Nuclearity and Thermal States in Conformal Field Theory

We introduce a new type of spectral density condition, that we call L^2-nuclearity. One formulation concerns lowest weight unitary representations of SL(2,R) and turns out to be equivalent to the existence of characters. A second formulation concerns inclusions of local observable von Neumann algebras in Quantum Field Theory. We show the two formulations to agree in chiral Conformal QFT and, starting from the trace class condition for the semigroup generated by the conformal Hamiltonian L_0, we infer and naturally estimate the Buchholz-Wichmann nuclearity condition and the (distal) split property. As a corollary, if L_0 is log-elliptic, the Buchholz-Junglas set up is realized and so there exists a beta-KMS state for the translation dynamics on the net of C*-algebras for every inverse temperature beta>0. We include further discussions on higher dimensional spacetimes. In particular, we verify that L^2-nuclearity is satisfied for the scalar, massless Klein-Gordon field.Comment: 37 pages, minor correction

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level

Searches for lepton number violating K+ decays

The NA62 experiment at CERN reports a search for the lepton number violating decays K+→π−e+e+ and K+→π−μ+μ+ using a data sample collected in 2017. No signals are observed, and upper limits on the branching fractions of these decays of 2.2 x 10^-10 and 4.2 x 10^-11 are obtained, respectively, at 90% confidence level. These upper limits improve on previously reported measurements by factors of 3 and 2, respectively

Search for heavy neutral lepton production in K+ decays to positrons

A search for heavy neutral lepton (N) production in K+→e+N decays using the data sample collected by the NA62 experiment at CERN in 2017-2018 is reported. Upper limits of the extended neutrino mixing matrix element |Ue4|^2 are established at the level of 10^−9 over most of the accessible heavy neutral lepton mass range 144-462 MeV/c^2, with the assumption that the lifetime exceeds 50 ns. These limits improve significantly upon those of previous production and decay searches. The |Ue4|^2 range favoured by Big Bang Nucleosynthesis is excluded up to a mass of about 340 MeV/c^2

Heterozygous ANKRD17 loss-of-function variants cause a syndrome with intellectual disability, speech delay, and dysmorphism

ANKRD17 is an ankyrin repeat-containing protein thought to play a role in cell cycle progression, whose ortholog in Drosophila functions in the Hippo pathway as a co-factor of Yorkie. Here, we delineate a neurodevelopmental disorder caused by de novo heterozygous ANKRD17 variants. The mutational spectrum of this cohort of 34 individuals from 32 families is highly suggestive of haploinsufficiency as the underlying mechanism of disease, with 21 truncating or essential splice site variants, 9 missense variants, 1 in-frame insertion-deletion, and 1 microdeletion (1.16 Mb). Consequently, our data indicate that loss of ANKRD17 is likely the main cause of phenotypes previously associated with large multi-gene chromosomal aberrations of the 4q13.3 region. Protein modeling suggests that most of the missense variants disrupt the stability of the ankyrin repeats through alteration of core structural residues. The major phenotypic characteristic of our cohort is a variable degree of developmental delay/intellectual disability, particularly affecting speech, while additional features include growth failure, feeding difficulties, non-specific MRI abnormalities, epilepsy and/or abnormal EEG, predisposition to recurrent infections (mostly bacterial), ophthalmological abnormalities, gait/balance disturbance, and joint hypermobility. Moreover, many individuals shared similar dysmorphic facial features. Analysis of single-cell RNA-seq data from the developing human telencephalon indicated ANKRD17 expression at multiple stages of neurogenesis, adding further evidence to the assertion that damaging ANKRD17 variants cause a neurodevelopmental disorder.Neurolog

Measurement of the very rare K+→π+ννˉK^+ \to \pi^+ \nu \bar\nu decay

The decay K+→π+νν¯ , with a very precisely predicted branching ratio of less than 10−10 , is among the best processes to reveal indirect effects of new physics. The NA62 experiment at CERN SPS is designed to study the K+→π+νν¯ decay and to measure its branching ratio using a decay-in-flight technique. NA62 took data in 2016, 2017 and 2018, reaching the sensitivity of the Standard Model for the K+→π+νν¯ decay by the analysis of the 2016 and 2017 data, and providing the most precise measurement of the branching ratio to date by the analysis of the 2018 data. This measurement is also used to set limits on BR(K+→π+X ), where X is a scalar or pseudo-scalar particle. The final result of the BR(K+→π+νν¯ ) measurement and its interpretation in terms of the K+→π+X decay from the analysis of the full 2016-2018 data set is presented, and future plans and prospects are reviewed

Search for lepton number and flavour violation in K+ and pi0 decays

The NA62 experiment at CERN collected a large sample of charged kaon decays into final states with multiple charged particles in 2016-2018. This sample provides sensitivities to rare decays with branching ratios as low as 10 −11 . Searches for the lepton number violating K + → π − µ + e+ decay and the lepton flavour violating K + → π + µ − e + and π 0 → µ − e + decays are reported. No evidence for these decays is found and upper limits of the branching ratios are obtained at 90% confidence level. These results improve by one order of magnitude over previous results for these decay modes

New measurement of the radiative decay Ke3g at the NA62 experiment at CERN

The NA62 experiment at CERN reports new results from the study of the radiative kaon decay K+→π0e+νγ (Ke3γ ), using a data sample recorded in 2017 and 2018. Preliminary results with the most precise measurement of the Ke3γ branching ratio, and a T-asymmetry measurement in the Ke3γ decay, are presented