In this thesis we present three research projects in classical General Relativity and Cosmology. In the first part of the thesis we investigate the definition of gravitational charge corresponding to the asymptotic boost symmetry of a spacetime and derive its role in the first law of black hole thermodynamics. In the cosmology part, we investigate the role of a scalar field in the early and late time evolution of the Universe. We find out observational constraints on the pseudo Nambu Goldstone Boson quintessence model using the latest supernova and Cosmic Microwave Background (CMB) data. In an attempt to explain a particular anomaly in the latest CMB data, we propose a modification to the standard single field inflation based on the initial kinetic energy domination with anisotropic initial conditions. Predictions of this mechanism can be tested in future data analysis.

This dissertation describes the measurement of asymmetries in neutral B meson decays to two-body final states of charged pions and kaons. The results are obtained from a data sample of 383 million ϒ(4 S) → BB¯ decays collected between 1999 and 2006 with the BABAR detector at the PEP-II asymmetric-energy B factory located at the Stanford Linear Accelerator Center, California. The maximum likelihood fit that incorporates kinematical, event-shape, and particle identification information is used to measure the CP asymmetries in B0 → π +π− and K± π∓ decays. The direct CP-violating asymmetry between decays to K−π + is AKπ = −0.107 ± [special characters omitted]. The time-dependent CP-violating parameters in B0 → π+π− decays are Sππ = −0.60 ± 0.11 ± 0.03, Cππ = −0.21 ± 0.09 ± 0.02. For all the measurements above, the first error is statistical and the second is systematic.

We have measured the polarization of $\Lambda\sp\circ$'s produced in the diffraction dissociation process $p\ +\ p\ \to\ p\ +\ \Lambda\sp\circ\ +\ X$ at 800 GeV/c using two million diffractive inclusive and 58,000 exclusive $\Lambda\sp\circ$ events. The $\Lambda\sp\circ$ kinematic variables in our data sample only have weak correlations. For the diffractive inclusive sample, we have studied the dependence of the $\Lambda\sp\circ$ polarization on the following variables: (1) $\Lambda\sp\circ$transverse momentum; (2) $\Lambda\sp\circ$ Feynman x; (3) missing mass squared of the beam system; and (4) event charge multiplicity. Our diffractive inclusive results agree well with the existing world results on inclusive $\Lambda\sp\circ$ polarization. We do not see a strong dependence on the missing mass squared of the beam system or event charge multiplicity. For the exclusive sample, we have studied two fully reconstructed reactions of the form p + p $\to$ p + $\Lambda\sp\circ$ + $K\sp+$ + ($\pi\sp+\pi\sp-)\sp{n}$, n = 1, 2 and the topology dependence of the polarization. Within the statistical uncertainties, the $\Lambda\sp\circ$ polarization does not depend on the final state. Our results show that the $\Lambda\sp\circ$ polarization of the exclusive sample is consistently larger than that of the diffractive inclusive sample, although the uncertainties are large. The study using exclusive events enables us to account for all possible backgrounds and to minimize the dilution of $\Lambda\sp\circ$'s from $\Sigma\sp\circ$ decays and resonance productions. These analyses represent the first study of the $\Lambda\sp\circ$ polarization in diffraction dissociation at 800 GeV/c. It is also the first study of the topology, missing mass squared and event charge multiplicity dependence of $\Lambda\sp\circ$ polarization at this energy.

The structure function of a virtual photon, representing the physics of the hard scattering of an electron off a massive photon target resulting in a hadronic final state, has been measured in the kinematic range $1.5\le Q\sp2\le 5.5\ {\rm GeV}\sp2,\ 0.1\le P\sp2\le 1.5\ {\rm GeV}\sp2$ and $2\le W\le 20$ GeV. The measurement was done using the TPC/Two-Gamma detector facility and employs a heretofore unique method to determine the W of the final state by using information from both the visible mass of the final state as well as the mass reconstructed from the two lepton tags. The results are compared to a variety of models, and are found to be consistent with an incoherent sum of the QPM and VDM models. In addition, the structure function of the virtual photon has been measured in the kinematic range $10\le Q\sp2\le 50\ {\rm GeV}\sp2, 0.1\le P\sp2\le 1.5\ {\rm GeV}\sp2,$ a heretofore unexplored region. The results are somewhat high, though statistically consistent with being physically allowed. The results might indicate the presence of an interesting background, or perhaps physics that has not yet been accounted for in the comparison to model expectations.

QCD inspired models are used to study the existence of correlations among quarks in hadronic matter at high densities. Specifically it is seen that pairs of quarks are correlated in high density hadronic matter, leading to the existence of diquarks at intermediate densities. A possible experimental signal for the diquarks is suggested. Similar techniques are used to understand 'anomalous' behavior of Pionic Atoms.

Phenomenological Lagrangians are introduced. They are applied to pion-pion scattering to get a positive test for QCD, and its Low energy Symmetries. QCD spectra is analyzed, with the help of Phenomenological Lagrangians. Finally we show how they can be an important tool to explore the Physics beyond the Standard Model.

