Level sets of multiple ergodic averages

We propose to study multiple ergodic averages from multifractal analysis point of view. In some special cases in the symbolic dynamics, Hausdorff dimensions of the level sets of multiple ergodic average limit are determined by using Riesz products.Comment: This note was refused by Proceedings of AMS although the referee said "In my opinion this is a nice application of the Riesz product technique to solve, in principle, a hard problem when considered in its full generality. Nevertheless, I think it needs some extra work to see how this example seats in a more general context and explore how far this technique can go." We should say that Riesz product works perfectly in the situation described in this note, but Riesz product has its limit--we don't think that Riesz product technique can solve the problem in its generalit

Radiative Neutrino Mass in Type III Seesaw Model

The simplest type III seesaw model as originally proposed introduces one lepton triplet. It thus contains four active neutrinos, two massive and two massless at tree level. We determine the radiative masses that the latter receive first at two loops. The masses are generally so tiny that they are definitely excluded by the oscillation data, if the heavy leptons are not very heavy, say, within the reach of LHC. To accommodate the data on masses, the seesaw scale must be as large as the scale of grand unification. This indicates that the most economical type III model would entail no new physics at low energies beyond the tiny neutrino masses.Comment: 21 pages, 1 figure; v2: added 3 sentences in sec 4 for clarifications, version published on 7 Apr 2009 in PR D79, 073003 (2009

Radiative and flavor-violating transitions of leptons from interactions with color-octet particles

It has been recently proposed that neutrino mass could originate from Yukawa interactions of leptons with new colored particles. This raises the interesting possibility of testing mass generation through copious production of those particles at hadron colliders. A realistic assessment of it however should take into account how large those interactions could be from available precision results. In this work we make a systematic analysis to the flavor structure in Yukawa couplings, provide a convenient parametrization to it, and investigate the rare radiative and pure leptonic decays of the muon and tau leptons. For general values of parameters the muon decays set stringent constraints on the couplings, and all rare tau decays are far below the current experimental sensitivity. However, there is room in parameter space in which the muon decays could be significantly suppressed by destructive interference between colored particles without generically reducing the couplings themselves. This is also the region of parameters that is relevant to collider physics. We show that for this part of parameter space some tau decays can reach or are close to the current level of precision.Comment: 20 pages, 7 figure