Browsing by Author "Gao, Haiyan"

The elastic electron-proton ($e-p$) scattering and the spectroscopy of hydrogen atoms are the two traditional methods to determine the proton charge radius ($r_{p}$). In 2010, a new method using the muonic hydrogen ($\mu$H)\footnote{A muonic hydrogen has its orbiting electron replaced by a muon.} spectroscopy reported a $r_{p}$ result that was nearly ten times more precise but significantly smaller than the values from the compilation of all previous $r_{p}$ measurements, creating the ``proton charge radius puzzle".

In order to investigate the puzzle,

the PRad experiment (E12-11-106\footnote{Spokespersons: A. Gasparian (contact), H. Gao, M. Khandaker, D. Dutta}) was first proposed in 2011 and performed in 2016 in Hall B at the Thomas Jefferson National Accelerator Facility, with both 1.1 and 2.2 GeV electron beams. The experiment measured the $e-p$ elastic scattering cross sections in an unprecedented low values of momentum transfer squared region ($Q^2 = 2.1\times10^{-4} - 0.06~\rm{(GeV/c)}^2$), with a sub-percent precision.

The PRad experiment utilized a calorimetric method that was magnetic-spectrometer-free. Its detector setup included a large acceptance and high resolution calorimeter (HyCal), and two large-area, high-spatial-resolution Gas Electron Multiplier (GEM) detectors. To have a better control over the systematic uncertainties, the absolute $e-p$ elastic scattering cross section was normalized to that of the well-known M$\o$ller scattering process, which was measured simultaneously during the experiment. For each beam energy, all data with different $Q^{2}$ were collected simultaneously with the same detector setup, therefore sharing a common normalization parameter. The windowless H$_2$ gas-flow target utilized in the experiment largely removed a typical background source, the target cell windows. The proton charge radius was determined as $r_{p} = 0.831 \pm 0.007_{\rm{stat.}} \pm 0.012_{\rm{syst.}}$~fm, which is smaller than the average $r_{p}$ from previous $e-p$ elastic scattering experiments, but in agreement with the $\mu$H spectroscopic results within the experimental uncertainties.

The $\eta$ meson is an interesting tool to study fundamental symmetries in Quantum Chromodynamics (QCD). In particular, its radiative decay width, $\Gamma\left(\eta\rightarrow\gamma\gamma\right)$, is an important quantity that can be predicted in the framework of Chiral Perturbation Theory. A precision measurement of this quantity would provide critical inputs to understanding the mixing of the $\eta$ and $\eta'$ mesons and extracting constants with wide-ranging applications in low-energy QCD. This decay width has been measured in the past using two different experimental techniques. The more popular technique utilized $e^{+}e^{-}$ collisions to produce $\eta$ mesons through electromagnetic interactions. Today, the Particle Data Group (PDG) averages the results of five such experiments to obtain their currently-accepted value of the decay width as: 0.515$\pm$0.018~keV. However the first measurement of this quantity was obtained from a fixed-target experiment that measured the cross section for photoproduction of $\eta$ mesons on a nuclear target via the Primakoff effect. Their result of 0.324$\pm$0.046~keV shows strong tension with the average of the collider measurements, motivating a new, high precision measurement using the Primakoff method.

For this purpose, the PrimEx-\textit{eta} experiment was conducted in Hall D of the Thomas Jefferson National Accelerator Facility (Jefferson Lab or JLab). The data is currently being analyzed to measure the differential cross section for the photoproduction of $\eta$ mesons on a liquid, $^{4}$He target. Preliminary results obtained from the analysis of the first phase of the PrimEx-\textit{eta} experiment show reasonable agreement with the currently-accepted PDG value of the radiative decay width. However, as will be discussed, there are many challenges to this precision measurement which must be studied before any results can be finalized and compared with previous measurements.

In parallel to the $\eta$ decay width measurement, the PrimEx-\textit{eta} experiment measured the total cross section for the fundamental, Quantum Electrodynamics (QED) process of Compton scattering from the atomic electrons inside the target. The results obtained from this measurement are in strong agreement with the next-to-leading order QED calculations, and the total combined uncertainties are below 3\% for incident photon energies between 7-10~GeV. In addition to providing the first precision measurement of the total Compton scattering cross section within this beam energy range, this measurement verifies the capability of the PrimEx-\textit{eta} experimental setup to perform absolute cross section measurements at forward angles, and serves as a reference process for the calibration of systematic uncertainties.

Experiments at Jefferson Lab have been conducted to extract the nucleon spin-dependent structure functions over a wide kinematic range. Higher moments of these quantities provide tests of QCD sum rules and predictions of chiral perturbation theory ($\chi$PT). While precise measurements of $g_{1}^n$, $g_{2}^n$, and $g_1^p$ have been extensively performed, the data of $g_2^p$ remain scarce. Discrepancies were found between existing data related to $g_2$ and theoretical predictions. Results on the proton at large $Q^2$ show a significant deviation from the Burkhardt-Cottingham sum rule, while results for the neutron generally follow this sum rule. The next-to-leading order $\chi$PT calculations exhibit discrepancy with data on the longitudinal-transverse polarizability $\delta_{LT}^n$. Further measurements of the proton spin structure function $g_2^p$ are desired to understand these discrepancies.

Experiment E08-027 (g2p) was conducted at Jefferson Lab in experimental Hall A in 2012. Inclusive measurements were performed with polarized electron beam and a polarized ammonia target to obtain the proton spin-dependent structure function $g_2^p$ at low Q$^2$ region (0.02$<$Q$^2$$<$0.2 GeV$^2$) for the first time. The results can be used to test the Burkhardt-Cottingham sum rule, and also allow us to extract the longitudinal-transverse spin polarizability of the proton, which will provide a benchmark test of $\chi$PT calculations. This thesis will present and discuss the very preliminary results of the transverse asymmetry and the spin-dependent structure functions $g_1^p$ and $g_2^p$ from the data analysis of the g2p experiment .

The neutral pion decays via chiral anomaly and this process historically led to the discovery of the chiral anomaly. The $\pi^0$ decay amplitude is among the most precise predictions of quantum chromodynamics (QCD) at low energy. However, the current experimental results are not commensurate with theoretical predictions. The Partical Data Group (PDG) average of the experimental results is $7.74\pm0.46$ eV, which is consistent with the chiral anomaly prediction (leading order). Recent theoretical calculations (NLO and NNLO) show an increase of about 4.5\% to the LO prediction with 1\% precision. As a result, a precise measurement of the neutral pion decay amplitude would be one of the most stringent tests of low energy QCD. PrimEx-II experiment measured the neutral pion decay amplitude via the Primakoff effect using two targets, silicon and $^{12}$C. The $\pi^0\rightarrow\gamma\gamma$ decay amplitude was extracted by fitting the measured cross sections using recently updated theoretical models for the process. The resulting value is $7.82 \pm 0.05(stat) \pm 0.10(syst)$ eV. With a total uncertainty of 1.8\%, this result is the most precise experimental estimation and is consistent with current theoretical predictions.

The electric and magnetic polarizabilities ($\alpha_E$ and $\beta_M$) are fundamental quantities encoding the internal structure of the nucleon. They characterize the response of the nucleon to an external electromagnetic field and can be probed via the Compton scattering process. In recent decades, nucleon polarizabilities have been extracted from low-energy Compton scattering data using dispersion relations and chiral effective field theories ($\chi$EFTs). However, due to the difficulties in experimental measurements, $\alpha_E$ and $\beta_M$ of the nucleon, particularly of the neutron, are still not precisely determined. Furthermore, lattice QCD has also been promising in making predictions on nucleon polarizabilities. Nowadays, high precision data are badly needed to benchmark theoretical calculations and to enable accurate extractions of nucleon polarizabilities. In aim of providing the most precise determination of $\alpha_E$ and $\beta_M$ of the nucleon, Compton scattering experiments have been performed at the High Intensity $\gamma$-ray Source (HI$\gamma$S) facility located at Duke University. In the experiments, intense, quasi-monoenergetic and nearly 100\% circularly or linearly polarized $\gamma$-ray beams were incident on a liquid $^4$He or a liquid hydrogen target. The scattered photons were detected by eight NaI(Tl) detectors placed at various scattering angles. Compton scattering cross sections of the proton have been measured with a circularly polarized photon beam at about 81\,MeV and a linearly polarized photon beam at about 83\,MeV to extract $\alpha_E$ and $\beta_M$ of the proton using the $\chi$EFT frameworks. In addition, differential cross sections of elastic Compton scattering from $^4$He at about 81\,MeV have been extracted with high precision to provide a complementary approach to determine the neutron polarizabilities. The $^4$He results strongly motivate the development of theoretical calculations of Compton scattering from $^4$He.

