arXiv subjects

Andre Walker-Loud

Publications and source records attributed to Andre Walker-Loud.

70 records · Page 4Linked to original sources

arXiv2008

Kaon Condensation with Lattice QCD

Kaon condensation may play an important role in the structure of hadronic matter at densities greater than that of nuclear matter, as exist in the interior of neutron stars. We present the results of the first lattice QCD investigation of kaon condensation obtained by studying systems containing up to twelve negatively charged kaons. Surprisingly, the properties of the condensate that we calculate are remarkably well reproduced by leading order chiral perturbation theory. In our analysis, we also determine the three-kaon interaction from the multi-kaon systems and update our results for pion condensates.

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arXiv2008

Mixed Meson Masses with Domain-Wall Valence and Staggered Sea Fermions

Mixed action lattice calculations allow for an additive lattice spacing dependent mass renormalization of mesons composed of one sea and one valence quark, regardless of the type of fermion discretization methods used in the valence and sea sectors. The value of the mass renormalization depends upon the lattice actions used. This mixed meson mass shift is an important lattice artifact to determine for mixed action calculations; because it modifies the pion mass, it plays a central role in the low energy dynamics of all hadronic correlation functions. We determine the leading order, $\mathcal{O}(a^2)$, and next to leading order, $\mathcal{O}(a^2 m_π^2)$, additive mass shift of \textit{valence-sea} mesons for a mixed lattice action with domain-wall valence fermions and rooted staggered sea fermions, relevant to the majority of current large scale mixed action lattice efforts. We find that on the asqtad improved coarse MILC lattices, this additive mass shift is well parameterized in lattice units by $Δ(am)^2 = 0.034(2) -0.06(2) (a m_π)^2$, which in physical units, using $a=0.125$ fm, corresponds to $Δ(m)^2 = (291\pm 8 \textrm{MeV})^2 -0.06(2) m_π^2$. In terms of the mixed action effective field theory parameters, the corresponding mass shift is given by $a^2 Δ_\mathrm{Mix} = (316 \pm 4 \textrm{MeV})^2$ at leading order plus next-to-leading order corrections including the necessary chiral logarithms for this mixed action calculation, determined in this work. Within the precision of our calculation, one can not distinguish between the full next-to-leading order effective field theory analysis of this additive mixed meson mass shift and the parameterization given above.

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arXiv2008

Broken Symmetries from Minimally Doubled Fermions

Novel chirally symmetric fermion actions containing the minimum amount of fermion doubling have been recently proposed in the literature. We study the symmetries and renormalization of these actions and find that in each case, discrete symmetries, such as parity and time-reversal, are explicitly broken. Consequently, when the gauge interactions are included, these theories radiatively generate relevant and marginal operators. Thus the restoration of these symmetries and the approach to the continuum limit require the fine-tuning of several parameters. With some assumptions, we show that this behavior is unavoidable for actions displaying minimal fermion doubling.

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arXiv2008

Search for Fermion Actions on Hyperdiamond Lattices

Fermions moving in a two-dimensional honeycomb lattice (graphene) have, at low energies, chiral symmetry. Generalizing this construction to four dimensions potentially provides fermions with chiral symmetry and only the minimal fermion doubling demanded by the Nielsen-Ninomiya no-go theorem. The practical usefulness of such fermions hinges on whether the action has a necessary set of discrete symmetries of the lattice. If this is the case, one avoids the generation of dimension three and four operators which require fine tuning. We construct hyperdiamond lattice actions with enough symmetries to exclude fine tuning; however, they produce multiple doublings. The limit where the actions exhibit minimal doubling does not possess the requisite symmetry.

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arXiv2007

The K+K+ Scattering Length from Lattice QCD

The K+K+ scattering length is calculated in fully-dynamical lattice QCD with domain-wall valence quarks on the MILC asqtad-improved gauge configurations with rooted staggered sea quarks. Three-flavor mixed-action chiral perturbation theory at next-to-leading order, which includes the leading effects of the finite lattice spacing, is used to extrapolate the results of the lattice calculation to the physical value of m_{K+}/f_{K+}. We find m_{K+} a_{K+K+} = -0.352 +- 0.016, where the statistical and systematic errors have been combined in quadrature.