The results of a partial wave analysis of the $K\sp{+}\overline{K\sp0}\pi\sp{-}$ system produced in the reaction $K\sp{-}p\to \ K\sp{+}\overline{K\sp0}\pi\sp{-}$ ($\Lambda/\Sigma\sp0$) at 8 GeV/c are presented. A total of 2043 events in the mass range 1.24 to 1.64 GeV/c$\sp2$ was collected using Brookhaven National Laboratory's Multiparticle Spectrometer facility. The $K\sp{+}\overline{K\sp0}\pi\sp{-}$ mass spectrum shows a small peak at 1.280 $\pm$.001 GeV/c$\sp2$ and a large peak at 1.438 $\pm$.003 GeV/c$\sp2$. The large peak is consistent with an enhancement at $K\sp{\*}K$ threshold which is cut off by our falling acceptance. There is some evidence for an accumulation of events in the region near 1.53 GeV/c$\sp2$ where previous experiments find an enhancement. The results of the partial wave analysis show that the small peak at 1.28 GeV/c$\sp2$ contains very little $J\sp{PG}$ = 1$\sp{++}$ with $a\sb0$ as the isobar, which implies that the $f\sb1$(1285) contains very little $s\overline s$. The large peak near 1.4 GeV/c$\sp2$ is largely produced by $J\sp{PG}$ = 1$\sp{+-}$ and, to a lesser extent, 1$\sp{++}$ partial waves with $K\sp\*$ as the isobar and with evidence for these waves being produced coherently, 180$\sp\circ$ out of phase. There is evidence for a below $K\sp\* K$ threshold resonance in the $J\sp{PG}$ = 1$\sp{+-}$ partial waves with mass 1344 + 29 $-$ 43 MeV/c$\sp2$ and width 40 + 38 $-$ 40 MeV/c$\sp2$. There is little evidence in the partial wave analysis results for the $f\sbsp{1}{\prime}$(1530). The $J\sp{PG}$ = 0$\sp{-+}$ partial wave with $a\sb0$ as the isobar, although small, shows rising phase in the region from 1.34 to 1.64 GeV/c$\sp2$ indicating resonance behavior.

The reaction E+p+A+n and E+p+2°+n were studied using 2402 visible polarized E produced by the reaction K+p+ with the center of mass energy in the vicinity of the Y(1520) resonance. The capture ratios for stop ping and in-flight E were measured, and were all about 0.5.The cross-sections were obtained for both reactions at lab. momenta from 1 to 650 MeV/c. The results indicated that in the momentum ranged of 1 to 120 MeV/c the cross-sections were much larger than the S-wave absorption limits, indicating a constructive interference between the Coulomb and nuclear interactions.The crosssections in the momentum range of 120-400 MeV/c followed very closely the S-waveption limits. The angulardistributions showed definite non-isotropy in this region, indicating the presence of P and D waves. Two enhancement were found in the cross-sections in the momentum range of 400 and 650 MeV/c. They were observed at 2171 and 2191 MeV Σp center of mass energies. Insufficient data prevented a Breit-Wigner fit to these enhancements.The polarization of the outgoing A was measured w.r.t. to the incoming polarization direction.

The mode sum in bag model field operators is truncated for the purpose of studying higher order effects of QCD in a cavity. A perturbation theory method is developed in order to calculate higher order effects in a noncovariant way, as is necessitated by the noncovariant nature of the static cavity approximation. O($\alpha\sbsp{\rm s}{2}$) energy shifts are calculated for the ground state hadrons and bag model parameters are determined by a fit to hadron masses. The quark self-energy due just to the quark-gluon interaction is determined to O($\alpha\sbsp{\rm s}{6}$) using a pattern recognition code which finds and calculates over 10,000 diagrams. This same quark self-energy is summed to all orders in the planar approximation. The O($\alpha\sbsp{\rm s}{2}$) energy shifts of the H dibaryon and several diquark systems are also calculated by using a pattern recognition code. We find that the diquark state which is most bound at O($\alpha\sb{\rm s}$) remains so at O($\alpha\sbsp{\rm s}{2}$). We find the mass of the H dibaryon to be 2.1 $\pm$ 0.1 GeV. O($\alpha\sbsp{\rm s}{2}$) energy shifts for the J$\sp{\rm PC}$ = 0$\sp{++}$ glueball are calculated. This glueball is found to have negative mass at O($\alpha\sb{\rm s}$), but the O($\alpha\sbsp{\rm s}{2}$) shift nearly cancels the O($\alpha\sb{\rm s}$) shift leading to a glueball mass of approximately 1.2 GeV. Problems regarding independent particle wave functions and the Coulomb interaction are also discussed.

Neutrino oscillation experiments have demonstrated evidence for three distinct neutrino masses. However, whether there are two light neutrinos and one heavy neutrino (normal), or the other way around (inverted), known as the neutrino mass ordering, remains undetermined. This thesis presents a search for indications of the neutrino mass ordering in 6511 live-days (484 kiloton-years) of atmospheric neutrino data collected with the Super-Kamiokande (SK) detector between 1996 and 2020. The data set is a 30% increase in exposure since the previous published analysis, and the analysis methodology includes improvements to the separation of neutrino and antineutrino data. This thesis also presents an analysis of the SK data with constraints on neutrino oscillation parameters from reactor neutrino experiments and the T2K long-baseline experiment. The constraints from the T2K experiment include, for the first time, an anti-neutrino-enhanced data sample. The atmospheric-only analysis favors the normal neutrino mass ordering with Δχ2I.O.−N.O. = 5.98, and the inclusion of external constraints increases the preference to Δχ2I.O.−N.O. = 10.13.