The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

Fuchs versus Painlev\'e

We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e VI. We then show that the polynomiality of the expressions of the correlation functions (and form factors) in terms of the complete elliptic integral of the first and second kind, $K$ and $E$, is a straight consequence of the fact that the differential operators corresponding to the entries of Toeplitz-like determinants, are equivalent to the second order operator $L_E$ which has $E$ as solution (or, for off-diagonal correlations to the direct sum of $L_E$ and $d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $\Pi_1$, the Jacobi's form of the complete elliptic integral of the third kind (or equivalently two second order linear partial differential operators associated with Appell functions, where one of these operators can be seen as a deformation of $L_E$). We finally explore the generalizations, to the anisotropic Ising models, of the links we made, in two previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and elliptic curves. In particular the elliptic representation of Painlev\'e VI has to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of Difference Equations, SIDE VII meeting held in Melbourne during July 200

MEG Upgrade Proposal

We propose the continuation of the MEG experiment to search for the charged lepton flavour violating decay (cLFV) \mu \to e \gamma, based on an upgrade of the experiment, which aims for a sensitivity enhancement of one order of magnitude compared to the final MEG result, down to the $6 \times 10^{-14}$ level. The key features of this new MEG upgrade are an increased rate capability of all detectors to enable running at the intensity frontier and improved energy, angular and timing resolutions, for both the positron and photon arms of the detector. On the positron-side a new low-mass, single volume, high granularity tracker is envisaged, in combination with a new highly segmented, fast timing counter array, to track positron from a thinner stopping target. The photon-arm, with the largest liquid xenon (LXe) detector in the world, totalling 900 l, will also be improved by increasing the granularity at the incident face, by replacing the current photomultiplier tubes (PMTs) with a larger number of smaller photosensors and optimizing the photosensor layout also on the lateral faces. A new DAQ scheme involving the implementation of a new combined readout board capable of integrating the diverse functions of digitization, trigger capability and splitter functionality into one condensed unit, is also under development. We describe here the status of the MEG experiment, the scientific merits of the upgrade and the experimental methods we plan to use.Comment: A. M. Baldini and T. Mori Spokespersons. Research proposal submitted to the Paul Scherrer Institute Research Committee for Particle Physics at the Ring Cyclotron. 131 Page

Measurement of the radiative decay of polarized muons in the MEG experiment

We studied the radiative muon decay $\mu^+ \to e^+\nu\bar{\nu}\gamma$ by using for the first time an almost fully polarized muon source. We identified a large sample (~13000) of these decays in a total sample of 1.8x10^14 positive muon decays collected in the MEG experiment in the years 2009--2010 and measured the branching ratio B($\mu^+ \to e^+\nu\bar{\nu}\gamma$) = (6.03+-0.14(stat.)+-0.53(sys.))x10^-8 for E_e > 45 MeV and E_{\gamma} > 40 MeV, consistent with the Standard Model prediction. The precise measurement of this decay mode provides a basic tool for the timing calibration, a normalization channel, and a strong quality check of the complete MEG experiment in the search for $\mu^+ \to e^+\gamma$ process.Comment: 8 pages, 7 figures. Added an introduction to NLO calculation which was recently calculated. Published versio

The MEG detector for μ+→e+γ{\mu}+\to e+{\gamma} decay search

The MEG (Mu to Electron Gamma) experiment has been running at the Paul Scherrer Institut (PSI), Switzerland since 2008 to search for the decay \meg\ by using one of the most intense continuous $\mu^+$ beams in the world. This paper presents the MEG components: the positron spectrometer, including a thin target, a superconducting magnet, a set of drift chambers for measuring the muon decay vertex and the positron momentum, a timing counter for measuring the positron time, and a liquid xenon detector for measuring the photon energy, position and time. The trigger system, the read-out electronics and the data acquisition system are also presented in detail. The paper is completed with a description of the equipment and techniques developed for the calibration in time and energy and the simulation of the whole apparatus.Comment: 59 pages, 90 figure