It is of great importance to identify new sources of discrete symmetry violations because it can explain the baryon number asymmetry of our universe and also test the validity of various models beyond the standard model. Neutron Electric Dipole Moment (nEDM) and short-range force are such candidates for the new sources of P&T violations. A new generation nEDM experiment was proposed in USA in 2002, aiming at improving the current nEDM upperlimit by two orders of magnitude. Polarized 3He is crucial in this experiment and Duke is responsible for the 3He injection, measurements of 3He nuclear magnetic resonance (NMR) signal and some physics properties related to polarized 3He.

A Monte-Carlo simulation is used to simulate the entire 3He injection process in order to study whether polarized 3He can be successfully delivered to the measurement cell. Our simulation result shows that it is achievable to maintain more than 95% polarization after 3He atoms travel through very complicated paths in the presence of non-uniform magnetic fiels.

We also built an apparatus to demonstrate that the 3He precession signal can be measured under the nEDM experimental conditions using the Superconducting Quantum Interference Device (SQUID). Based on the measurement result in our lab, we project that the signal-to-noise ratio in the nEDM experiment will be at least 10.

During this SQUID test, two interesting phenomena were discovered. One is the pressure dependence of the T₁ of the polarized 3He which has never been reported before. The other is the discrepancy between the theoretically predicted T₂ and the experimentally measured T₂ of the 3He precession signal. To investigate these two interesting phenomena, two dedicated experiments were built, and two papers have been published in Physical Review A.

In addition to the nEDM experiment, polarized 3He is also used in the search for the exotic short-range force. The high pressure 3He cell used in this experiment has a very thin window (~250 μm) to maximize the effect from the force. We demonstrate that our new method could improve the current best experimental limit by two orders of magnitude. A rapid communication demonstrating the technique and the result was published in Physical Review D.

This dissertation describes the first study of three-body photodisintegration of polarized 3He (γ3He → npp) with a circularly polarized photon beam.

This measurement was carried out at the High Intensity γ-Ray Source(HIγS) facility located at Duke University Free Electron Laser Laboratory and the incoming photon energy was 11.4 MeV. A high-pressure polarized 3He target based on spin exchange optical pumping (SEOP) of hybrid alkali was employed. Two methods--Nuclear Magnetic Resonance (NMR) and Electron

Paramagnetic Resonance (EPR)--were used to measure the polarization, which was determined to be ∼ 42%.

The data from the experiment were analyzed and a GEANT4 simulation was carried out to determine the corrections for finite geometry, neutron multiple scattering and detector efficiencies used in this experiment. The results are compared to the state-of-the-art three-body calculations and agreements are observed within rather large statistical uncertainties of the measurement. This experiment represents the first measurement of the asymmetry using spin-dependent 3He photodisintegration.

The unpolarized differential cross section and helicity-dependent differential cross-section difference results are also presented and compared to the same theoretical calculations followed by a discussion of the results. Total cross section is also extracted using two different methods and agrees well with the theoretical prediction.

New developments including a Sol-Gel coated pyrex 3He cell since the experiment are then presented. The in-beam test results of the aforementioned target cell from May 2009 test run are included and the prospect of future three-body photodisintegration is discussed in the end.

