2008 NSF Proposal

Physics Program

\hspace{0.5in}The [math]Q_{weak}[/math] experiment and the measurement of [math]A_1[/math] at large[math] x[/math] in Jefferson Lab's Hall B represent the main components of the principal investigator's physics program. Both components are the continuation of the PI's previous work in parity violating electron scattering as a Ph.D. student and polarized structure functions as a postdoctoral researcher based at Jefferson Lab. While the main goal of the [math]Q_{weak}[/math] experiment is to measure the weak mixing angle sin[math]^2[/math]([math]\theta_W[/math]), the PI has found an opportunity to use the same apparatus to measure a new low energy fundamental constant known as [math]d_{\Delta}[/math] described below. Such an experiment using the [math]Q_{weak}[/math] apparatus would require 1 week to measure an inelastic parity-violating asymmetry which is an order of magnitude larger than the [math]Q_{weak}[/math] asymmetry. While a postdoctoral researcher based at Jefferson Lab, the PI began developing a program to measure the polarized to unpolarized down quark distribution ([math]\frac{\Delta d}{d}[/math]) in the nucleon. The program was recently awarded 80 days of beam time by Jefferson Lab's PAC 30. Further details of the physics program are given in the subsections below.

Q_{weak}

\hspace{0.5in}The [math]Q_{weak}[/math] experiment (E05-008) will use parity violating (PV) electron-proton scattering at very low momentum transfers $(Q^2 \sim 0.03$~GeV$^2$) to measure the weak mixing angle sin$^2$($\theta_W$). The dominant contribution to the PV asymmetry measured by [math]Q_{weak}[/math] is given by the weak charge of the proton, $Q_W^p = 1-4\sin ^2 \theta _W$, with small corrections at order $Q^4$ from nucleon electromagnetic form factors. This measurement will provide a precision standard model test of the running of the electroweak coupling constant sin$^2$($\theta_W$). Any significant deviation of $\sin ^2 \theta _W$ from the standard model prediction at low $Q^2$ would be a signal of new physics, whereas agreement would place new and significant constraints on possible standard model extensions including new physics. The experiment is considered a new initiative for the future of Jefferson Lab, about which the JLab Program Advisory Committee (PAC) wrote ``The PAC is very impressed with the discovery potential of this experiment and regards it as an important addition to the Jefferson Lab program. The role of the principal investigator in this program is described in section~\ref{section:QweakDetector}. A brief description of the physics is given below.

The PV asymmetry measured by inclusive electron scattering reactions is driven by the exchange of a neutral weak Z$^0$ boson. The asymmetry is amplified by the interference between the weak and electromagnetic interactions, a feature that has been exploited as a means for determining the strange quark contribution to ground state nucleon properties~\cite{Be01}. The asymmetry may be expressed as

\begin{eqnarray}

A ~=~ {{\sigma _+ -\sigma _-}\over{\sigma _+ + \sigma _-}}~=~{{G_F}\over{\sqrt{2}}}{{Q^2}\over{\pi \alpha}}{{1}\over{\sigma _p}}\{ \varepsilon G^{\gamma}_{E} G^{Z}_{E} + \tau G^{\gamma}_{M} G^{Z}_{M} - {{1}\over{2}}(1-4\sin ^2 \theta _W )\varepsilon ^{\prime} G^{\gamma}_{M} G^{Z}_{A}\}~\cite{ReyaSchilcher74},

