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.

We have measured low relative momentum correlations between like sign pions produced in the reactions pp $\to$ pp($\pi\sp+,\pi\sp{-})\sp{\rm n}$ with n ranging from 2 to 6. The data sample consisted of $0.93\times10\sp6$ fully reconstructed exclusive interactions, with incident proton momentum of 27.5 GeV/c, recorded by experiment E766 at the AGS in Brookhaven National Laboratory. By parametrizing the correlation with a function of Q$\sp2$ representing the dynamics of the reaction and the correlation itself, it was shown that the Q$\sp2$ scale does not depend on the final state multiplicity and has a value of 1.08 fermi. The "strength" of the correlation does depend on multiplicity. For negative pions the "strength" is 26% larger than for positive pions.

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There are several anomalies within the Standard Model of particle physics that may be explained by means of light new physics. These may be associated with muons, with the gyromagnetic ratio of the muon being different from theory at the level of 3.4σ, and with the 7σ muonic Hydrogen proton radius extraction. Previous, current, and new experiments may be able to place stringent limits on the existence of a new scalar force, with a coupling to leptons proportional to their mass. We investigate the sensitivity to the parameter space of the muon decay experiment Mu3e, the kaon decay experiments NA48/2 and NA62, and the experiments at asymmetric electron-positron colliders, BaBar, Belle, Belle2. Using Monte Carlo techniques to generate events for processes corresponding to each experiment, we find that these experiments could be sensitive to muonic couplings down to 10^−5, and over a wide mass range of 10 MeV − 3.5 GeV, fully covering the parameter space relevant for explanations of these anomalies. The possibility exists to later extend to masses up to 10 GeV. / Graduate

The proposed neutrino factory, a facility for precision measurements of neutrino oscillations, requires directional neutrino beams to reach the required sensitivities. Among the few sources of such beams is the decay of muons travelling at relativistic speeds, therefore an intense source of muons and subsequent rapid acceleration must be designed so they can reach the required energy before decaying. This thesis considers several stages in this process: pions are produced from a proton beam hitting a target and pion yield optima are determined as a function of target design parameters and the proton energy. Issues related to producing the original proton beam are also discussed. The pions decay to a beam of muons, confined by a channel of solenoids and other components known as the muon front end. A design for this is found that meets the requirement of 10^21 muons per operational year [1]. The computer code MARS15 [2] is used to simulate the target, with benchmarks against GEANT4 [3] and initial results from the HARP experiment [4]. The author's code Muon1 [5] is used for muon tracking, with its techniques also explained in the thesis. To find the highest-yielding arrangement of magnets and accelerating components from the target onwards, Muon1 incorporates an optimisation feature where almost all parameters of the beamline can be varied. This produces a high-dimensionality search space where the best muon yield is sought using a genetic algorithm. As each individual evaluation of a design is itself a time-consuming simulation with tens of thousands of particles, the code has been deployed as a distributed computing project that is able to perform millions of simulations per optimisation. [1] "GROUP REPORT: Physics at a Neutrino Factory", C. Albright et al. (Eds. S. Geer and H. Schellman), Report to the Fermilab Directorate, FERMILAB-FN-692, hep-ex/0008064 (2000). [2] "The MARS Code System" version 15.07, by N.V. Mokhov, available from http://www-ap.fnal.gov/MARS/ [3] "GEANT4 - a simulation toolkit", S. Agostinelli et al., Nuclear Instruments and Methods A 506, pp.250-303 (2003), available from http://geant4.web.cern.ch/geant4/ [4] "Status and prospects of the HARP experiment", M. Ellis, J. Phys. G 29, pp.1613-1620 (2003). [5] Muon1 Distributed Particle Accelerator Design project website, http://stephenbrooks.org/muon1