A few remarks on "On certain Vandermonde determinants whose variables separate"

In the recent paper \u201cOn certain Vandermonde determinants whose variables separate\u201d [Linear Algebra and its Applications 449 (2014) pp. 17\u201327], there was established a factorized formula for some bivariate Vandermonde determinants (associated to almost square grids) whose basis functions are formed by Hadamard products of some univariate polynomials. That formula was crucial for proving a conjecture on the Vandermonde determinant associated to Padua-like points. In this note we show that the same formula holds when those polynomials are replaced by arbitrary functions and we extend this formula to general rectangular grids. We also show that the Vandermonde determinants associated to Padua-like points are nonvanishing

A Numerical Study of Partially Twisted Boundary Conditions

We investigate the use of partially twisted boundary conditions in a lattice simulation with two degenerate flavours of improved Wilson sea quarks. The use of twisted boundary conditions on a cubic volume (L^3) gives access to components of hadronic momenta other than integer multiples of 2*pi/L. Partial twisting avoids the need for new gluon configurations for every choice of momentum, while, as recently demonstrated, keeping the finite-volume errors exponentially small for the physical quantities investigated in this letter. In this study we focus on the spectrum of pseudo scalar and vector mesons, on their leptonic decay constants and on Z_P, the matrix element of the pseudo scalar density between the pseudo scalar meson and the vacuum. The results confirm the momentum shift imposed by these boundary conditions and in addition demonstrate that they do not introduce any appreciable noise. We therefore advocate the use of partially twisted boundary conditions in applications where good momentum resolution is necessary.Comment: 10 pages, 3 figure

An Exploratory Lattice Study of Spectator Effects in Inclusive Decays of the Lambda_b Baryon

A possible explanation of the apparent disrepency between the theoretical prediction and experimental measurement of the ratio of lifetimes $\tau(\Lambda_b)/\tau(B_d)$ is that ``spectator effects'', which appear at $O(1/m_b^3)$ in the heavy quark expansion, contribute significantly. We investigate this possibility by computing the corresponding operator matrix elements in a lattice simulation. We find that spectator effects are indeed significant, but do not appear to be sufficiently large to account for the full discrepency. We stress, however, that this is an exploratory study, and it is important to check our conclusions on a larger lattice and using a larger sample of gluon configurations.Comment: 12 pages, Latex. One correction: in the original version of the paper, in eqs.10, 11, 12 and 39, the values of the pion masses appeared interchange

Hadronic Decays of Excited Heavy Mesons

We studied the hadronic decays of excited states of heavy mesons (D, D_s, B and B_s) to lighter states by emission of pi, eta or K. Wavefunctions and energy levels of these excited states are determined using a Dirac equation for the light quark in the potential generated by the heavy quark (including first order corrections in the heavy quark expansion). Transition amplitudes are computed in the context of the Heavy Chiral Quark Model.Comment: 4 pages (incl. figures), proceedings of the IV International Conference on "Hyperons, Charm and Beauty Hadrons", Valencia (Spain