ChPT parameters from tau-decay data

Using the updated ALEPH V-A spectral function from tau decays, we determine the lowest spectral moments of the left-right correlator and extract dynamical information on order parameters of the QCD chiral symmetry breaking. Uncertainties associated with violations of quark-hadron duality are estimated from the data, imposing all known short-distance constraints on a resonance-based parametrization. Employing proper pinched weight functions, we obtain an accurate determination of the effective chiral couplings L10 and C87 and the dimension-six and -eight contributions in the Operator Product Expansion.Comment: 5 pages, 3 figures, QCD2015 Montpellie

Inertial and dimensional effects on the instability of a thin film

We consider here the effects of inertia on the instability of a flat liquid film under the effects of capillary and intermolecular forces (van der Waals interaction). Firstly, we perform the linear stability analysis within the long wave approximation, which shows that the inclusion of inertia does not produce new regions of instability other than the one previously known from the usual lubrication case. The wavelength, $\lambda_m$, corresponding to he maximum growth, $\omega_m$, and the critical (marginal) wavelength do not change at all. The most affected feature of the instability under an increase of the Laplace number is the noticeable decrease of the growth rates of the unstable modes. In order to put in evidence the effects of the bidimensional aspects of the flow (neglected in the long wave approximation), we also calculate the dispersion relation of the instability from the linearized version of the complete Navier-Stokes (N-S) equation. Unlike the long wave approximation, the bidimensional model shows that $\lambda_m$ can vary significantly with inertia when the aspect ratio of the film is not sufficiently small. We also perform numerical simulations of the nonlinear N-S equations and analyze to which extent the linear predictions can be applied depending on both the amount of inertia involved and the aspect ratio of the film

On algebraic classification of quasi-exactly solvable matrix models

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie algebras of the dimension up to three by first-order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2,R). These results enable constructing multi-parameter families of first- and second-order quasi-exactly solvable models. In particular, we have obtained two classes of quasi-exactly solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge

Interplay of Coulomb and electron-phonon interactions in graphene

We consider mutual effect of the electron-phonon and strong Coulomb interactions on each other by summing up leading logarithmic corrections via the renormalization group approach. We find that the Coulomb interaction enhances electron coupling to the intervalley A1 optical phonons, but not to the intravalley E2 phonons