\label{eq:PVelasticAsym} \end{eqnarray}

where $\sigma _+(\sigma_-)$ is the cross section for the elastic scattering of electrons of positive (negative) helicity, $\tau$, $\varepsilon$, and $\varepsilon ^{\prime}$ are kinematic factors depending on $Q^2$, $M$ is the mass of the proton, $G_F$ is the Fermi coupling constant, $\alpha$ is the electromagnetic coupling constant, $Q^2$ is the square of the four momentum transfer, $\sin ^2 \theta _W$ is the weak mixing angle, $\theta _e$ is the electron laboratory scattering angle, and $\sigma _p$ is the Mott cross section. The Sachs electromagnetic and neutral weak electric and magnetic form factors [math]$G^{\gamma ,Z}_{E}$[/math] and [math]$G^{\gamma ,Z}_{M}$[/math], respectively, as well as the nucleon axial vector form factor $G^{Z}_{A}$, can each be expressed in terms of individual quark distribution functions. A system of equations is constructed within this framework which describes the extraction of the strange quark contribution to the electric and magnetic form factors of the nucleon, $G^{s}_{E}$ and $G^{s}_{M}$, as well as the axial form factor $G_A^Z$~\cite{Kap88} from the asymmetry measurements made.

The limit $\theta \rightarrow 0$, $\epsilon \rightarrow 1$, and $\tau \ll 1$, in Eq.~\ref{eq:PVelasticAsym} is taken in order to see how a measurement of the PV asymmetry in elastic electron-proton scattering at very low $Q^2$ and very small electron scattering angles can be used to test the Standard Model. The resulting asymmetry becomes: \begin{eqnarray} A = -{{G_F}\over{4\pi \alpha \sqrt{2}}}[Q^2 Q_W^p + F^p (Q^2 ,\theta )] \rightarrow -{{G_F}\over{4\pi \alpha \sqrt{2}}}[Q^2 Q_W^p + Q^4 B(Q^2 )], \end{eqnarray} where $F^p$ is a form factor. Neglecting radiative corrections, the leading term in this equation is simply $Q_W^p = 1-4\sin ^2 \theta _W$. The $B(Q^2 )$ is the leading term in the nucleon structure defined in terms of neutron and proton electromagnetic and weak form factors. The contributions contained in $B(Q^2 )$ (which enters to order $Q^4$) can be reduced by going to lower $Q^2$ values; however, this also reduces the sensitivity to $Q_W^p$ (which enters to leading order in $Q^2$) making it statistically more difficult to measure. The value of $B(Q^2 )$ can be determined experimentally by extrapolating measurements made by the ongoing program of forward angle PV experiments at higher $Q^2$~\cite{HAPEX,G0,A4}. The optimum value of $Q^2$ to minimize hadron structure uncertainties and at the same time maximize our sensitivity to $Q_W^p$ is estimated to be near $Q^2 = 0.03$~(GeV/c)$^2$ \cite{Qweak}.

\begin{figure}[htbp] %\vspace{-1in} \centerline{ \scalebox{0.5} [0.5]{\includegraphics{Graphs/s2w_2004_4_new_2.eps}}} \caption{The dependence of $\sin^2 \theta_W$ as a function of $Q^2$ cast in the MS bar scheme by reference~\cite{Erler}. The solid line represents the Standard Model prediction. The results from three experiments (APV~\cite{APV}, $Q_W(e)$~\cite{E158}, $\nu$-DIS~\cite{NuTeV} ,Z-pole~\cite{Zpole} are shown together with the expected precision from the [math]Q_{weak}[/math] experiment (Q$_W(p)$~\cite{Qweak}. } \label{fig:newphysics} \end{figure}

An essential prediction of the Standard Model is the variation of $\sin ^2 \theta _W$ with $Q^2$, often referred to as the ``running of $\sin ^2 \theta _W$. Testing this prediction requires a set of precision measurements at a variety of $Q^2$ points, with sufficiently small and well understood theoretical uncertainties associated with the extraction of $\sin ^2 \theta _W$. It also requires a careful evaluation of the radiative corrections to $\sin ^2 \theta _W$ in the context of the renormalization group evolution (RGE) of the gauge couplings. Such tests have been crucial in establishing QCD as the correct theory of strong interactions \cite{Hin00}, and the RGE evolution of the QED coupling has also been demonstrated experimentally \cite{TOP97,VEN98,OPAL00,L300}. The gauge coupling of the weak interaction, however, represented at low energies by the weak mixing angle $\sin ^2 \theta _W$, has not yet been studied successfully in this respect.

