Staggered Chiral Perturbation Theory for All-Staggered Heavy-Light Mesons

In HISQ simulations by the MILC and Fermilab Lattice collaborations, both the light quarks and the charm quark are staggered. We extend staggered chiral perturbation theory (\schpt) to include such all-staggered heavy-light mesons. We assume that the heavy quark action is sufficiently improved that we may take $a m_Q <<1$ (where $m_Q$ is the heavy quark mass), but also that $m_Q>>\Lambda_{QCD}$ so that a continuum heavy quark expansion is appropriate. Using this \schpt, the leptonic decay constant of the heavy-light meson is calculated at next-to-leading-order. The pattern of taste splittings in the heavy-light meson masses is also investigated.Comment: 7 pages, 1 figures, 2 tables. Proceedings of the 30th International Symposium on Lattice Field Theory - Lattice 2012; June 24-29, 2012; Cairns, Australi

The Palm measure and the Voronoi tessellation for the Ginibre process

We prove that the Palm measure of the Ginibre process is obtained by removing a Gaussian distributed point from the process and adding the origin. We obtain also precise formulas describing the law of the typical cell of Ginibre--Voronoi tessellation. We show that near the germs of the cells a more important part of the area is captured in the Ginibre--Voronoi tessellation than in the Poisson--Voronoi tessellation. Moment areas of corresponding subdomains of the cells are explicitly evaluated.Comment: Published in at http://dx.doi.org/10.1214/09-AAP620 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Regularizing QCD with staggered fermions and the fourth root trick

We investigate the properties of staggered-fermion lattice QCD in which the fourth root of the fermion determinant is taken. We show that this theory is non-local at non-zero lattice spacing $a$, and that the non-locality is caused by the breaking of taste symmetry at $a\ne 0$. We then present a renormalization-group based argument that the theory restores taste symmetry in the continuum limit. As a consequence the theory is local in that limit, and falls into the correct universality class. Finally, we argue that the correct effective theory for the physics of Goldstone bosons at $a\ne 0$ is given by staggered chiral perturbation theory with the replica trick.Comment: 21 pages, combined contribution to Lattice 2006 proceeding