arXiv subjects

Maarten Golterman

Publications and source records attributed to Maarten Golterman.

At least 145 records · Page 8Linked to original sources

arXiv2005

Before sailing on a domain-wall sea

We discuss the very different roles of the valence-quark and the sea-quark residual masses ($m_{res}^v$ and $m_{res}^s$) in dynamical domain-wall fermions simulations. Focusing on matrix elements of the effective weak hamiltonian containing a power divergence, we find that $m_{res}^v$ can be a source of a much bigger systematic error. To keep all systematic errors due to residual masses at the 1% level, we estimate that one needs $a m_{res}^s \le 10^{-3}$ and $a m_{res}^v \le 10^{-5}$, at a lattice spacing $a\sim 0.1$ fm. The practical implications are that (1) optimal use of computer resources calls for a mixed scheme with different domain-wall fermion actions for the valence and sea quarks; (2) better domain-wall fermion actions are needed for both the sea and the valence sectors.

hep-lat↗

arXiv2004

Is there an Aoki phase in quenched QCD?

We argue that quenched QCD has non-trivial phase structure for negative quark mass, including the possibility of a parity-flavor breaking Aoki phase. This has implications for simulations with domain-wall or overlap fermions.

hep-lat↗

arXiv2004

SU(N) chiral gauge theories on the lattice: a quick overview

We describe how an SU(N) chiral gauge theory can be put on the lattice using non-perturbative gauge fixing. In particular, we explain how the Gribov problem is dealt with. Our construction is local, avoids doublers, and weak-coupling perturbation theory applies at the critical point which defines the continuum limit of our lattice chiral gauge theory.

hep-lat↗

arXiv2004

SU(N) chiral gauge theories on the lattice

We extend the construction of lattice chiral gauge theories based on non-perturbative gauge fixing to the non-abelian case. A key ingredient is that fermion doublers can be avoided at a novel type of critical point which is only accessible through gauge fixing, as we have shown before in the abelian case. The new ingredient allowing us to deal with the non-abelian case as well is the use of equivariant gauge fixing, which handles Gribov copies correctly, and avoids Neuberger's no-go theorem. We use this method in order to gauge fix the non-abelian group (which we will take to be SU(N)) down to its maximal abelian subgroup. Obtaining an undoubled, chiral fermion content requires us to gauge-fix also the remaining abelian gauge symmetry. This modifies the equivariant BRST identities, but their use in proving unitarity remains intact, as we show in perturbation theory. On the lattice, equivariant BRST symmetry as well as the abelian gauge invariance are broken, and a judiciously chosen irrelevant term must be added to the lattice gauge-fixing action in order to have access to the desired critical point in the phase diagram. We argue that gauge invariance is restored in the continuum limit by adjusting a finite number of counter terms. We emphasize that weak-coupling perturbation theory applies at the critical point which defines the continuum limit of our lattice chiral gauge theory.

hep-lat↗

arXiv2003

A note on the power divergence in lattice calculations of $ΔI = 1/2$ $K\toππ$ amplitudes at $M_{K}=M_π$

In this note, we clarify a point concerning the power divergence in lattice calculations of $ΔI = 1/2$ $K\toππ$ decay amplitudes. There have been worries that this divergence might show up in the Minkowski amplitudes at $M_{K}=M_π$ with all the mesons at rest. Here we demonstrate, via an explicit calculation in leading-order Chiral Perturbation Theory, that the power divergence is absent at the above kinematic point, as predicted by CPS symmetry.

hep-lat↗

arXiv2003

On the phase diagram of quenched QCD with Wilson fermions

In this talk, I reported on recent work on the Aoki phase diagram for quenched QCD with two flavors of Wilson fermions. Part of this work was done in collaboration with Yigal Shamir, and a shorter account of this part appeared recently. In this write-up, I will therefore limit myself to reporting on work done with Steve Sharpe and Robert Singleton, Jr, which has not been published yet. We discuss the symmetries of quenched QCD, paying careful attention to non-perturbative issues. This allows us to derive an effective lagrangian which agrees with standard quenched chiral perturbation theory, but which can also be used to address questions of a non-perturbative nature.

