Axial anomaly and the precise value of the π0→2γ\pi^0 \to 2 \gamma decay width

The anomaly in the vacuum expectation value of the product of axial and two vector currents (AVV) in QCD is investigated. The goal is to determine from its value the $\pi^0 \to 2 \gamma$ decay width with high precision. The sum rule for AVV formfactor is studied. The difference $f_{\pi^0} - f_{\pi^+}$ caused by strong interaction is calculated and appears to be small. The $\pi^0 - \eta$ mixing is accounted. The $\pi^0 \to 2 \gamma$ decay width determined theoretically from the axial anomaly is found to be $\Gamma(\pi^0 \to 2 \gamma) = 7.93 eV$ with an error $\sim 1.5$. The measurement of the $\pi^0 \to 2 \gamma$ decay width at the same level of accuracy would allow one to achieve a high precision test of QCD.Comment: 8 pages, few misprints are correcte

The critical Ising model via Kac-Ward matrices

The Kac-Ward formula allows to compute the Ising partition function on any finite graph G from the determinant of 2^{2g} matrices, where g is the genus of a surface in which G embeds. We show that in the case of isoradially embedded graphs with critical weights, these determinants have quite remarkable properties. First of all, they satisfy some generalized Kramers-Wannier duality: there is an explicit equality relating the determinants associated to a graph and to its dual graph. Also, they are proportional to the determinants of the discrete critical Laplacians on the graph G, exactly when the genus g is zero or one. Finally, they share several formal properties with the Ray-Singer \bar\partial-torsions of the Riemann surface in which G embeds.Comment: 30 pages, 10 figures; added section 4.4 in version

Thermodynamics of pyrope-majorite, Mg3Al2Si3O12-Mg4Si4O12, solid solution from atomistic model calculations

Static lattice energy calculations, based on empirical pair potentials have been performed for a large set of different structures with compositions between pyrope and majorite, and with different states of order of octahedral cations. The energies have been cluster expanded using pair and quaternary terms. The derived ordering constants have been used to constrain Monte Carlo simulations of temperature-dependent properties in the ranges of 1073 3673K and 0 20 GPa. The free energies of mixing have been calculated using the method of thermodynamic integration. At zero pressure the cubic/tetragonal transition is predicted for pure majorite at 3300 K. The transition temperature decreases with the increase of the pyrope mole fraction. A miscibility gap associated with the transition starts to develop at about 2000K and xmaj 0.8, and widens with the decrease in temperature and the increase in pressure. Activity composition relations in the range of 0 20 GPa and 1073 2673K are described with the help of a high-order Redlich Kister polynomial

Invariant mass distributions for the pp to p p eta reaction at Q=10 MeV

Proton-proton and proton-eta invariant mass distributions and the total cross section for the pp to pp eta reaction have been determined near the threshold at an excess energy of Q=10 MeV. The experiment has been conducted using the COSY-11 detector setup and the cooler synchrotron COSY. The determined invariant mass spectra reveal significant enhancements in the region of low proton-proton relative momenta, similarly as observed previously at higher excess energies of Q=15.5 MeV and Q= 40MeV.Comment: 6 pages, 3 figures, submitted to Eur.Phys. J.

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele