CP, T and CPT violation in future long baseline experiments

I give a short overview about the possibilities and problems related to the measurement of CP violation in long baseline experiments. Special attention is paid to the issue of degeneracies and a method for their resolution is quantitatively discussed. The CP violation reach for different experiments is compared in dependence of $\sin^22\theta_{13}$ and \dm{21}. Furthermore a short comment about the possible effects of matter induced T violation is made. Finally the limits on CPT violation obtainable at a neutrino factory are shown.Comment: Talk presented at NUFACT02, London, 1-6 July, 2002. 3 pages, 2 figure

Characterizing Block Graphs in Terms of their Vertex-Induced Partitions

Given a finite connected simple graph $G=(V,E)$ with vertex set $V$ and edge set $E\subseteq \binom{V}{2}$, we will show that $1.$ the (necessarily unique) smallest block graph with vertex set $V$ whose edge set contains $E$ is uniquely determined by the $V$-indexed family ${\bf P}_G:=\big(\pi_0(G^{(v)})\big)_{v \in V}$ of the various partitions $\pi_0(G^{(v)})$ of the set $V$ into the set of connected components of the graph $G^{(v)}:=(V,\{e\in E: v\notin e\})$, $2.$ the edge set of this block graph coincides with set of all $2$-subsets $\{u,v\}$ of $V$ for which $u$ and $v$ are, for all $w\in V-\{u,v\}$, contained in the same connected component of $G^{(w)}$, $3.$ and an arbitrary $V$-indexed family ${\bf P}p=({\bf p}_v)_{v \in V}$ of partitions $\pi_v$ of the set $V$ is of the form ${\bf P}p={\bf P}p_G$ for some connected simple graph $G=(V,E)$ with vertex set $V$ as above if and only if, for any two distinct elements $u,v\in V$, the union of the set in ${\bf p}_v$ that contains $u$ and the set in ${\bf p}_u$ that contains $v$ coincides with the set $V$, and $\{v\}\in {\bf p}_v$ holds for all $v \in V$. As well as being of inherent interest to the theory of block graphs, these facts are also useful in the analysis of compatible decompositions and block realizations of finite metric spaces

Block-Transitive Designs in Affine Spaces

This paper deals with block-transitive $t$-$(v,k,\lambda)$ designs in affine spaces for large $t$, with a focus on the important index $\lambda=1$ case. We prove that there are no non-trivial 5-$(v,k,1)$ designs admitting a block-transitive group of automorphisms that is of affine type. Moreover, we show that the corresponding non-existence result holds for 4-$(v,k,1)$ designs, except possibly when the group is one-dimensional affine. Our approach involves a consideration of the finite 2-homogeneous affine permutation groups.Comment: 10 pages; to appear in: "Designs, Codes and Cryptography

Resolving Octant Degeneracy at LBL experiment by combining Daya Bay Reactor Setup

Long baseline Experiment (LBL) have promised to be a very powerful experimental set up to study various issues related to Neutrinos. Some ongoing and planned LBL and medium baseline experiments are - T2K, MINOS, NOvA, LBNE, LBNO etc. But the long baseline experiments are crippled due to presence of some parameter degeneracies, like the Octant degeneracy. In this work, we first show the presence of Octant degeneracy in LBL experiments, and then combine it with Daya Bay Reactor experiment, at different values of CP violation phase. We show that the Octant degeneracy in LBNE can be resolved completely with this proposal.Comment: 4 pages, 8 figure

Untangling CP Violation and the Mass Hierarchy in Long Baseline Experiments

In the overlap region, for the normal and inverted hierarchies, of the neutrino-antineutrino bi-probability space for $\nu_\mu \to \nu_e$ appearance, we derive a simple identity between the solutions in the ($\sin^2 2\theta_{13}$, $\sin \delta$) plane for the different hierarchies. The parameter $\sin^2 2\theta_{13}$ sets the scale of the $\nu_\mu \to \nu_e$ appearance probabilities at the atmospheric $\delta m^2_{atm} \approx 2.4 \times 10^{-3}$ eV$^2$ whereas $\sin \delta$ controls the amount of CP violation in the lepton sector. The identity between the solutions is that the difference in the values of $\sin \delta$ for the two hierarchies equals twice the value of $\sqrt{\sin^2 2\theta_{13}}$ divided by the {\it critical} value of $\sqrt{\sin^2 2\theta_{13}}$. We apply this identity to the two proposed long baseline experiments, T2K and NO$\nu$A, and we show how it can be used to provide a simple understanding of when and why fake solutions are excluded when two or more experiments are combined. The identity demonstrates the true complimentarity of T2K and NO$\nu$A.Comment: 15 pages, Latex, 4 postscript figures. Submitted to New Journal of Physics, ``Focus on Neutrino Physics'' issu