hep-lat↗

arXiv2003

Analytic estimates of quenched penguins

When we embed the strong penguin operator Q_6 in the quenched theory, it does not remain a singlet under right-handed chiral transformations. As a consequence, more low-energy constants associated with this operator appear than in the unquenched theory. We give analytic estimates of the leading constants. The results suggest that the effects of quenching on this operator are large.

hep-lat↗

arXiv2003

Analytic estimates for penguin operators in quenched QCD

Strong penguin operators are singlets under the right-handed flavor symmetry group SU(3)_R. However, they do not remain singlets when the operator is embedded in (partially) quenched QCD, but instead they become linear combinations of two operators with different transformation properties under the (partially) quenched symmetry group. This is an artifact of the quenched approximation. Each of these two operators is represented by a different set of low-energy constants in the chiral effective theory. In this paper, we give analytic estimates for the leading low-energy constants, in quenched and partially quenched QCD. We conclude that the effects of quenching on Q_6 are large.

hep-lat↗

arXiv2003

Localization in lattice QCD (with emphasis on practical implications)

When Anderson localization takes place in a quenched disordered system, a continuous symmetry can be broken spontaneously without accompanying Goldstone bosons. Elaborating on this observation we propose a unified, microscopic physical picture of the phase diagram of both quenched and unquenched QCD with two flavors of Wilson fermions. The phase with Goldstone bosons -- by definition the Aoki phase -- is always identified as the region where the mobility edge of the (hermitian) Wilson operator is zero. We then discuss the implications for domain-wall and overlap fermions. We conclude that both formulations are valid only well outside the Aoki phase of the associated Wilson-operator kernel, because this is where locality and chirality can be both maintained.

hep-lat↗

arXiv2003

Localization in Lattice QCD

In this paper, we examine the phase diagram of quenched QCD with two flavors of Wilson fermions, proposing the following microscopic picture. The super-critical regions inside and outside the Aoki phase are characterized by the existence of a density of near-zero modes of the (hermitian) Wilson-Dirac operator, and thus by a non-vanishing pion condensate. Inside the Aoki phase, this density is built up from extended near-zero modes, while outside the Aoki phase, there is a non-vanishing density of exponentially localized near-zero modes, which occur in "exceptional" gauge-field configurations. Nevertheless, no Goldstone excitations appear outside the Aoki phase, and the existence of Goldstone excitations may therefore be used to define the Aoki phase in both the quenched and unquenched theories. We show that the density of localized near-zero modes gives rise to a divergent pion two-point function, thus providing an alternative mechanism for satisfying the relevant Ward identity in the presence of a non-zero order parameter. This divergence occurs when we take a "twisted" quark mass to zero, and we conclude that quenched QCD with Wilson fermions is well-defined only with a non-vanishing twisted mass. We show that this peculiar behavior of the near-zero-mode density is special to the quenched theory by demonstrating that this density vanishes in the unquenched theory outside the Aoki phase. We discuss the implications for domain-wall and overlap fermions constructed from a Wilson-Dirac kernel. We argue that both methods work outside the Aoki phase, but fail inside because of problems with locality and/or chiral symmetry, in both the quenched and unquenched theories.

hep-lat↗

arXiv2003

On the use of the Operator Product Expansion to constrain the hadron spectrum

We call into question a recently proposed idea on how the short-distance behavior of QCD correlation functions constrains hadronic states to become degenerate parity eigenstates as one goes up in the spectrum. In particular, we point out that the sum rules which have been proposed in this context are in general regulator dependent, and thus ill-defined.

hep-ph↗

arXiv2002

Fermion-number violation in regularizations that preserve fermion-number symmetry

