD} 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 also contribute substantially to our knowledge of polarized parton distribution functions for all quark flavors and even the polarized gluon distribution $\Delta g$, which is also being

pursued at Relativistic Heavy Ion Collider (RHIC).


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.

JLab's energy upgrade to 12 GeV will facilitate the above measurements. The CEBAF Large Acceptance Spectrometer in Hall~B is currently undergoing an upgrade of its detector systems to accommodate the increased energy as well. As a service to Hall~B and to satisfy the needs of experiment PR12-06-109, co-PI Forest has become responsible for the construction of five drift chambers. These drift chambers are approximately 6 feet high and contain over 5,000 wires. ISU has successfully constructed and tested one chamber with two more nearing completion. The ISU clean room being used for this work is shown in Fig.~\ref{delqJLab}.

\begin{figure}[htbp] \begin{center} \includegraphics[width=9cm]{DeltaDoverD.pdf} \vspace{-1.45in} \caption{\small 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 up triangles are measurements from X.~Zheng {\it et al.}~\cite{Zhang04}, the diamonds are from A.~Airapetian {\it et al.}~\cite{AirapetianHERMES05}, and the down triangles are from K.V. Dharmawardane~\cite{Vipuli06}. 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{fig:DeltaDoverD} \end{center} \end{figure}

 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.