First time measurements of polarization observables for the charged cascade hyperon in photoproduction

The parity violating weak decay of hyperons offers a valuable means of measuring their polarization, providing insight into the production of strange quarks and the matter they compose. Jefferson Lab's CLAS collaboration has utilized this property of hyperons, publishing the most precise polarization measurements for the Λ and Σ in both photoproduction and electroproduction to date. In contrast, cascades, which contain two strange quarks, can only be produced through indirect processes and as a result, exhibit low cross sections thus remaining experimentally elusive.^ At present, there are two aspects in cascade physics where progress has been minimal: characterizing their production mechanism, which lacks theoretical and experimental developments, and observation of the numerous excited cascade resonances that are required to exist by flavor SU(3) F symmetry. However, CLAS data were collected in 2008 with a luminosity of 68 pb−1 using a circularly polarized photon beam with energies up to 5.45 GeV, incident on a liquid hydrogen target. This dataset is, at present, the world's largest for meson photoproduction in its energy range and provides a unique opportunity to study cascade physics with polarization measurements.^ The current analysis explores hyperon production through the γ p → K+K +Ξ− reaction by providing the first ever determination of spin observables P, Cx and Cz for the cascade. Three of our primary goals are to test the only cascade photoproduction model in existence, examine the underlying processes that give rise to hyperon polarization, and to stimulate future theoretical developments while providing constraints for their parameters. Our research is part of a broader program to understand the production of strange quarks and hadrons with strangeness. The remainder of this document discusses the motivation behind such research, the method of data collection, details of their analysis, and the significance of our results.^

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Measurement of single spin asymmetry and fifth structure function for the p( e&ar; ,e'K +)Λ reaction with CEBAF Large Acceptance Spectrometer (CLAS)

The single spin asymmetry, ALT ′, and the polarized structure function, σ LT′, for the p( e&ar; , e′K +)Λ reaction in the resonance region have been measured and extracted using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. Data were taken at an electron beam energy of 2.567 GeV. The large acceptance of CLAS allows for full azimuthal angle coverage over a large range of center-of-mass scattering angles. Results were obtained that span a range in Q 2 from 0.5 to 1.3 GeV2 and W from threshold up to 2.1 GeV and were compared to existing theoretical calculations. The polarized structure function is sensitive to the interferences between various resonant amplitudes, as well as to resonant and non-resonant amplitudes. This measurement is essential for understanding the structure of nucleons and searching for previously undetected nucleon excited states (resonances) predicted by quark models. The W dependence of the σ LT′ in the kinematic regions dominated by s and u channel exchange (cos qcmk = −0.50, −0.167, 0.167) indicated possible resonance structures not predicted by theoretical calculations. The σLT ′ behavior around W = 1.875 GeV could be the signature of a resonance predicted by the quark models and possibly seen in photoproduction. In the very forward angles where the reaction is dominated by the t-channel, the average σLT ′ was zero. There was no indication of the interference between resonances or resonant and non-resonant amplitudes. This might be indicating the dominance of a single t-channel exchange. Study of the sensitivity of the fifth structure function data to the resonance around 1900 MeV showed that these data were highly sensitive to the various assumptions of the models for the quantum number of this resonance. This project was part of a larger CLAS program to measure cross sections and polarization observables for kaon electroproduction in the nucleon resonance region. ^

Measurement of the induced polarization of Λ(1116) in kaon electroproduction with CLAS

The CLAS Collaboration is using the p(e, e&feet; K+ p)π- reaction to perform a measurement of the induced polarization of the electroproduced Λ(1116). The parity-violating weak decay of the Λ into pπ- (64%) allows extraction of the recoil polarization of the Λ. The present study uses the CEBAF Large Acceptance Spectrometer (CLAS) to detect the scattered electron, the kaon, and the decay proton. CLAS allows for a large kinematic acceptance in Q2 (0.8 ≤ Q2 ≤ 3.5 GeV2 ), W (1.6 ≤ W ≤ 3.0 GeV), as well as the kaon scattering angle. In this experiment a 5.499 GeV electron beam was incident upon an unpolarized liquid-hydrogen target. The goal is to map out the kinematic dependencies for this polarization observable to provide new constraints for theoretical models of the electromagnetic production of kaon-hyperon final states. Along with previously published photo- and electroproduction cross sections and polarization observables from CLAS, SAPHIR, and GRAAL, these data are needed in a coupled-channel analysis to identify previously unobserved s-channel resonances.^