Shown in Fig.~\ref{fig:newphysics} is the Standard Model prediction in a particular scheme \cite{QweakAp} for $\sin ^2 \theta _W$ versus $Q^2$ along with existing and proposed world data. As seen in this figure, the very precise measurements near the $Z^0$ pole merely set the overall magnitude of the curve; to test its shape one needs precise off-peak measurements. To date, there are only three off-peak measurements of $\sin ^2 \theta _W$ which test the running at a significant level: one from APV~\cite{APV}, one from high energy neutrino-nucleus scattering~\cite{NuTeV}, and the recently completed SLAC experiment E-158(Q$_w$(e))~\cite{E158}. The measurement of $Q_W^p$ described here will be performed with smaller statistical and systematic errors and has a much cleaner theoretical interpretation than existing low $Q^2$ data. In addition, this measurement resides in the semi-leptonic sector, and is therefore complimentary to experiment E-158 at SLAC, which has determined $\sin ^2 \theta _W$ from PV $\vec e e$ (Moller) scattering (which resides in the pure leptonic sector) to roughly a factor of two less precision at low $Q^2$ \cite{E158}. The total statistical and systematic error anticipated on $Q_W^p$ from these measurements is around 4\% \cite{Qweak}, corresponding to an uncertainty in $\sin ^2 \theta _W$ of $\pm$0.0007, and would establish the difference in radiative corrections between $\sin ^2 \theta _W (Q^2 \approx 0)$ and $\sin ^2 \theta _W (M_Z )$ as a 10 standard deviation effect.

Measuring $d_{\Delta}$ using the PV $N\rightarrow \Delta$ Transition at Low $Q^2$

Interest in inelastic PV physics has been bolstered by the discovery of a new radiative correction for the PV $N\rightarrow \Delta$ transition~\cite{Zhu012} resulting in a $Q^2$ independent asymmetry that does not contribute to elastic PV electron scattering. The result is a non-vanishing PV asymmetry at $Q^2 = 0$ . The new correction is the result of a photon coupling to a PV hadron vertex and is referred to as the so called ``anapole contribution which has no analog in the elastic channel. The authors in Ref.~\cite{Zhu012} use Siegert's theorem to show that the $Q^2$ independence is the result of a cancellation of the 1/$Q^2$ term from the photon propagator and the leading $Q^2$ dependence from the anapole term. The leading component from the contribution of this transition amplitude is proportional to $\omega ~(\omega = E_f -E_i )$ times the PV electric dipole matrix element and is characterized by a low energy constant $d_{\Delta}$. A measurement of the PV asymmetry in the $N\rightarrow \Delta$ transition at the photon point, or at very low $Q^2$, henceforth called the Siegert contribution, would provide a direct measurement of the low energy constant $d_{\Delta}$.