Precise Measurement of the Pi+ -> Pi0 e+ nu Branching Ratio

Using a large acceptance calorimeter and a stopped pion beam we have made a precise measurement of the rare Pi+ -> Pi0 e+ Nu,(pi_beta) decay branching ratio. We have evaluated the branching ratio by normalizing the number of observed pi_beta decays to the number of observed Pi+ -> e+ Nu, (pi_{e2}) decays. We find the value of Gamma(Pi+ -> Pi0 e+ Nu)/Gamma(total) = [1.036 +/- 0.004(stat.) +/- 0.004(syst.) +/- 0.003(pi_{e2})] x 10^{-8}$, where the first uncertainty is statistical, the second systematic, and the third is the pi_{e2} branching ratio uncertainty. Our result agrees well with the Standard Model prediction.Comment: 4 pages, 5 figures, 1 table, revtex4; changed content; updated analysi

New constraint on the existence of the mu+-> e+ gamma decay

The analysis of a combined data set, totaling 3.6 \times 10^14 stopped muons on target, in the search for the lepton flavour violating decay mu^+ -> e^+ gamma is presented. The data collected by the MEG experiment at the Paul Scherrer Institut show no excess of events compared to background expectations and yield a new upper limit on the branching ratio of this decay of 5.7 \times 10^-13 (90% confidence level). This represents a four times more stringent limit than the previous world best limit set by MEG.Comment: 5 pages, 3 figures, a version accepted in Phys. Rev. Let

Muon Physics: A Pillar of the Standard Model

Since its discovery in the 1930s, the muon has played an important role in our quest to understand the sub-atomic theory of matter. The muon was the first second-generation standard-model particle to be discovered, and its decay has provided information on the (Vector -Axial Vector) structure of the weak interaction, the strength of the weak interaction, G_F, and the conservation of lepton number (flavor) in muon decay. The muon's anomalous magnetic moment has played an important role in restricting theories of physics beyond the standard standard model, where at present there is a 3.4 standard-deviation difference between the experiment and standard-model theory. Its capture on the atomic nucleus has provided valuable information on the modification of the weak current by the strong interaction which is complementary to that obtained from nuclear beta decay.Comment: 8 pages, 9 figures. Invited paper for the Journal of Physical Society in Japan (JPSJ), Special Topics Issue "Frontiers of Elementary Particle Physics, The Standard Model and beyond

Examining leptogenesis with lepton flavor violation and the dark matter abundance

Within a supersymmetric (SUSY) type-I seesaw framework with flavor-blind universal boundary conditions, we study the consequences of requiring that the observed baryon asymmetry of the Universe be explained by either thermal or non-thermal leptogenesis. In the former case, we find that the parameter space is very constrained. In the bulk and stop-coannihilation regions of mSUGRA parameter space (that are consistent with the measured dark matter abundance), lepton flavor-violating (LFV) processes are accessible at MEG and future experiments. However, the very high reheat temperature of the Universe needed after inflation (of about 10^{12} GeV) leads to a severe gravitino problem, which disfavors either thermal leptogenesis or neutralino dark matter. Non-thermal leptogenesis in the preheating phase from SUSY flat directions relaxes the gravitino problem by lowering the required reheat temperature. The baryon asymmetry can then be explained while preserving neutralino dark matter, and for the bulk or stop-coannihilation regions LFV processes should be observed in current or future experiments.Comment: 20 pages, 5 figures, 1 tabl

Interplay of LFV and slepton mass splittings at the LHC as a probe of the SUSY seesaw

We study the impact of a type-I SUSY seesaw concerning lepton flavour violation (LFV) both at low-energies and at the LHC. The study of the di-lepton invariant mass distribution at the LHC allows to reconstruct some of the masses of the different sparticles involved in a decay chain. In particular, the combination with other observables renders feasible the reconstruction of the masses of the intermediate sleptons involved in $\chi_2^0\to \tilde \ell \,\ell \to \ell \,\ell\,\chi_1^0$ decays. Slepton mass splittings can be either interpreted as a signal of non-universality in the SUSY soft breaking-terms (signalling a deviation from constrained scenarios as the cMSSM) or as being due to the violation of lepton flavour. In the latter case, in addition to these high-energy processes, one expects further low-energy manifestations of LFV such as radiative and three-body lepton decays. Under the assumption of a type-I seesaw as the source of neutrino masses and mixings, all these LFV observables are related. Working in the framework of the cMSSM extended by three right-handed neutrino superfields, we conduct a systematic analysis addressing the simultaneous implications of the SUSY seesaw for both high- and low-energy lepton flavour violation. We discuss how the confrontation of slepton mass splittings as observed at the LHC and low-energy LFV observables may provide important information about the underlying mechanism of LFV.Comment: 50 pages, 42 eps Figures, typos correcte