arXiv subjects

Maarten Golterman

Publications and source records attributed to Maarten Golterman.

At least 91 records · Page 5Linked to original sources

arXiv2014

Vacuum alignment and lattice artifacts

When a subgroup of the flavor symmetry group of a gauge theory is weakly coupled to additional gauge fields, the vacuum tends to align such that the gauged subgroup is unbroken. At the same time, the lattice discretization typically breaks the flavor symmetry explicitly, and can give rise to new lattice-artifact phases with spontaneously broken symmetries. We discuss the interplay of these two phenomena, using chiral lagrangian techniques. Our first example is two-flavor Wilson QCD coupled to electromagnetism. We also consider examples of theories with staggered fermions, and demonstrate that recent claims in the literature based on the use of staggered fermions are incorrect.

hep-lat↗

arXiv2014

A new strategy for evaluating the LO HVP contribution to $(g-2)_μ$ on the lattice

A highly physical model of the subtracted $I=1$ vector polarization, obtained using a dispersive representation with precise hadronic $τ$ decay data as input, is used to investigate systematic issues in the lattice evaluation of the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. The model is also employed to study possible resolutions of these problems. A hybrid approach to analyzing lattice data, involving low-order Padé, low-degree conformal-variable polynomial, or supplemented NNLO ChPT fits for $Q^2$ below $\sim 0.1-0.2$ GeV$^2$ and direct numerical integration of lattice data above this point, is shown to bring the systematic issues identified under control at the sub-$1\%$ level.

hep-lat↗

arXiv2014

Dimensional transmutation in the longitudinal sector of equivariantly gauge-fixed Yang-Mills theory

We study the pure-gauge sector of an $SU(N)$ gauge theory, equivariantly gauge fixed to $SU(N-1)\times U(1)$, which is an asymptotically free non-linear sigma model in four dimensions. We show that dimensional transmutation takes place in the large-$N$ limit, and elaborate on the relevance of this result for a speculative scenario in which the strong longitudinal dynamics gives rise to a novel Higgs-Coulomb phase.

hep-lat↗

arXiv2014

Functional-analysis based tool for testing quark-hadron duality

Quark-hadron duality is a key concept in QCD, allowing for the description of physical hadronic observables in terms of quark-gluon degrees of freedom. The modern theoretical framework for its implementation is Wilson's operator product expansion (OPE), supplemented by analytic extrapolation from large Euclidean momenta, where the OPE is defined, to the Minkowski axis, where observable quantities are defined. Recently, the importance of additional terms in the expansion of QCD correlators near the Minkowski axis, responsible for quark-hadron duality violations (DVs), was emphasized. In this paper we introduce a mathematical tool that might be useful for the study of DVs in QCD. It is based on finding the minimal distance, measured in the $L^\infty$ norm along a contour in the complex momentum plane, between a class of admissible functions containing the physical amplitude and the asymptotic expansion predicted by the OPE. This minimal distance is given by the norm of a Hankel matrix that can be calculated exactly, using as input the experimental spectral function on a finite interval of the timelike axis. We also comment on the relation between the new functional tool and the more commonly used $χ^2$-based analysis. The approach is illustrated on a toy model for the QCD polarization function recently proposed in the literature.

hep-ph↗

arXiv2014

Chiral perturbation theory for gradient flow observables

We construct the next-to-leading order chiral lagrangian for scalar and pseudo-scalar densities defined using the gradient flow. We calculate the chiral condensate and the pion decay constant to this order from operators at positive flow time, and confirm results obtained earlier in the chiral limit. We also calculate the quark mass dependence of the scales $t_0$ and $w_0$ defined from the scalar gluon density and find that nonanalytic terms in the quark mass only enter at next-to-next-to-leading order.

hep-lat↗

arXiv2014

A New Strategy for the Lattice Evaluation of the Leading Order Hadronic Contribution to $(g-2)_μ$

