Methods for Probing New Physics at High Energies
Denton, Peter Bennert
This thesis covers two distinct topics: integral dispersion relations (IDRs) and ultra high energy cosmic ray (UHECR) anisotropy. Many models of electroweak symmetry breaking predict new physics scales near LHC energies. Even if these particles are too massive to be produced on shell, it may be possible to infer their existence through the use of IDRs. Making use of Cauchy's integral formula and the analyticity of the scattering amplitude, IDRs are sensitive to changes in the cross section at all energies. We find that a sudden order one increase in the cross section can be detected well below the threshold energy. For two more physical models, the reach of the IDR technique is greatly reduced. The peak sensitivity for the IDR technique is shown to occur when the new particle masses are near the machine energy. Thus, IDRs do extend the reach of the LHC, but only to a window around M_X^2~s_LHC. Determining anisotropies in the arrival directions of UHECRs (>5e19 eV) is an important task in astrophysics. Spherical harmonics are a useful measure of anisotropy. The two lowest nontrivial spherical harmonics, the dipole and the quadrupole, are of particular interest, since they encapsulate a single source and a planar source. The best current UHECR experiments are all ground based, with highly nonuniform exposures which increases the complexity and error in inferring anisotropies. The two main advantages of space based observation of UHECRs are the increased field of view and the full sky coverage with uniform systematics. It turns out that there is an optimal latitude, which runs near the two largest experiments, for an experiment at which nonuniform exposure does not diminish the inference of the quadrupole moment. Consequently, assuming a quadrupole distribution, these experiments can reconstruct a quadrupole distribution to a high precision, without concern for their partial sky exposure. We then investigate the reach of a full sky experiment to detect anisotropies compared to these partial sky experiments. Simulations with dipoles and quadrupoles quantify the advantages of space based, all sky coverage.