arXiv subjects

Maarten Golterman

Publications and source records attributed to Maarten Golterman.

At least 19 recordsLinked to original sources

arXiv2026

Comparison of the hadronic vacuum polarization between hadronic $τ$-decay data and lattice QCD

We compare the isospin-one, vector-current hadronic vacuum polarization (HVP) obtained from isospin-symmetric lattice QCD with that obtained from a dispersive representation employing inclusive hadronic $τ$ decay data corrected for isospin breaking. We consider the subtracted HVP evaluated at squared Euclidean momenta ranging from $0.5$ GeV$^2$ to $12$ GeV$^2$, together with the light-quark-connected HVP contribution to the muon anomalous magnetic moment and the short-, intermediate- and long-distance RBC/UKQCD window components thereof. Dispersive contributions from the region of hadronic invariant masses above the $τ$ mass are evaluated using perturbative QCD. We also consider dispersive determinations using $τ$ data only for contributions from two-pion, or two-pion and four-pion, modes, and evaluating the remaining contributions using exclusive-mode $e^+e^-\to\mbox{hadrons}$ cross sections up to about 2 GeV, lessening the dependence on perturbation theory. We find generally good agreement between lattice and $τ$-based results. However, a comparison of $τ$-based window-quantity contributions for the two four-pion modes to expectations for those contributions based on the Pais relations and $e^+e^-$ four-pion cross sections, reveals significant differences for the $2π^-π^+π^0$ mode.

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arXiv2026

Symmetric mass generation and the Nielsen-Ninomiya theorem

The symmetric mass generation (SMG) approach to the construction of lattice chiral gauge theories attempts to use interactions to render mirror fermions massive without symmetry breaking, to obtain the desired chiral massless spectrum (before the gauge field is turned on). If the zeros that often replace the mirror poles of fermion two-point functions in an SMG phase are ``kinematical'' singularities, general constraints can be formulated on the existence of a chiral fermion spectrum which are valid in the presence of (non-gauge) interactions of arbitrary strength, including in any SMG phase. Constructing a one-particle lattice hamiltonian describing the fermion spectrum, we discuss the conditions for the applicability of the Nielsen-Ninomiya theorem to this hamiltonian. If these conditions are satisfied, the massless fermion spectrum must be vector-like.

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arXiv2026

The Light Quark Connected Hadronic Vacuum Polarization Contribution to the muon anomaly via Sparsened Meson Fields

We present an update on our determination of the light-quark connected contribution to the hadronic vacuum polarization (HVP) of the muon anomalous magnetic moment, $a_μ$, on a finer lattice with 2+1+1 highly-improved staggered quark (HISQ) ensemble from the MILC collaboration with physical pion mass, 0.042 fm lattice spacing, and size $144^3 \times 288$ sites. Within the low-mode averaging (LMA) framework, the HVP correlator is decomposed into low-low (LL), high-low (HL), low-high (LH) and high-high (HH) components. Since the LL part dominates the total statistical uncertainty but is also the most computationally expensive to evaluate, we implement a sparsening strategy to construct the meson fields efficiently. This approach significantly reduces the computational cost while preserving signal quality. By combining the sparsened LL contribution with HL, LH and HH components, we achieve an improved determination of the light-quark connected HVP contribution to $a_μ$.

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arXiv2026

Progress on computing the hadronic vacuum polarization contribution to the muon anomalous magnetic moment with staggered fermions

We give an update of our calculation of the light-quark, connected, hadronic vacuum polarization contribution to the muon anomalous magnetic moment, or muon $g-2$. The update includes preliminary results on a $2 + 1 + 1$ highly-improved staggered quark (HISQ) ensemble from the MILC collaboration with physical pion mass, $0.042$ fm lattice spacing, and volume $144^3 \times 288$. We discuss code and algorithm improvements for these calculations to compute the vector-vector correlation function more efficiently.

