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

Identifying RNAs from Invading Viruses

Organisms must regulate gene expression and also distinguish their RNA molecules (self) from the RNAs of invading viruses (non-self). Biochemical and structural studies from Bass, Shen, Iwasa, and colleagues revealed how Dicer-2, an RNA processing, and antiviral defense enzyme, distinguishes and differentially processes double-stranded RNA (dsRNA) substrates by sensing the unique chemistry at their termini. The study also revealed that human Dicer evolved with distinct activities from invertebrate Dicers, and this discovery is paving the way for altering the antiviral defense for therapeutic benefits