A reliable evaluation of the integral giving the hadronic vacuum polarization contribution to the muon anomalous magnetic moment should be possible using a simple trapezoid-rule integration of lattice data for the subtracted electromagnetic current polarization function in the Euclidean momentum interval $Q^2>Q^2_{min}$, coupled with an $N$-parameter Padé or other representation of the polarization in the interval $0<Q^2<Q^2_{min}$, for sufficiently high $Q^2_{min}$ and sufficiently large $N$. Using a physically motivated model for the $I=1$ polarization, and the covariance matrix from a recent lattice simulation to generate associated fake "lattice data," we show that systematic errors associated with the choices of $Q^2_{min}$ and $N$ can be reduced to well below the 1% level for $Q^2_{min}$ as low as 0.1 GeV$^2$ and rather small $N$. For such low $Q^2_{min}$, both an NNLO chiral representation with one additional NNNLO term and a low-order polynomial expansion employing a conformally transformed variable also provide representations sufficiently accurate to reach this precision for the low-$Q^2$ contribution. Combined with standard techniques for reducing other sources of error on the lattice determination, this hybrid strategy thus looks to provide a promising approach to reaching the goal of a sub-percent precision determination of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment on the lattice.

hep-lat↗

arXiv2013

The muon anomalous magnetic moment, a view from the lattice

We review some of the issues that arise in attempts to compute the hadronic corrections to the muon anomalous magnetic moment using Lattice QCD. We concentrate on the dominant contribution, which requires an accurate evaluation of the hadronic vacuum polarization.

hep-lat↗

arXiv2013

A possible new phase in non-perturbatively gauge-fixed Yang-Mills theory

The standard expectation is that gauge fixing cannot alter the physics in the physical sector of a Yang-Mills theory. Here we argue that this may not always be true: in an SU(2) Yang-Mills theory in which the $SU(2)/U(1)$ coset is non-perturbatively gauge fixed, we find that a new phase, with spontaneous symmetry breaking and a Higgs-like mechanism, appears to be a possibility.

hep-lat↗

arXiv2013

The hadronic vacuum polarization with twisted boundary conditions

The leading-order hadronic contribution to the muon anomalous magnetic moment is given by a weighted integral over the subtracted hadronic vacuum polarization. This integral is dominated by euclidean momenta of order the muon mass, i.e., momenta not accessible on current lattice volumes with periodic boundary conditions. Twisted boundary conditions can in principle help in accessing momenta of any size even in a finite volume, but their use leads to a modification of the Ward-Takahashi identity that normally guarantees transversality of the vacuum polarization. As a result, the vacuum polarization contains a non-transversal, quadratically divergent term, which arises as an artifact of using twisted boundary conditions in a finite volume. In this article, we show how to determine and remove this term from the vacuum polarization.

hep-lat↗

arXiv2013

Tests of hadronic vacuum polarization fits for the muon anomalous magnetic moment

Using experimental spectral data for hadronic tau decays from the OPAL experiment, supplemented by a phenomenologically successful parameterization for the high-s region not covered by the data, we construct a physically constrained model of the isospin-one vector-channel polarization function. Having such a model as a function of Euclidean momentum Q^2 allows us to explore the systematic error associated with fits to the Q^2 dependence of lattice data for the hadronic electromagnetic current polarization function which have been used in attempts to compute the leading order hadronic contribution, a_μ^HLO, to the muon anomalous magnetic moment. In contrast to recent claims made in the literature, we find that a final error in this quantity of the order of a few percent does not appear possible with current lattice data, given the present lack of precision in the determination of the vacuum polarization at low Q^2. We also find that fits to the vacuum polarization using fit functions based on Vector Meson Dominance are unreliable, in that the fit error on a_μ^HLO is typically much smaller than the difference between the value obtained from the fit and the exact model value. The use of a sequence of Pade approximants known to converge to the true vacuum polarization appears to represent a more promising approach.

hep-lat↗

arXiv2013

On the foundations of partially quenched chiral perturbation theory

It has been widely assumed that partially quenched chiral perturbation theory is the correct low-energy effective theory for partially quenched QCD. Here we present arguments supporting this assumption. First, we show that, for partially quenched QCD with staggered quarks, a transfer matrix can be constructed. This transfer matrix is not Hermitian, but it is bounded, and it can be used to construct correlation functions in the usual way. Combining these observations with an extension of the Vafa--Witten theorem to the partially quenched theory allows us to argue that the partially quenched theory satisfies the cluster property. By extending Leutwyler's analysis of the unquenched case to the partially quenched theory, we then conclude that the existence and properties of the transfer matrix as well as clustering are sufficient for partially quenched chiral perturbation theory to be the correct low-energy theory for partially quenched QCD.