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arXiv2026

Constraints on the symmetric mass generation paradigm for lattice chiral gauge theories

Within the symmetric mass generation (SMG) approach to the construction of lattice chiral gauge theories, one attempts to use interactions to render mirror fermions massive without symmetry breaking, thus obtaining the desired chiral massless spectrum. If successful, the gauge field can be turned on, and thus a chiral gauge theory can be constructed in the phase in which SMG takes place. In this paper we argue that the zeros that often replace the mirror poles of fermion two-point functions in an SMG phase should be ``kinematical'' singularities. We conjecture that the SMG interactions generate opposite-chirality bound states, which combine with the gapped elementary mirror states to form massive Dirac fermions. The propagator zeros can then be avoided by choosing an appropriate set of interpolating fields that contains both elementary and composite fields. This allows us to apply general constraints on the existence of a chiral fermion spectrum which are valid in the presence of (non-gauge) interactions of arbitrary strength, including in any SMG phase. Using a suitably constructed one-particle lattice hamiltonian describing the fermion spectrum, we formulate a generalized no-go theorem which establishes the conditions for the applicability of the Nielsen-Ninomiya theorem to this hamiltonian. If these conditions are satisfied, the massless fermion spectrum must be vector-like. We add some general observations on the strong coupling limit of SMG models. We also elaborate on the qualitative differences between four-dimensional and two-dimensional theories that limit the lessons that can be drawn from two-dimensional models. Finally, we compile a list of open questions which must be addressed in any SMG model in order to determine whether or not it is subject to the generalized no-go theorem.

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arXiv2025

The strong coupling from hadronic $τ$-decay data including $τ\toπ^-π^0ν_τ$ from Belle

In previous work we have combined the $π^-π^0$, $2π^-π^+π^0$ and $π^-3π^0$ spectral data obtained from hadronic $τ$ decays measured by the ALEPH and OPAL experiments, together with electroproduction data for several of the subleading hadronic modes and BaBar data for the $K\bar{K}$ mode to construct an inclusive non-strange vector spectral function entirely based on experimental data, with no Monte-Carlo generated input. In this paper, we include, for the first time, the Belle $τ\toπ^-π^0ν_τ$ high-statistics decay data to construct a new inclusive non-strange vector spectral function that combines more of the world's available data. As no Belle data are at present available for the two $4π$ modes, this requires a revised data analysis in comparison with our previous work. From the resulting new spectral function, we obtain a new determination of the strong coupling, $α_s$, using our previously developed strategy based on finite-energy sum rules. We find, at the $Z$ mass scale, $α_s(m_Z^2)=0.1159(14)$. We discuss the smaller central value and larger error of our new result compared to our previous result, showing the shifts to be due mainly to significant changes in updated HFLAV results for the $π^-3π^0$ decay mode.

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arXiv2025

Quark-hadron duality and the determination of $α_s$ from hadronic $τ$ decay: facts vs. myths

Non-perturbative effects have a small but non-trivial impact on the determination of the strong coupling from hadronic $τ$ decay data. Several approaches have been proposed to take these into account, the two most important of which are the ``truncated OPE'' approach and ``DV-model'' approach. Recently, Pich and Rodríguez-Sánchez have raised a number of criticisms of the latter approach, including, most notably, claims of the existence of (i) a supposed instability with respect to variations of the model for incorporating quark-hadron duality violations, and (ii) an alleged redundancy in the fitting strategy employed in the DV-model approach. In this paper, we address these criticisms one by one, showing they fail to survive more detailed scrutiny of the mathematical or numerical arguments that underpin them. We also show that, while the redundancy claim does not apply to the DV-model approach, it does, in fact, apply to the truncated OPE approach. In particular, the $α_s$ value determined in the latter turns out to derive purely from perturbation theory, with no role played by the non-perturbative condensates determined in the rest of the analysis. This leads to the conclusion that a revision of the conventional understanding of what is learned from truncated OPE analyses is necessary and that only very limited self-consistency checks are possible within this framework. These observations raise new, non-trivial issues for the truncated OPE approach.