The low energy constant $d_{\Delta}$ is a fundamental constant which has implications to other long standing physics questions. The same PV electric dipole matrix element which results in $d_{\Delta}$ also drives the asymmetry parameter ($\alpha_{\gamma}$) in radiative hyperon decays, e.g. $\Sigma ^+ \rightarrow p\gamma$. Although Hara's theorem \cite{Hara64} predicts that the asymmetry parameter ( $\alpha_{\gamma}(\Sigma ^+ \rightarrow p\gamma$)) should vanish in the exact SU(3) limit, the Particle Data Group~\cite{PDGAlphaSigma} reports a measured value of $\alpha_{\gamma}(\Sigma ^+ \rightarrow p\gamma) =$-0.72$\pm$ 0.08. While typical SU(3) breaking effects are of order $(m_s - m_u )/1$GeV $\sim$ 15\%, the above asymmetry parameter is experimentally found to be more than four times larger. A solution proposed by the authors of Ref.~\cite{Bor99} involves including high mass intermediate state resonances $(1/2 ^- )$, where the weak Lagrangian allows the coupling of both the hyperon and daughter nucleon to the intermediate state resonances, driving the asymmetry parameter to large negative values. This same reaction mechanism was also shown to simultaneously reproduce the $s-$ and $p-$ wave amplitudes in non-leptonic hyperon decays, which has also been a long standing puzzle in hyperon decay physics. If the same underlying dynamics is present in the non-strange sector ($\Delta S = 0$) as in the strangeness changing sector ($\Delta S = 1$), one would expect $d_{\Delta}$ to be enhanced over its natural scale ($g_{\pi}$ = 3.8$\times 10^{-8}$, corresponding to the scale of charged current hadronic PV effects \cite{Des80,Zhu00}). The authors of Reference\cite{Zhu012} estimate that this enhancement may be as large as a factor of 100, corresponding to an asymmetry of $\sim$ 4 ppm, comparable to the size of the effects due to the axial response and therefore easily measurable. Thus, a measurement of this quantity could provide a window into the underlying dynamics of the unexpectedly large QCD symmetry breaking effects seen in hyperon decays.

The PI submitted a Letter of Intent (LOI-03-105) to JLab PAC24 which outlined an experiment to measure $d_{\Delta}$ using the $Q_{weak}$ apparatus \cite{Qweak}. As shown in Figure~\ref{fig:N2Delta_Asym}, a statistical precision of $<$ 0.1 ppm can be achieved at a $Q^2$ value of 0.028 GeV$^2$ in less than a week. The favorable reviews received have encouraged the PI to submit a full proposal once the Q$_{weak}$ run schedule has become firm.

\begin{figure}[htbp] \begin{center}{ %\scalebox{0.4}[0.3]{\rotatebox{-90}{\includegraphics{Graphs/N2Delta_Asym.eps}}} \scalebox{0.4} [0.4]{\includegraphics{Graphs/A_d_Delta_Prec.xfig.eps}} } \caption{Expected precision of the measured asymmetry using the Q$_{weak}$ apparatus compared with the expected asymmetry for several values of the low energy constant $d_{\Delta}$. The rectangular box indicates both the Q$^2$ bin and the asymmetry uncertainty.} \label{fig:N2Delta_Asym} \end{center} \end{figure}

The Longitudinal Spin Structure of the Nucleon

\hspace{0.5in}Spin structure functions of the nucleon have been measured in deep inelastic (DIS)

lepton scattering for nearly 30 years since the first

experiments at SLAC. Interest increased substantially in the 80's when the EMC collaboration reported that the quark helicities made a small contribution to the overall helicity of the proton, according to their data. This ``spin crisis led to a vigorous theoretical and experimental effort over the next 20 years, with a large data set collected at CERN, SLAC, DESY and Jefferson Lab. As of today, the data indicate that between 25\% - 35\% of the nucleon spin is carried by the quark spins, with the remainder being attributed to gluon polarization and orbital angular momentum. The world data set however, has yet to resolve whether the three valence quark spins ($uud$ in the proton) follow the ``naive expectation of relativistic quark models that 60\% -- 70\% of the nucleon spin carried by quark helicities.

The interest in this field continues unabated as new experiments (COMPASS %~\cite{COMPASS} at CERN and the nucleon spin program at RHIC %~\cite{RHIC} ) are attempting to measure the low-$x$ gluon and sea quark polarization in a polarized nucleon with high precision. At large-$x$, 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. Examples of these results are shown in Fig.~\ref{delqJLab}. 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.