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arXiv2007

Effective Field Theory for the Anisotropic Wilson Lattice Action

We construct the effective field theory appropriate for describing the low energy behavior of anisotropic Wilson lattice actions and the O(a) improved variant thereof. We then apply this effective field theory to the hadron spectrum and dispersion relations, focussing on the corrections due to the anisotropy. We point out an important feature of anisotropic lattices regarding the Aoki-regime; for a given set of fermion masses and spatial lattice spacing, if an isotropic action is in the QCD-phase, this does not guarantee that the anisotropic action is outside the Aoki-regime. This may be important in the tuning of bare parameters for anisotropic lattices using domain-wall and overlap fermions as well as Wilson and O(a)-improved Wilson fermions.

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arXiv2007

Restless pions: orbifold boundary conditions and noise suppression in lattice QCD

The study of one or more baryons in lattice QCD is severely hindered by the exponential decay in time of the signal-to-noise ratio. The rate at which the signal-to-noise decreases is a function of the the pion mass. More precisely, it depends on the minimum allowed pion energy in the box, which, for periodic boundary conditions, is equal to its mass. We propose a set of boundary conditions, given by a "parity orbifold'' construction, which eliminates the zero momentum pion modes, raising the minimum pion energy without altering the QCD ground state, and thereby improving the signal-to-noise ratio of (multi)-baryon correlation functions at long Euclidean times. We discuss variations of these "restless pions" boundary conditions and focus on their impact on the study of nuclear forces.

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arXiv2007

Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD

The I=2 pipi scattering length is calculated in fully-dynamical lattice QCD with domain-wall valence quarks on the asqtad-improved coarse MILC configurations (with fourth-rooted staggered sea quarks) at four light-quark masses. Two- and three-flavor mixed-action chiral perturbation theory at next-to-leading order is used to perform the chiral and continuum extrapolations. At the physical charged pion mass, we find m_pi a_pipi(I=2) = -0.04330 +- 0.00042, where the error bar combines the statistical and systematic uncertainties in quadrature.

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arXiv2007

Two Meson Systems with Ginsparg-Wilson Valence Quarks

Unphysical effects associated with finite lattice spacing and partial quenching may lead to the presence of unphysical terms in chiral extrapolation formulae. These unphysical terms must then be removed during data analysis before physical predictions can be made. In this work, we show that through next-to-leading order, there are no unphysical counterterms in the extrapolation formulae, expressed in lattice-physical parameters, for meson scattering lengths in theories with Ginsparg-Wilson valence quarks. Our work applies to most sea quark discretization, provided that chiral perturbation theory is a valid approximation. We demonstrate our results with explicit computations and show that, in favorable circumstances, the extrapolation formulae do not depend on the unknown constant C_Mix appearing at lowest order in the mixed action chiral Lagrangian. We show that the I=1 KK scattering length does not depend on C_Mix in contrast to the I=3/2 K-pi scattering length. In addition, we show that these observables combined with f_K / f_pi and the I=2 pi-pi scattering length share only two linearly independent sets of counterterms, providing a means to test the mixed action theory at one lattice spacing. We therefore make a prediction for the I=1 KK scattering length.

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arXiv2006

Topics in Effective Field Theory for Lattice QCD

In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we compare to existing lattice QCD calculations. In particular, we extend the heavy baryon Lagrangian to the next order in partially quenched chiral perturbation theory and use it to compute the masses of the lightest spin-1/2 and spin-3/2 baryons to next-to-next-to leading order. We then construct the twisted mass chiral Lagrangian for baryons and apply it to compute the lattice spacing corrections to the baryon masses simulated with twisted mass lattice QCD. We extend computations of the nucleon electromagnetic structure to account for finite volume effects, as these observables are particularly sensitive to the finite extent of the lattice. We resolve subtle peculiarities for lattice QCD simulations of polarizabilities and we show that using background field techniques, one can make predictions for the 4 spin-dependent nucleon polarizabilities, quantities which are difficult to access experimentally. We then discuss the two-pion system in finite volume, determining the exponentially small volume corrections necessary for lattice determinations of the scattering parameters. We also determine the lattice spacing artifacts that arise for a mixed-action lattice simulation of the two-pion system with Ginsparg-Wilson valence quarks and staggered sea quarks. We show that the isospin 2 scattering length has a near continuum like behavior, differing from the chiral perturbation theory calculation by a computable difference.