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arXiv2025

Power counting of the pion-dilaton effective field theory

Confining QCD-like theories close to the conformal window have a ``walking'' coupling. This is believed to lead to a light singlet scalar meson in the low-energy spectrum, a dilaton, which is the pseudo Nambu--Goldstone boson for the approximate scale symmetry. Extending chiral perturbation theory to include the dilaton requires a new small parameter to control the dilaton mass and its interactions. In our previous work we derived a systematic power counting for the dilaton couplings by matching the effective low-energy theory to the underlying theory using mild assumptions. In this paper we examine two alternative power countings which were proposed in the literature based on a phenomenological picture for the conformal transition. We find that one of these power countings fails, in fact, to generate a systematic expansion; the other coincides with the power counting we derived. We also point out that the so-called $Δ$-potential coincides with the tree-level potential of the former, invalid, power counting.

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arXiv2024

Data-driven results for light-quark connected and strange-plus-disconnected hadronic $g-2$ short- and long-distance windows

A key issue affecting the attempt to reduce the uncertainty on the Standard Model prediction for the muon anomalous magnetic moment is the current discrepancy between lattice-QCD and data-driven results for the hadronic vacuum polarization. Progress on this issue benefits from precise data-driven determinations of the isospin-limit light-quark-connected (lqc) and strange-plus-light-quark-disconnected (s+lqd) components of the related RBC/UKQCD windows. In this paper, using a strategy employed previously for the intermediate window, we provide data-driven results for the lqc and s+lqd components of the short- and long-distance RBC/UKQCD windows. Comparing these results with those from the lattice, we find significant discrepancies in the lqc parts but good agreement for the s+lqd components. We also explore the impact of recent CMD-3 $e^+e^-\to π^+π^-$ cross-section results, demonstrating that an upward shift in the $ρ$-peak region of the type seen in the CMD-3 data serves to eliminate the discrepancies for the lqc components without compromising the good agreement between lattice and data-driven s+lqd results.

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arXiv2024

Conserved currents in five-dimensional proposals for lattice chiral gauge theories

We apply the Grabowska-Kaplan framework, originally proposed for lattice chiral gauge theories, to QCD. We show that the resulting theory contains a conserved and gauge invariant singlet axial current, both on the lattice and in the continuum limit. This must give rise to a difference with QCD, with the simplest possibility being a superfluous Nambu-Goldstone boson in the physical spectrum not present in QCD. We find a similar unwanted conserved current in the recent "disk" formalism [Kaplan, Kaplan & Sen], this time limiting ourselves to the continuum formulation. A similar problem is expected when either of these formalisms is used for its original goal of constructing lattice chiral gauge theories. Finally we discuss a conjecture about the possible dynamics that might be associated with the unwanted conserved current, and the fate of 't Hooft vertices.

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arXiv2024

Staggered fermions

These notes are based on a series of lectures on staggered fermions given at the Centre de Physique Théorique, Luminy, in Marseille, France, January 17-25, 2024.

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arXiv2024

Propagator zeros and lattice chiral gauge theories

Symmetric mass generation (SMG) has been advocated as a mechanism to render mirror fermions massive without symmetry breaking, ultimately aiming for the construction of lattice chiral gauge theories. It has been argued that in an SMG phase, the poles in the mirror fermion propagators are replaced by zeros. Using an effective lagrangian approach, we investigate the role of propagator zeros when the gauge field is turned on, finding that they act as coupled ghost states. In four dimensions, a propagator zero makes an opposite-sign contribution to the one-loop beta function as compared to a normal fermion. In two dimensional abelian theories, a propagator zero makes a negative contribution to the photon mass squared. In addition, propagator zeros generate the same anomaly as propagator poles. Thus, gauge invariance will always be maintained in an SMG phase, in fact, even if the target chiral gauge theory is anomalous, but unitarity of the gauge theory is lost.

