arXiv subjects
Publications and source records attributed to Yoshihiro Takeuchi.
We make an analogy of Culler-Morgan-Shalen theory. Our main goal is to show that there exists a non-empty system of essential 2-suborbifolds respecting a given splitting of the orbifold fundamental group.
For an orbifold M we define a homology group, called t-singular homology group t-H_q(M), which depends not only on the topological structure of the underlying space of M, but also on the orbifold structure of M. We prove that it is a b-homotopy invariant of orbifolds. If M is a manifold, t-H_q(M) coincides with the usual singular homology group. We calculate the t-singular homology groups with Z-coefficients of several orbifolds. The t-singular homology group with rational coefficients of an orbifold M is isomorphic to the singular homology group with rational coefficients of M (and to that of |M|). For each q we define a homomorphism from the orbifold homotopy group π_q(M,x_0) to t-H_q(M) by using of t-modifications. Especially, t-H_1(M) is isomorphic to the abelianization of π_1(M,x_0) if M is arcwise connected.
Possible violation of CP, T and/or CPT symmetries in the $\ko$-$\kob$ system is studied from a phenomenological point of view. For this purpose, we first introduce parameters which represent violation of these symmetries in mixing parameters and decay amplitudes in a convenient and well-defined way and, treating these parameters as small, derive formulas which relate them to the experimentally measured quantities. We then perform numerical analyses, with the aid of the Bell-Steinberger relation, to derive constraints to these symmetry-violating parameters, firstly paying particular attention to the results reported by KTeV Collaboration and NA48 Collaboration, and then with the results reported by CPLEAR Collaboration as well taken into account. A case study, in which either CPT symmetry or T symmetry is assumed, is also carried out. It is demonstrated that CP and T symmetries are violated definitively at the level of 10^{-4} in $2π$ decays and presumably at the level of 10^{-3} in the $\ko-\kob$ mixing, and that the Bell-Steinberger relation helps us to establish CP and T violations being definitively present in the $\ko-\kob$ mixing and to test CPT symmetry to a level of 10^{-4} ~ 10^{-5}.