arXiv subjects

Pilar Hernandez

Publications and source records attributed to Pilar Hernandez.

27 records · Page 2Linked to original sources

arXiv2001

Scalar condensate and light quark masses from overlap fermions

We have studied pseudoscalar correlation functions computed using the overlap operator. Within the accuracy of our calculation we find that the quark mass dependence agrees with the prediction of lowest-order Chiral Perturbation Theory (ChPT) for quark masses in the range of m ~ m_s/2-2m_s. We present the results of an analysis which assumes lowest-order ChPT to be valid to extract the low-energy constants Sigma and f_P, as well as the strange quark mass. Non-perturbative renormalization is implemented via a matching procedure with data obtained using Wilson fermions in the Schroedinger functional set-up. We find that the scalar condensate computed here agrees with the one obtained previously through a finite-size scaling analysis.

hep-lat↗

arXiv2001

Non-perturbative renormalization of the quark condensate in Ginsparg-Wilson regularizations

We present a method to compute non-perturbatively the renormalization constant of the scalar density for Ginsparg-Wilson fermions. It relies on chiral symmetry and is based on a matching of renormalization group invariant masses at fixed pseudoscalar meson mass, making use of results previously obtained by the ALPHA Collaboration for O(a)-improved Wilson fermions. Our approach is quite general and enables the renormalization of scalar and pseudoscalar densities in lattice regularizations that preserve chiral symmetry and of fermion masses in any regularization. As an application we compute the non-perturbative factor which relates the renormalization group invariant quark condensate to its bare counterpart, obtained with overlap fermions at beta=5.85 in the quenched approximation.

hep-lat↗

arXiv1999

Chiral symmetry breaking from Ginsparg-Wilson fermions

We calculate the large-volume and small-mass dependences of the quark condensate in quenched QCD using Neuberger's operator. We find good agreement with the predictions of quenched chiral perturbation theory, enabling a determination of the chiral lagrangian parameter Σ, up to a multiplicative renormalization.

hep-lat↗

arXiv1996

A New Lattice Action for Studying Topological Charge

We review our recent proposal for a new lattice action for non-abelian gauge theories which reduces short-range lattice artifacts in the computation of the topological susceptibility. The standard Wilson action is replaced by the Wilson action of a gauge covariant interpolation of the original fields to a finer lattice. We illustrate the improved behavior of a same-philosophy new lattice action in the $O(3)$ $σ$-model in two dimensions.

hep-lat↗

arXiv1996

Lattice Gauge Field Interpolation for Chiral Gauge Theories

The importance of lattice gauge field interpolation for our recent non-perturbative formulation of chiral gauge theory is emphasized. We illustrate how the requisite properties are satisfied by our recent four-dimensional non-abelian interpolation scheme, by going through the simpler case of U(1) gauge fields in two dimensions.

hep-lat↗

arXiv1996

Interpolation of Non-abelian Lattice Gauge Fields

We propose a method for interpolating non-abelian lattice gauge fields to the continuum, or to a finer lattice, which satisfies the properties of (i) transverse continuity, (ii) (lattice) rotation and translation covariance, (iii) gauge covariance, (iv) locality. These are the properties required for use in our earlier proposal for non-perturbative formulation and simulation of chiral gauge theories.

hep-lat↗

arXiv1996

A New Lattice Action for Studying Topological Charge

We propose a new lattice action for non-abelian gauge theories, which will reduce short-range lattice artifacts in the computation of the topological susceptibility. The standard Wilson action is replaced by the Wilson action of a gauge covariant interpolation of the original fields to a finer lattice. If the latter is fine enough, the action of all configurations with non-zero topological charge will satisfy the continuum bound. As a simpler example we consider the $O(3)$ $σ$-model in two dimensions, where a numerical analysis of discretized continuum instantons indicates that a finer lattice with half the lattice spacing of the original is enough to satisfy the continuum bound.

hep-lat↗

arXiv1995

Lattice Chiral Gauge Theory with Finely-Grained Fermions

We discuss the problem of formulating the continuum limit of chiral gauge theories ($χ$GT) in the absence of an explicitly gauge-invariant regulator for the fermions. A solution is proposed which is independent of the details of the regulator, wherein one considers two cutoff scales, $Λ_f >> Λ_b$, for the fermions and the gauge bosons respectively. Our recent non-perturbative lattice construction in which the fermions live on a finer lattice than do the gauge bosons, is seen to be an example of such a scheme, providing a finite algorithm for simulating $χ$GT. The essential difference with previous (one-cutoff) lattice schemes is clarified: in our formulation the breakage of gauge invariance is small, $O(Λ^2_b/Λ^2_f)$, and vanishes in the continuum limit. Finally, we argue against 2-D models being significant testing grounds for 4-D regulators of $χ$GT.

hep-ph↗

arXiv1995

A Lattice Construction of Chiral Gauge Theories

We formulate chiral gauge theories non-perturbatively, using two different cuttoffs for the fermions and gauge bosons. We use a lattice with spacing $b$ to regulate the gauge fields in standard fashion, while computing the chiral fermion determinant on a finer lattice with spacing $f << b$. This determinant is computed in the background of $f$-lattice gauge fields, obtained by gauge-covariantly interpolating $b$-lattice gauge fields. The notorious doublers that plague lattice theories containing fermions are decoupled by the addition of a Wilson term. In chiral theories such a term breaks gauge invariance explicitly. However, the advantage of the two-cutoff regulator is that gauge invariance can be restored to $O(f^2/b^2)$ by a {\it one-loop} subtraction of calculable local gauge field counterterms. We show that the only obstruction to this procedure is the presence of an uncancelled gauge anomaly among the fermion representations. We conclude that for practical purposes, it suffices to choose $f/b \sim b/L$, where $L^4$ is the physical volume of the system. In our construction it is simple to prove the Adler-Bardeen theorem for anomalies in global currents to all orders. The related subject of fermion number violation is also studied. Finally, we discuss the prospects for improving the efficiency of our algorithm.

hep-ph↗