Antihydrogen, CPT, and Naturalness

Studying fundamental symmetries of Nature has proven fruitful in particle physics. I argue that recent results at the LHC, and the naturalness problem highlighted by them, provide a renewed motivation for tests of CPT symmetry as a probe for physics beyond quantum field theory. I also discuss prospects for antihydrogen CPT tests with sensitivities to Planck scale suppressed effects.Comment: Based on an invited talk at CPT'13 -- the Sixth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 17-21, 201

Detecting Antihydrogen: The Challenges and the Applications

ATHENA's first detection of cold antihydrogen atoms relied on their annihilation signatures in a sophisticated particle detector. We will review the features of the ATHENA detector and its applications in trap physics. The detector for a new experiment ALPHA will have considerable challenges due to increased material thickness in the trap apparatus as well as field non-uniformity. Our studies indicate that annihilation vertex imaging should be still possible despite these challenges. An alternative method for trapped antihydrogen, via electron impact ionization, will be also discussed.Comment: Invited paper at International Workshop on Physics with Ultra-Slow Antiprotons, RIKEN, Japan, March 2005. To be published in AIP Conference Proceeding

Supersymmetric U(N) Gauge Model and Partial Breaking of N=2 Supersymmetry

Guided by the gauging of U(N) isometry associated with the special Kahler geometry, and the discrete R symmetry, we construct the N=2 supersymmetric action of a U(N) invariant nonabelian gauge model in which rigid N=2 supersymmetry is spontaneously broken to N=1. This generalizes the abelian model considered by Antoniadis, Partouche and Taylor. We shed light on complexity of the supercurrents of our model associated with a broken N=2 supermultiplet of currents, and discuss the spontaneously broken supersymmetry as an approximate fermionic shift symmetry.Comment: 32 pages; typos corrected and references added; the version to be published in Prog. Theor. Phys, a pedagogical appendix adde

Prenex normalization and the hierarchical classification of formulas

Akama et al. [1] introduced a hierarchical classification of first-order formulas for a hierarchical prenex normal form theorem in semi-classical arithmetic. In this paper, we give a justification for the hierarchical classification in a general context of first-order theories. To this end, we first formalize the standard transformation procedure for prenex normalization. Then we show that the classes $\mathrm{E}_k$ and $\mathrm{U}_k$ introduced in [1] are exactly the classes induced by $\Sigma_k$ and $\Pi_k$ respectively via the transformation procedure in any first-order theory.Comment: 15 page