\begin{figure} [!hbp] \begin{center}{ \scalebox{0.4} [0.5]{\includegraphics{Graphs/delq_new1.eps}} \scalebox{0.4} [0.5]{\includegraphics{Graphs/deltad_CLAS12.eps}} } \caption{The polarized to unpolarized up and down quark distribution ratio. The left figure shows the results from recent JLab experiments on the virtual photon asymmetry $A_1$ for the proton, Deuteron~\cite{EG2DeltaD} and neutron ($^3$He)~\cite{HallADeltaD}. The right figure represents the proposed measurements. The expected data have been draw along the pQCD and CQM prediction. } \label{delqJLab} \end{center} \end{figure}

The comprehensive data set to be collected by experiment PR12-06-109 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 yield further dramatic reductions in the errors on these distributions. In addition, semi-inclusive DIS (SIDIS) data will also be collected, where in addition to the scattered electron we will detect some of the leading hadrons produced when the struck quark hadronizes. These data will further constrain the NLO fits and improve the separation of the various quark flavors' contribution to the nucleon spin.

==Detector Development==\label{section:QweakDetector}

\hspace{0.5in}Support from this proposal will be used to develop the Region 1 Tracking system for the Q$_{weak}$ experiment at Jefferson Lab. Dr. Forest was awarded a grant under the Major Research Instrumentation (MRI) program ( Proposal \#PHYS-0321197) to develop this tracking system. A prototype detector and a detector positioning system have already been built using support from a previous NSF grant in combination with the instrumentation support from the MRI grant. As a result of this work, the final design has been completed which will construct ionization chambers equipped with Gas Electron Multipliers (GEM)~\cite{Sauli} as the first tracking element in the Qweak tracking system. The use of GEM preamplifiers increases the rate capabilities of the chambers allowing them to be used close to the target. As work package manager of the Region 1 tracking system, Dr. Forest is responsible for the construction, testing and installation of this tracking system.

A prototype detector was built and calibrated by Dr. Forest and his physics student Jeremy Dobbins in early 2004. The detector, shown in Figure~\ref{fig:QweakProducts} was a 2cm thick ionization chamber equipped with three gas electron multiplier preamplification stages~\cite{Sauli} and having an active area of 10cm x 10cm. The detector gain of 10$^5$ and a response uniformity less than 1\% was observed which is consistent with the findings of other groups. The detectors output signal was observed to have a 25ns rise time making it ideal for use in the high rate environment expected in the Q$_{weak}$ experiment. The effect of gas pressure on the detector's gain and quantum efficiency was then quantified by Louisiana Tech graduate student Jena Kraft in her M.S. physics thesis of Nov. 2004. It was discovered during operation of the first prototype that the wire bonds used to connect the charge collection strips to 24 pin output connectors were unreliable and too fragile. As a result, the detector was redesigned to eliminate the need for these wire bonds. Preliminary testing of the new design has shown no degradation of detector performance.

\begin{figure}[htbp] \centerline{ \scalebox{0.3} [0.49]{\rotatebox{0}{\includegraphics{Graphs/Glue2DchargeCollectr_1stPrototype.eps}}} \scalebox{0.7} [0.7]{\rotatebox{0}{\includegraphics{Graphs/QweakRotatorPicture.eps}}} } \caption{A prototype Region 1 ionization chamber (left) and the support structure (right) to be used to position the tracking system for Qweak. The left image shows an ionization chamber and readout board only. Rows of black 20 pin connectors are now wave soldered directly to the readout board replacing fragile wire bonds used previously. The right image shows the detector rotation system composed of a main aluminum rotation ring upon which two liner bi-slide systems are mounted. A oil impregnated brass worm gear, underneath the main aluminum ring, is remotely controlled to turn the ring to a desired octant.} \label{fig:QweakProducts} \end{figure}

ISU's Role

Work Package manager of the Detector and Front End electronics.