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arXiv2006

Ginsparg-Wilson Pions Scattering in a Sea of Staggered Quarks

We calculate isospin 2 pion-pion scattering in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We point out that for some scattering channels, the power-law volume dependence of two pion states in nonunitary theories such as partially quenched or mixed action QCD is identical to that of QCD. Thus one can extract infinite volume scattering parameters from mixed action simulations. We then determine the scattering length for both 2 and 2+1 sea quarks in the isospin limit. The scattering length, when expressed in terms of the pion mass and the decay constant measured on the lattice, has no contributions from mixed valence-sea mesons, thus it does not depend upon the parameter, C_Mix, that appears in the chiral Lagrangian of the mixed theory. In addition, the contributions which nominally arise from operators appearing in the mixed action O(a^2 m_q) Lagrangian exactly cancel when the scattering length is written in this form. This is in contrast to the scattering length expressed in terms of the bare parameters of the chiral Lagrangian, which explicitly exhibits all the sicknesses and lattice spacing dependence allowed by a partially quenched mixed action theory. These results hold for both 2 and 2+1 flavors of sea quarks.

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arXiv2006

Finite volume corrections to pi-pi scattering

Lattice QCD studies of hadron-hadron interactions are performed by computing the energy levels of the system in a finite box. The shifts in energy levels proportional to inverse powers of the volume are related to scattering parameters in a model independent way. In addition, there are non-universal exponentially suppressed corrections that distort this relation. These terms are proportional to exp(-m_pi L) and become relevant as the chiral limit is approached. In this paper we report on a one-loop chiral perturbation theory calculation of the leading exponential corrections in the case of I=2 pi-pi scattering near threshold.

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arXiv2005

Strong Isospin Breaking in the Nucleon and Delta Masses on the Lattice

Strong isospin breaking in the spectrum of the nucleons and deltas can be studied in lattice QCD with the help of chiral perturbation theory. At leading order in the chiral expansion, the mass splittings between the proton and neutron and between the deltas are linear in the quark mass difference. The next-to-leading order contributions to these splittings vanish even away from the strong-isospin limit. Therefore, any non-linear quark mass dependence of these mass splittings is a signal of the next-to-next-to-leading order mass contributions, thus providing access to LECs at this order. We determine the mass splittings of the nucleons and deltas in two-flavor, heavy baryon chiral perturbation theory to next-to-next-to-leading order. We also derive expressions for the nucleon and delta masses in partially quenched chiral perturbation theory to the same order. The resulting mass expressions will be useful both for the extrapolation of lattice data on baryon masses, and for the study of strong isospin breaking.

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arXiv2005

Nucleon and Delta masses in twisted mass chiral perturbation theory

We calculate the masses of the nucleons and deltas in twisted mass heavy baryon chiral perturbation theory. We work to quadratic order in a power counting scheme in which we treat the lattice spacing and the quark masses to be of the same order. We give expressions for the mass and the mass splitting of the nucleons and deltas both in and away from the isospin limit. We give an argument using the chiral Lagrangian treatment that, in the strong isospin limit, the nucleons remain degenerate and the delta multiplet breaks into two degenerate pairs to all orders in chiral perturbation theory. We show that the mass splitting between the degenerate pairs of the deltas first appears at quadratic order in in the lattice spacing. We discuss the subtleties in the effective chiral theory that arise from the inclusion of isospin breaking.

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arXiv2004

Octet Baryon Masses in Partially Quenched Chiral Perturbation Theory

The mass spectrum of the lowest lying octet baryons is calculated to next-to-next-to-leading order in heavy baryon chiral perturbation theory and partially quenched heavy baryon chiral perturbation theory. We work in the isospin limit and treat the decuplet baryons as dynamical fields. These results are necessary for extrapolating QCD and partially quenched QCD lattice simulations of the octet baryon masses.

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arXiv2004

Decuplet Baryon Masses in Partially Quenched Chiral Perturbation Theory

The masses of the spin-3/2 baryons are calculated to next-to-next-to-leading order in heavy baryon chiral perturbation theory and partially quenched heavy baryon chiral perturbation theory. The calculation is performed for three light flavors in the isospin limit. These results are necessary for extrapolating QCD and partially quenched QCD lattice calculations of the decuplet baryon masses.

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