4,834 research outputs found
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
is that ``spectator effects'', which appear at
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
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