arXiv subjects

Michael I. Buchoff

Publications and source records attributed to Michael I. Buchoff.

28 records · Page 2Linked to original sources

arXiv2010

Topics in Lattice QCD and Effective Field Theory

Effective field theories provide a formalism for categorizing low-energy effects of a high-energy fundamental theory in terms of the low-energy degrees of freedom. This process has been well established in mapping the fundamental theory of QCD in terms of the hadronic degrees of freedom, which allows for quantitative connections and predictions between hardronic observables. A more direct approach to performing the non-perturbative QCD calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. However, the fundamental theory of interest here is lattice QCD, as opposed to the usual continuum QCD. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 $ππ$ scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a usage of effective field theories and the employment of an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.

hep-lat↗

arXiv2009

Meson-Baryon Scattering Parameters from Lattice QCD with an Isospin Chemical Potential

The extraction of meson-baryon scattering parameters from lattice QCD is complicated by the necessity, in some channels, of including annihilation diagrams. We consider a strategy to avoid the need for these extremely costly and noisy contributions. The strategy is based on simulations with an isospin chemical potential which, contrary to a baryon chemical potential, has no sign problem. When the isospin chemical potential is larger than a critical value, a charged pion condensate forms. Baryons propagating in the pion condensate will have their masses modified by pion-baryon scattering parameters. Consequently these parameters can be extracted from lattice QCD simulations in an isospin chemical potential, and we detail precisely which low-energy constants using baryon chiral perturbation theory.

hep-lat↗

arXiv2009

Color Superconductivity at Large N: A New Hope

At zero density, the `t Hooft large N_c limit often provides some very useful qualitative insights into the non-perturbative physics of QCD. However, it is known that at high densities the `t Hooft large N_c world looks very different from the N_c=3 world, which is believed to be in a color superconducting phase at high densities. At large N_c, on the other hand, the DGR instability causes a chiral-density wave phase to dominate over the color superconducting phase. There is an alternative large N_c limit, with the quarks transforming in the two-index antisymmetric representation of the gauge group, which at N_c=3 reduces to QCD but looks quite different at large N_c. We show that in this alternative large N_c limit, the DGR instability does not occur, so that it may be plausible that the ground state of high-density quark matter is a color superconductor even when N_c is large. This revives the hope that a large N_c approximation might be useful for getting some insights into the high-density phenomenology of QCD.

hep-ph↗

arXiv2009

Can fermions save large N dimensional reduction?

This paper explores whether Eguchi-Kawai reduction for gauge theories with adjoint fermions is valid. The Eguchi-Kawai reduction relates gauge theories in different numbers of dimensions in the large $N$ limit provided that certain conditions are met. In principle, this relation opens up the possibility of learning about the dynamics of 4D gauge theories through techniques only available in lower dimensions. Dimensional reduction can be understood as a special case of large $N$ equivalence between theories related by an orbifold projection. In this work, we focus on the simplest case of dimensional reduction, relating a 4D gauge theory to a 3D gauge theory via an orbifold projection. A necessary condition for the large N equivalence between the 4D and 3D theories to hold is that certain discrete symmetries in the two theories must not be broken spontaneously. In pure 4D Yang-Mills theory, these symmetries break spontaneously as the size of one of the spacetime dimensions shrinks. An analysis of the effect of adjoint fermions on the relevant symmetries of the 4D theory shows that the fermions help stabilize the symmetries. We consider the same problem from the point of view of the lower dimensional 3D theory and find that, surprisingly, adjoint fermions are not generally enough to stabilize the necessary symmetries of the 3D theory. In fact, a rich phase diagram arises, with a complicated pattern of symmetry breaking. We discuss the possible causes and consequences of this finding.

hep-th↗

arXiv2009

Sommerfeld enhancement from Goldstone pseudo-scalar exchange

We point out that the exchange of a Goldstone pseudo-scalar can provide an enhancement in the dark matter annihilation rate capable of explaining the excess flux seen in high energy cosmic ray data. The mechanism of enhancement involves the coupling of s and d waves through the tensor force that is very strong and, in fact, singular at short distances. The results indicate that large enhancements require some amount of fine tuning. We also discuss the enhancement due to other singular attractive potentials, such as WIMP models with a permanent electric dipole.

hep-ph↗

arXiv2008

Search for Chiral Fermion Actions on Non-Orthogonal Lattices

The graphene-inspired fermion actions recently proposed by Creutz and Borici have sparked interest in the use of non-orthogonal lattices in lattice QCD. These fermion actions have the desired chiral symmetry and have the minimal doubling required by the Nielsen-Ninomiya no-go theorem. However, due to the lack of discrete symmetries, radiative corrections in the gauged lattice theory will lead to the generation of unwanted relevant and marginal operators. Other similarly motivated non-orthogonal fermion actions avoid these unwanted operators, but introduce incorrect continuum behavior or excessive fermion doubling. A delicate balance of symmetry is required for chiral symmetry, minimal doubling, and no relevant operators, and to date, no non-orthogonal lattice action has accomplished this balance.

hep-lat↗

arXiv2008

Isotropic and Anisotropic Lattice Spacing Corrections for I=2 pi-pi Scattering from Effective Field Theory

The calculation of the finite lattice spacing corrections for I=2 pi-pi scattering is carried out for isotropic and anisotropic Wilson lattice actions. Pion masses and decay constants are also determined in this context. These results correct the phase shift calculated from the lattice, which is connected to the scattering length and effective range in this low energy scattering process. When in terms of the lattice-physical parameters for either Wilson action, these lattice spacing effects first appear at the next-to-leading order counter-terms.

hep-lat↗

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.

hep-lat↗

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.

hep-lat↗

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.

hep-lat↗