Despite the success of QCD at high energies where the perturbation calculations can be carried out because of the asymptotic freedom, many fundamental questions, regarding the confinement of quarks and gluons, the nuclear forces, and the nucleon mass and structure, still remain in the non-perturbative regime. Dispersive sum rules, based on universal principles, provide a data-driven approach to study the nucleon structure without model-dependencies. Among those sum rules, the well known Gerasimov-Drell-Hearn (GDH) sum rule relates the anomalous magnetic moment to a weighted integral over the photo-absorption cross section. Its generalized form is extended for the virtual photon absorption at an arbitrary four momentum transfer square ($Q^2$) and thus provides a unique relation to study the nucleon spin structure over an experimentally accessible range of $Q^2$. The measured integrals can be compared with theoretical predictions for the spin dependent Compton amplitudes. Such experimental tests at intermediate and low $Q^2$ deepen our knowledge of the transition from the asymptotic freedom regime to the color confinement regime in QCD.

Experiment E97-110 has been performed at the Thomas Jefferson National Accelerator Facility to precisely measure the generalized GDH sum rule and the moments of the neutron and $^3$He spin structure functions in the low energy region. During the experiment, a longitudinally-polarized electron beam with energies from 1.1 to 4.4 GeV was scattered from a $^3$He gas target which was polarized longitudinally or transversely at the Hall A center. Inclusive asymmetries and polarized cross-section differences, as well as the unpolarized cross sections, were measured in the quasielastic and resonance regions. In this work, the $^3$He spin dependent structure functions of $g_1(\nu, Q^2)$ and $g_2(\nu, Q^2)$ at $Q^2 = 0.032\mhyphen0.230$ GeV$^2$ have been extracted from the experimental data, and the generalized GDH sum rule of $^3$He is firstly obtained for $Q^2 < 0.1$ GeV$^2$. The results exhibit a ``turn-over'' behavior at $Q^2 = 0.1$ GeV$^2$, which strongly indicates that the GDH sum rule for real photons will be recovered at $Q^2 \rightarrow 0$.

Parton distribution functions (PDFs) provide important information about the flavor and spin structure of nucleon, which is one of the most fundamental building blocks of nature. Furthermore, they can also shed light on quantum chromodynamics (QCD) in the confinement region. Inclusive deep inelastic scattering (DIS) has been one of the most common tools in accessing PDFs through the measurement

of structure functions. Moreover, the cross section in semi-inclusive deep inelastic scattering (SIDIS), which is the product of PDFs and fragmentation functions (FF), which describe the parton hadronization process due to the color force, provides additional information about PDFs. With recent theoretical developments in the framework of the transverse momentum dependent parton distribution functions

(TMDs), the importance of SIDIS process have been widely recognized and accepted, since the inclusive DIS will not be able to attain the information of parton transverse momentum.

JLab experiment E06-010 is measuring the target single spin asymmetry (SSA) in SIDIS from the n (e, e′π+,−)X reaction with a transversely polarized 3He (effective polarized neutron) target at JLab Hall A with a 5.89 GeV incident electron beam. The kinematic coverage is 0.13 < x < 0.41 and 1.31 < Q2 < 3.1 (GeV2). This experiment represents the first SSA measurement from the SIDIS n (e, e′π±)X process. One of the main objectives of the experiment is to measure the Collins asymmetry,

which in turn constrains the "transversity", one of the PDFs whose direct physical interpretation is the probability of finding a transversely polarized parton inside a transversely polarized nucleon. The other main objective of the experiment is to measure the Sivers asymmetry which reveals important information about correlations between the parton transverse momentum and the nucleon spin. The Sivers asymmetry is closely linked to the parton's orbital angular momentum, which is one important piece in understanding the nucleon spin in terms of quark and gluon

degrees of freedom.

This dissertation will first give an introduction to QCD, SIDIS and current

theoretical and the experimental status of SSA. Next the experimental setup of E06-010 will be described, followed by the data analysis procedure to extract the Collins/Sivers asymmetries. In the end, the preliminary results from the data analysis will be shown and discussed.