There exist both continuum and lattice regularizations of gauge theories with fermions which preserve chiral U(1) invariance ("fermion number"). Such regularizations necessarily break gauge invariance but, in a covariant gauge, one recovers gauge invariance to all orders in perturbation theory by including suitable counterterms. At the non-perturbative level, an apparent conflict then arises between the chiral U(1) symmetry of the regularized theory and the existence of 't Hooft vertices in the renormalized theory. The only possible resolution of the paradox is that the chiral U(1) symmetry is broken spontaneously in the enlarged Hilbert space of the covariantly gauge-fixed theory. The corresponding Goldstone boson is unphysical. The theory must therefore be defined by introducing a small fermion-mass term that breaks explicitly the chiral U(1) invariance, and is sent to zero after the infinite-volume limit has been taken. Using this careful definition (and a lattice regularization) for the calculation of correlation functions in the one-instanton sector, we show that the 't Hooft vertices are recovered as expected.

hep-th↗

arXiv2002

Non-perturbative BRST invariance and what it might be good for

We construct a local, gauge-fixed, lattice Yang-Mills theory with an exact BRST invariance, and with the same perturbative expansion as the standard Yang-Mills theory. The ghost sector, and some of its BRST transformation rules, are modified to get around Neuberger's theorem. A special term is introduced in the action to regularize the Gribov horizons, and the limit where the regulator is removed is discussed. We conclude with a few comments on what might be the physical significance of this theory. We speculate that there may exist new strong-interaction phases apart from the anticipated confinement phase.

hep-lat↗

arXiv2002

On systematic errors due to quenching in epsilon-prime over epsilon

Recently, we pointed out that chiral transformation properties of penguin operators change in the transition from unquenched to (partially) quenched QCD. As a consequence, new operators appear in (partially) quenched QCD penguins, introducing ambiguities which should be considered a quenching artifact. Here we discuss more specifically the effects of this phenomenon on the quenched Delta I=1/2 K to pi pi amplitude, and in particular, its potential numerical effect on recent lattice estimates for epsilon-prime over epsilon.

hep-lat↗

arXiv2002

Lattice chiral gauge theories through gauge fixing

After an introduction in which we review the fundamental difficulty in constructing lattice chiral gauge theories, we discuss the analytic and numerical evidence that abelian lattice chiral gauge theories can be non-perturbatively constructed through the gauge-fixing approach. While a complete non-abelian extension is still under construction, we also show how fermion-number violating processes are realized in this approach.

hep-lat↗

arXiv2001

Effects of Quenching and Partial Quenching on QCD Penguin Matrix Elements

We point out that chiral transformation properties of penguin operators change in the transition from unquenched to (partially) quenched QCD. The way in which this affects the lattice determination of weak matrix elements can be understood in the framework of (partially) quenched chiral perturbation theory.

hep-lat↗

arXiv2001

Effects of Quenching and Partial Quenching on Penguin Matrix Elements

In the calculation of non-leptonic weak decay rates, a "mismatch" arises when the QCD evolution of the relevant weak hamiltonian down to hadronic scales is performed in unquenched QCD, but the hadronic matrix elements are then computed in (partially) quenched lattice QCD. This mismatch arises because the transformation properties of penguin operators under chiral symmetry change in the transition from unquenched to (partially) quenched QCD. Here we discuss QCD-penguin contributions to $ΔS=1$ matrix elements, and show that new low-energy constants contribute at leading order in chiral perturbation theory in this case. In the partially quenched case (in which sea quarks are present), these low-energy constants are related to electro-magnetic penguins, while in the quenched case (with no sea quarks) no such relation exists. As a simple example, we give explicit results for $K^+\toπ^+$ and $K^0\to vacuum$ matrix elements, and discuss the implications for lattice determinations of $K\toππ$ amplitudes from these matrix elements.

hep-lat↗

arXiv2001

Using Lattice QCD and ChPT to obtain non-leptonic K-decay amplitudes

We summarize some of the difficulties that confront lattice calculations of non-leptonic kaon decay matrix elements. We review some of the methods that have been proposed to overcome these difficulties, and discuss the importance of one-loop ChPT in this respect, including the role of O(p^4) operators.

hep-lat↗