Studies of Zγ production and constraints on anomalous triple gauge couplings in pp collisions at √s = 7 TeV

In this thesis, we test the electroweak sector of the Standard Model of particle physics through the measurements of the cross section of the simultaneous production of the neutral weak boson Z and photon γ, and the limits on the anomalous Zγγ and ZZγ triple gauge couplings h3 and h4 with the Z decaying to leptons (electrons and muons). We analyze events collected in proton-proton collisions at center of mass energy of sqrt(s) = 7 TeV corresponding to an integrated luminosity of 5.0 inverse femtobarn. The analyzed events were recorded by the Compact Muon Solenoid detector at the Large Hadron Collider in 2011.

The production cross section has been measured for hard photons with transverse momentum greater than 15 GeV that are separated from the the final state leptons in the eta-phi plane by Delta R greater than 0.7, whose sum of the transverse energy of hadrons over the transverse energy of the photon in a cone around the photon with Delta R less than 0.3 is less than 0.5, and with the invariant mass of the dilepton system greater than 50 GeV. The measured cross section value is 5.33 +/- 0.08 (stat.) +/- 0.25 (syst.) +/- 0.12 (lumi.) picobarn. This is compatible with the Standard Model prediction that includes next-to-leading-order QCD contributions: 5.45 +/- 0.27 picobarn.

The measured 95 % confidence-level upper limits on the absolute values of the anomalous couplings h3 and h4 are 0.01 and 8.8E-5 for the Zγγ interactions, and, 8.6E-3 and 8.0E-5 for the ZZγ interactions. These values are also compatible with the Standard Model where they vanish in the tree-level approximation. They extend the sensitivity of the 2012 results from the ATLAS collaboration based on 1.02 inverse femtobarn of data by a factor of 2.4 to 3.1.

Relative mirror symmetry and ramifications of a formula for Gromov-Witten invariants

For a toric Del Pezzo surface S, a new instance of mirror symmetry, said relative, is introduced and developed. On the A-model, this relative mirror symmetry conjecture concerns genus 0 relative Gromov-Witten of maximal tangency of S. These correspond, on the B-model, to relative periods of the mirror to S. Furthermore, for S not necessarily toric, two conjectures for BPS state counts are related. It is proven that the integrality of BPS state counts of the total space of the canonical bundle on S implies the integrality for the relative BPS state counts of S. Finally, a prediction of homological mirror symmetry for the open complement is explored. The B-model prediction is calculated in all cases and matches the known A-model computation for the projective plane.

Charge symmetry in ^(13)N and ^(13)C a coupled-channel model

A set of coupled-channel differential equations based on a rotationally distorted optical potential is used to calculate the wave functions required to evaluate the gamma ray transition rate from the first excited state to the ground state in ^(13)C and ^(13)N. The bremsstrahlung differential cross section of low energy protons is also calculated and compared with existing data. The marked similarity between the potentials determined at each resonance level in both nuclei supports the hypothesis of the charge symmetry of nuclear forces by explaining the deviation of the ratios of the experimental E1 transition strengths from unity.

Gauge Invariant Spectral Cauchy Characteristic Extraction of Gravitational Waves in Computational General Relativity

We present a complete system for Spectral Cauchy characteristic extraction (Spectral CCE). Implemented in C++ within the Spectral Einstein Code (SpEC), the method employs numerous innovative algorithms to efficiently calculate the Bondi strain, news, and flux.

Spectral CCE was envisioned to ensure physically accurate gravitational wave-forms computed for the Laser Interferometer Gravitational wave Observatory (LIGO) and similar experiments, while working toward a template bank with more than a thousand waveforms to span the binary black hole (BBH) problem’s seven-dimensional parameter space.

The Bondi strain, news, and flux are physical quantities central to efforts to understand and detect astrophysical gravitational wave sources within the Simulations of eXtreme Spacetime (SXS) collaboration, with the ultimate aim of providing the first strong field probe of the Einstein field equation.

In a series of included papers, we demonstrate stability, convergence, and gauge invariance. We also demonstrate agreement between Spectral CCE and the legacy Pitt null code, while achieving a factor of 200 improvement in computational efficiency.

Spectral CCE represents a significant computational advance. It is the foundation upon which further capability will be built, specifically enabling the complete calculation of junk-free, gauge-free, and physically valid waveform data on the fly within SpEC.

I. Non-linear effects in a self-consistent calculation of SU_3 symmetry breaking in strong interaction coupling constants. II. Direct-channel reggeization of strong interaction scattering amplitudes

The thesis is divided into two parts. Part I generalizes a self-consistent calculation of residue shifts from SU₃ symmetry, originally performed by Dashen, Dothan, Frautschi, and Sharp, to include the effects of non-linear terms. Residue factorizability is used to transform an overdetermined set of equations into a variational problem, which is designed to take advantage of the redundancy of the mathematical system. The solution of this problem automatically satisfies the requirement of factorizability and comes close to satisfying all the original equations.

Part II investigates some consequences of direct channel Regge poles and treats the problem of relating Reggeized partial wave expansions made in different reaction channels. An analytic method is introduced which can be used to determine the crossed-channel discontinuity for a large class of direct-channel Regge representations, and this method is applied to some specific representations.

It is demonstrated that the multi-sheeted analytic structure of the Regge trajectory function can be used to resolve apparent difficulties arising from infinitely rising Regge trajectories. Also discussed are the implications of large collections of "daughter trajectories."

Two things are of particular interest: first, the threshold behavior in direct and crossed channels; second, the potentialities of Reggeized representations for us in self-consistent calculations. A new representation is introduced which surpasses previous formulations in these two areas, automatically satisfying direct-channel threshold constraints while being capable of reproducing a reasonable crossed channel discontinuity. A scalar model is investigated for low energies, and a relation is obtained between the mass of the lowest bound state and the slope of the Regge trajectory.