Proton Form Factor Puzzle and the CEBAF Large Acceptance Spectrometer (CLAS) two-photon exchange experiment

The electromagnetic form factors are the most fundamental observables that encode information about the internal structure of the nucleon. The electric (GE) and the magnetic ( GM) form factors contain information about the spatial distribution of the charge and magnetization inside the nucleon. A significant discrepancy exists between the Rosenbluth and the polarization transfer measurements of the electromagnetic form factors of the proton. One possible explanation for the discrepancy is the contributions of two-photon exchange (TPE) effects. Theoretical calculations estimating the magnitude of the TPE effect are highly model dependent, and limited experimental evidence for such effects exists. Experimentally, the TPE effect can be measured by comparing the ratio of positron-proton elastic scattering cross section to that of the electron-proton [R = σ(e +p)/σ(e+p)]. The ratio R was measured over a wide range of kinematics, utilizing a 5.6 GeV primary electron beam produced by the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab. This dissertation explored dependence of R on kinematic variables such as squared four-momentum transfer (Q2) and the virtual photon polarization parameter (&epsis;). A mixed electron-positron beam was produced from the primary electron beam in experimental Hall B. The mixed beam was scattered from a liquid hydrogen (LH2) target. Both the scattered lepton and the recoil proton were detected by the CEBAF Large Acceptance Spectrometer (CLAS). The elastic events were then identified by using elastic scattering kinematics. This work extracted the Q2 dependence of R at high &epsis;(&epsis; > 0.8) and the $&epsis; dependence of R at ⟨Q 2⟩ approx 0.85 GeV2. In these kinematics, our data confirm the validity of the hadronic calculations of the TPE effect by Blunden, Melnitchouk, and Tjon. This hadronic TPE effect, with additional corrections contributed by higher excitations of the intermediate state nucleon, largely reconciles the Rosenbluth and the polarization transfer measurements of the electromagnetic form factors.

Proton Form Factor Puzzle and the CEBAF Large Acceptance Spectrometer(CLAS) Two-Photon Exchange Experiment

The electromagnetic form factors are the most fundamental observables that encode information about the internal structure of the nucleon. The electric ($G_{E}$) and the magnetic ($G_{M}$) form factors contain information about the spatial distribution of the charge and magnetization inside the nucleon. A significant discrepancy exists between the Rosenbluth and the polarization transfer measurements of the electromagnetic form factors of the proton. One possible explanation for the discrepancy is the contributions of two-photon exchange (TPE) effects. Theoretical calculations estimating the magnitude of the TPE effect are highly model dependent, and limited experimental evidence for such effects exists. Experimentally, the TPE effect can be measured by comparing the ratio of positron-proton elastic scattering cross section to that of the electron-proton $\large(R = \frac{\sigma (e^{+}p)}{\sigma (e^{-}p)}\large)$. The ratio $R$ was measured over a wide range of kinematics, utilizing a 5.6 GeV primary electron beam produced by the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab. This dissertation explored dependence of $R$ on kinematic variables such as squared four-momentum transfer ($Q^{2}$) and the virtual photon polarization parameter ($\varepsilon$). A mixed electron-positron beam was produced from the primary electron beam in experimental Hall B. The mixed beam was scattered from a liquid hydrogen (LH$_{2}$) target. Both the scattered lepton and the recoil proton were detected by the CEBAF Large Acceptance Spectrometer (CLAS). The elastic events were then identified by using elastic scattering kinematics. This work extracted the $Q^{2}$ dependence of $R$ at high $\varepsilon$ ($\varepsilon > $ 0.8) and the $\varepsilon$ dependence of $R$ at $\langle Q^{2} \rangle \approx 0.85$ GeV$^{2}$. In these kinematics, our data confirm the validity of the hadronic calculations of the TPE effect by Blunden, Melnitchouk, and Tjon. This hadronic TPE effect, with additional corrections contributed by higher excitations of the intermediate state nucleon, largely reconciles the Rosenbluth and the polarization transfer measurements of the electromagnetic form factors.