Inelastic PV measurements ([math]d_{\Delta}[/math])

CLAS

Physics Program

Polarized Structure Functions

[math]\frac{\Delta d}{d}[/math]

CLAS 12 DC Design and Construction

List of Currently supported students:

Student	Classification	Expected Grad Yr
Julian Slamanca	Ph. D.	2009
Tamar Didbarize	Ph. D.	2010
Danny Martinez	Ph. D.	2012
Alexi	Ph. D.	2012
Adrianne Spilker	M.S.	2009
Saitiniyazi Shadike	M.S.	2009
Jordan Keonough	BA	2011
Nathan Lebaron	BA	2012

Prior and Future use of NSF Funds

\hspace{0.5in}While at Louisiana Tech University, the PI received three prior NSF awards as a member of the Louisiana Tech Particle Physics Group. The first proposal entitled ``Parity Violating Electron Scattering at Jefferson Lab, was awarded in 2002 for three years in the amount of \$670,230 (NSF Award \#0244998) to Louisiana Tech University. The award supported the groups efforts building triggering electronics for the G0 backward angle measurements and for the initial development of the $Q_{weak}$ experiment. The second proposal, ``Precision Electroweak Measurements at Jefferson Lab, was awarded \$204,594 in 2006 (NSF Award \#0555390) with similar support for the next two years to continuing the Lousiana Group's efforts. Dr. Forest's MRI Proposal (\#PHYS-0321197) entitled {\small ``Collaborative Research:Development of a Particle Tracking System for the Qweak Experiment} was awarded \$131,770 on July 26, 2003 to develop the Region 1 tracking system for the Q$_{weak}$ experiment. The status of the work supported by the above awards which the PI was responsible for is given in section~\ref{section:QweakDetector} and shown in Figure~\ref{fig:QweakProducts}.

Facilities

\hspace{0.5in}The Idaho State University Department of Physics Strategic Plan identifies the use of experimental nuclear physics techniques as its focus area to addressing problems in both fundamental and applied science. The major efforts of the department include fundamental nuclear and particle physics, nuclear reactor fuel cycle physics, nuclear non-proliferation and homeland security, accelerator applications, radiation effects in materials and devices, biology and health physics. Because of this focus, the department has been characterized as one of the largest nuclear physics graduate programs in the nation with an average of over 50 graduate students. One of the key ingredients to the department's success has been the completion of the Idaho Accelerator Center (IAC) on April 30, 1999. A substantial amount of lab space (4000 sq. ft.) within the department has become available due to a combination of the IAC and a remodeling of the physics building. A detector lab with the potential to construct proto-type drift chambers in a clean room environment is currently planned as part of the lab space renovation.

The Idaho Accelerator Center (IAC) is located less than a mile away from campus and will provide a machining facility for detector construction, an electronics shop for installation of instrumentation, and beam time for detector performance studies. The IAC houses ten operating accelerators as well as a machine and electronics shop with a permanent staff of 8 Ph.D.'s and 6 engineers. Among its many accelerator systems, the Center houses a Linac capable of delivering 20 ns to 2 $\mu$s electron pulses with an instantaneous current of 80 mA up to an energy of 25 MeV at pulse rates up to 1kHz. The IAC has donated beam time to the Q$_{weak}$ project for the purpose of testing detector performance. One of the goals of these tests will be to evaluate the Q$_{weak}$ detector at high rates. The IAC is well suited for these rate tests as the Q$_{weak}$ calibration rates will be much lower than the electron and photon rates the IAC is capable of generating. A full description of the facility is available at the web site (www.iac.isu.edu).

The Beowulf REsource for Monte-carlo Simulations (BREMS) is a 12 node, 64 bit cluster housed in the ISU physics department which can support the high performance computing needs of the physics research program. This facility is the result of an investment made by NSF award PHYS-987453. This infrastructure will be an effective means for performing GEANT4 simulations of the Q$_{weak}$ experiment as well as Garfield simulations of the Region II drift chamber design. Simulation speed is increased on BREMS by running the simulation in parallel on many CPUs. A version of GEANT4 known as ParGeant4~\cite{ParGeant4} has recently been distributed which will allow these simulations to be run in parallel.

The Broader Impact of the Idaho State University Nuclear Physics Research Program

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