hep-lat↗

arXiv2013

Low-energy constants and condensates from the tau hadronic spectral functions

We use results of fits to the OPAL spectral data, obtained from non-strange hadronic τdecays, to evaluate the difference between the vector and axial current correlators, Π_{V-A}(Q^2). The behavior of Π_{V-A}(Q^2) near euclidean momentum Q^2=0 is used to determine the effective low-energy constants L_10^eff and C_87^eff related to the renormalized low-energy constants L_10^r and C_87^r in the chiral lagrangian. We also investigate how well two-loop chiral perturbation theory describes Π_{V-A}(Q^2) as a function of Q^2. This is the first determination of L_10^eff and C_87^eff to employ a fully self-consistent model for the violations of quark-hadron duality in both the vector and axial channels. We also discuss the values of the coefficients C_{6,V-A} and C_{8,V-A} governing the dimension six and eight contributions to the operator product expansion representation of Π_{V-A}(Q^2).

hep-ph↗

arXiv2013

Two-pion excited state contribution to pseudo-scalar correlators

We study multi-particle state contributions to the QCD two-point functions of pseudo-scalar quark bilinears in a finite spatial volume. For sufficiently small quark masses one expects three-meson states with two additional pions at rest to have the lowest total energy after the ground state. Using chiral perturbation theory, we find the amplitude of this state to be too small to be seen in present-day lattice simulations. We speculate that curvature in the effective mass plot extracted from the pseudo-scalar density two-point function instead corresponds to a genuine resonance, the π(1300).

hep-lat↗

arXiv2013

Phase with no mass gap in non-perturbatively gauge-fixed Yang--Mills theory

An equivariantly gauge-fixed non-abelian gauge theory is a theory in which a coset of the gauge group, not containing the maximal abelian subgroup, is gauge fixed. Such theories are non-perturbatively well-defined. In a finite volume, the equivariant BRST symmetry guarantees that expectation values of gauge-invariant operators are equal to their values in the unfixed theory. However, turning on a small breaking of this symmetry, and turning it off after the thermodynamic limit has been taken, can in principle reveal new phases. In this paper we use a combination of strong-coupling and mean-field techniques to study an SU(2) Yang--Mills theory equivariantly gauge fixed to a U(1) subgroup. We find evidence for the existence of a new phase in which two of the gluons becomes massive while the third one stays massless, resembling the broken phase of an SU(2) theory with an adjoint Higgs field. The difference is that here this phase occurs in an asymptotically-free theory.

hep-lat↗

arXiv2012

The strong coupling from tau decays without prejudice

We review our recent determination of the strong coupling α_s from the OPAL data for non-strange hadronic tau decays. We find that α_s(m^2_τ) =0.325+-0.018 using fixed-order perturbation theory, and α_s(m^2_τ)=0.347+-0.025 using contour-improved perturbation theory. At present, these values supersede any earlier determinations of the strong coupling from hadronic tau decays, including those from ALEPH data.

hep-ph↗

arXiv2012

Pade approximants and g-2 for the muon

The leading hadronic contribution to the muon anomalous magnetic moment is given by a weighted euclidean momentum integral of the hadronic vacuum polarization. This integral is dominated by momenta of order the muon mass. Since in lattice QCD it is difficult to compute the vacuum polarization at a large number of low momenta, a parametrization of the vacuum polarization is required to extrapolate the data. Most fits to date are based on vector meson dominance, which introduces model dependence into the lattice computation of the magnetic moment. Here we introduce a model-independent extrapolation method, and present a few first tests of this new method.

hep-lat↗

arXiv2012

Excited-state contribution to the axial-vector and pseudo-scalar correlators with two extra pions

We study multi-particle state contributions to the QCD two-point functions of the axial-vector and pseudo-scalar quark bilinears in a finite spatial volume. For sufficiently small quark masses one expects three-meson states with two additional pions at rest to have the lowest total energy after the ground state. We calculate this three-meson state contribution using chiral perturbation theory. We find it to be strongly suppressed and too small to be seen in present-day lattice simulations.

hep-lat↗

arXiv2012

Model-independent parametrization of the hadronic vacuum polarization and g-2 for the muon on the lattice

The leading hadronic contribution to the muon anomalous magnetic moment is given by a weighted integral over euclidean momentum of the hadronic vacuum polarization. This integral is dominated by momenta of order the muon mass. Since the finite volume in lattice QCD makes it difficult to compute the vacuum polarization at a large number of low momenta with high statistics (combined with the fact that one cannot compute it at zero momentum), a parametrization of the vacuum polarization is required to extrapolate the data. A much used functional form is based on vector meson dominance, which introduces model dependence into the lattice computation of the magnetic moment. Here we introduce a model-independent extrapolation method, and present a few first tests of this new method.

hep-lat↗