The first measurements of the two- and three-body photodisintegration of longitudinally

polarized 3He with a circularly-polarized gamma-ray beam were carried out at the High Intensity gamma-ray Source facility located at Triangle Universities Nuclear Laboratory (TUNL). A high pressure 3He target, polarized via spin exchange optical pumping with alkali metals, was used in the experiments. The protons from the two-body photodisintegration experiment were detected using seventy two silicon surface barrier detectors of various thicknesses while the neutrons from the three-body photodisintegration were detected with sixteen 12.7 cm diameter liquid scintillator detectors. The spin-dependent cross sections and the contributions from the two- and three-body photodisintegration to the 3He Gerasimov-Drell-Hearn sum rule integrand were extracted and compared with state-of-the-art three-body calculations at the incident photon energies of 29.0 MeV (two-body) and 12.8, 14.7, and 16.5 MeV (three-body).

These are the first measurements of the contributions of the two- and three-body photodisintegration of 3He to the GDH integrand. These measurements were found to be in good agreement with the theoretical calculations which include the Coulomb interaction between protons in the final state. They also reveal-for the first time-the importance of the three-nucleon forces and the relativistic single-nucleon charge corrections which are responsible in the calculations for the observed difference

between the spin-dependent cross sections.

In recent years, the strangeness production reactions in NN collisions have attracted a considerable amount of interest. These reactions are expected to provide valuable information on the manifestation of Quantum chromodynamics (QCD) in the nonperturbative region. For example, the φ meson is expected to probe the admixture of strange quark pairs in the nucleon wave function. The near-threshold reactions are expected to provide valuable information about the meson-meson, meson-baryon,

and hyperon-nucleon interactions.

We report the differential and total cross sections for the pp → ppKK/φ reaction at Tp= 2.567 (below the φ meson threshold) and 2.83 GeV (above the φ meson threshold). We use detailed model descriptions to fit a variety of one dimensional distributions in order to separate the pp → ppφ cross section from that of non- φ production. The differential spectra show that higher partial waves represent the majority of the pp → pp φ total cross section at an excess energy of 76 MeV, whose energy dependence would then seem to require some s-wave φp enhancement near threshold. On the other hand, strong preferences to the low Kp and Kpp invariant masses are observed in non- kaon pair productions. The cusp effect in the KK distribution at the K0 K0 threshold is clear and some evidence is also found for coupling between the Kp and K0n channels. Beside of the mentioned reactions, we also show the preliminary results for the search for a possible Kpp bound state in the pp → pKΛ reaction at Tp=2.567 GeV.

The unpolarized semi-inclusive deep-inelastic scattering (SIDIS) differential cross sections in $^3$He($e,e^{\prime}\pi^{\pm}$)$X$ have been measured for the first time in Jefferson Lab experiment E06-010 performed with a $5.9\,$GeV $e^-$ beam on a $^3$He target. The experiment focuses on the valence quark region, covering a kinematic range $0.12 < x_{bj} < 0.45$, $1 < Q^2 < 4 \, \textrm{(GeV/c)}^2$, $0.45 < z_{h} < 0.65$, and $0.05 < P_t < 0.55 \, \textrm{GeV/c}$. The extracted SIDIS differential cross sections of $\pi^{\pm}$ production are compared with existing phenomenological models while the $^3$He nucleus approximated as two protons and one neutron in a plane wave picture, in multi-dimensional bins. Within the experimental uncertainties, the azimuthal modulations of the cross sections are found to be consistent with zero.

In this dissertation, the studies for the unpolarized SIDIS differential cross sections are presented. The dissertation will start with the introduction on the physics related to SIDIS, then the experiment E06-010 will be described, followed by the data analysis. The results of the unpolarized SIDIS differential cross sections will be shown afterwards with discussions.

In addition to the work on the unpolarized SIDIS, the author also updated the approximated formalism for radiative effects (REs) for inclusive scattering channels (lifted the energy peaking approximation of the formalism). This updated formalism and a detailed discussion of the approximations in different formalisms of REs are presented in the appendix.