A Common Explanation for the Atmospheric, Solar-Neutrino and Double Beta Decay Anomalies

We make a number of small changes, including correcting an error in our heavy-neutrino decay rate. None of our analysis is changed, either in substance or detail.Comment: 25 pages, 6 Figures, McGill-93/1

Ping Pong in Dangerous Graphs: Optimal Black Hole Search with Pebbles

International audienceWe prove that, for the black hole search problem in networks of arbitrary but known topology, the pebble model of agent interaction is computationally as powerful as the whiteboard model; furthermore the complexity is exactly the same. More precisely, we prove that a team of two asynchronous agents, each endowed with a single identical pebble (that can be placed only on nodes, and with no more than one pebble per node), can locate the black hole in an arbitrary network of known topology; this can be done with Θ(nlog n) moves, where n is the number of nodes, even when the links are not FIFO. These results are obtained with a novel algorithmic technique, ping-pong, for agents using pebbles

Resolving the Large-N Nuclear Potential Puzzle

The large $N_c$ nuclear potential puzzle arose because three- and higher-meson exchange contributions to the nucleon-nucleon potential did not automatically yield cancellations that make these contributions consistent with the general large $N_c$ scaling rules for the potential. Here it is proposed that the resolution to this puzzle is that the scaling rules only apply for energy-independent potentials while all of the cases with apparent inconsistencies were for energy-dependent potentials. It is shown explicitly how energy-dependent potentials can have radically different large N behavior than an equivalent energy-independent one. One class of three-meson graphs is computed in which the contribution to the energy-independent potential is consistent with the general large N rules even though the energy-dependent potential is not.Comment: Corrections to the toy mode

Large independent sets in triangle-free cubic graphs: beyond planarity

Every $n$-vertex planar triangle-free graph with maximum degree at most $3$ has an independent set of size at least $\frac{3}{8}n$. This was first conjectured by Albertson, Bollob\'as and Tucker, and was later proved by Heckman and Thomas. Fraughnaugh and Locke conjectured that the planarity requirement could be relaxed into just forbidding a few specific nonplanar subgraphs: They described a family $\mathcal{F}$ of six nonplanar graphs (each of order at most $22$) and conjectured that every $n$-vertex triangle-free graph with maximum degree at most $3$ having no subgraph isomorphic to a member of $\mathcal{F}$ has an independent set of size at least $\frac{3}{8}n$. In this paper, we prove this conjecture. As a corollary, we obtain that every $2$-connected $n$-vertex triangle-free graph with maximum degree at most $3$ has an independent set of size at least $\frac{3}{8}n$, with the exception of the six graphs in $\mathcal{F}$. This confirms a conjecture made independently by Bajnok and Brinkmann, and by Fraughnaugh and Locke.Comment: v2: Referees' comments incorporate

Neutrino Masses and Mixings in a Predictive SO(10) Model with CKM CP Violation

It has recently been shown that a minimal SO(10) model with a single {\bf 10} and single {\bf 126} Higgs field breaking B-L symmetry predicts large solar and atmospheric mixings in agreement with observations if it is assumed that the neutrino mass obeys the type II seesaw formula. No additional symmetries need to be assumed for this purpose. Understanding CP violation in the renormalizable version of the model however requires a significant non-CKM source. In this paper we show that if we extend the model by the inclusion of a heavy {\bf 120} dimensional Higgs field, then it can accomodate CKM CP violation while remaining predictive in the neutrino sector. Among the predictions are:(i) solar mixing angle in the observed range; (ii)\theta_{13} in the range of 0.1 to 0.26; (iii) the Dirac phase close to maximal for the central value of the solar mixing angle.Comment: 16 pages, 10 figures, Comments are added, Typos are corrected, An erroneous sentence on discrete symmetry is modified, Results are unchange

A Generalization of Slavnov-Extended Non-Commutative Gauge Theories

We consider a non-commutative U(1) gauge theory in 4 dimensions with a modified Slavnov term which looks similar to the 3-dimensional BF model. In choosing a space-like axial gauge fixing we find a new vector supersymmetry which is used to show that the model is free of UV/IR mixing problems, just as in the previously discussed model in arXiv:hep-th/0604154. Finally, we present generalizations of our proposed model to higher dimensions.Comment: 25 pages, no figures; v2 minor correction

O(1/N_f) Corrections to the Thirring Model in 2<d<4

The Thirring model, that is, a relativistic field theory of fermions with a contact interaction between vector currents, is studied for dimensionalities 2<d<4 using the 1/N_f expansion, where N_f is the number of fermion species. The model is found to have no ultraviolet divergences at leading order provided a regularization respecting current conservation is used. Explicit O(1/N_f) corrections are computed, and the model shown to be renormalizable at this order in the massless limit; renormalizability appears to hold to all orders due to a special case of Weinberg's theorem. This implies there is a universal amplitude for four particle scattering in the asymptotic regime. Comparisons are made with both the Gross-Neveu model and QED.Comment: 22 pages in plain TeX, with 7 figs included using psfig.tex (Minor conceptual changes - algebra unaffected