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arXiv2023

Data-driven determination of the light-quark connected component of the intermediate-window contribution to the muon $g-2$

We present the first data-driven result for $a_μ^{\rm win,lqc}$, the isospin-limit light-quark connected component of the intermediate-window Hadronic-Vacuum-Polarization contribution to the muon anomalous magnetic moment. Our result, $(198.8\pm 1.1)\times 10^{-10}$, is in significant tension with eight recent mutually compatible high-precision lattice-QCD determinations, and provides enhanced evidence for a puzzling discrepancy between lattice and data-driven determinations of the intermediate window quantity, one driven largely by a difference in the light-quark connected component.

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arXiv2023

Data-driven estimates for light-quark-connected and strange-plus-disconnected hadronic $g-2$ window quantities

A number of discrepancies have emerged between lattice computations and data-driven dispersive evaluations of the RBC/UKQCD Intermediate-window-hadronic contribution to the muon anomalous magnetic moment. It is therefore interesting to obtain data-driven estimates for the light-quark-connected and strange-plus-disconnected components of this window quantity, allowing for a more detailed comparison between the lattice and data-driven approaches. The aim of this paper is to provide these estimates, extending the analysis to several other window quantities, including two windows designed to focus on the region in which the two-pion contribution is dominant. Clear discrepancies are observed for all light-quark-connected contributions considered, while good agreement with lattice results is found for strange-plus disconnected contributions to the quantities for which corresponding lattice results exist. The largest of these discrepancies is that for the RBC/UKQCD intermediate window, where, as previously reported, our data-driven result, $a_μ^{W1,{\rm lqc}}=198.9(1.1)\times 10^{-10}$, is in significant tension with the results of 8 different recent lattice determinations. Our strategy is the same as recently employed in obtaining data-driven estimates for the light-quark-connected and strange-plus-disconnected components of the full leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. Updated versions of those earlier results are also presented, for completeness.

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arXiv2023

Dilaton chiral perturbation theory at next-to-leading order

We apply dilaton chiral perturbation theory (dChPT) at next-to-leading order to lattice data from the LatKMI collaboration for the eight-flavor SU(3) gauge theory. In previous work, we found that leading-order dChPT does not account for these data, but that a model extension of leading-order dChPT with a varying mass anomalous dimension describes these data well. Here we calculate the next-to-leading order corrections for the pion mass and decay constant. We focus on these quantities, as data for the dilaton mass are of poorer quality. The application of next-to-leading order dChPT is difficult because of the large number of new low-energy constants, and the results of our fits turn out to be inconclusive. They suggest -- yet cannot firmly establish -- that the LatKMI mass range might be outside the scope of dChPT.

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arXiv2023

On the difference between Fixed-Order and Contour-Improved Perturbation Theory

Using standard mathematical methods for asymptotic series and the large-$β_0$ approximation, we define a Minimum Distance between the Fixed-Order perturbative series and the Contour-Improved perturbative series in the strong coupling $α_s$ for finite-energy sum rules as applied to hadronic $τ$ decays. This distance is similar, but not identical, to the Asymptotic Separation of Hoang and Regner, which is defined in terms of the difference of the two series after Borel resummation. Our results confirm a nonzero nonperturbative result in $α_s$ for this Minimum Distance as a measure of the intrinsic difference between the two series, as well as a conflict with the Operator Product Expansion for Contour-Improved Perturbation Theory.

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arXiv2023

Spectral-weight sum rules for the hadronic vacuum polarization

We develop a number of sum rules comparing spectral integrals involving judiciously chosen weights to integrals over the corresponding Euclidean two-point function. The applications we have in mind are to the hadronic vacuum polarization that determines the most important hadronic correction $a_μ^{\rm HVP}$ to the muon anomalous magnetic moment. First, we point out how spectral weights may be chosen that emphasize narrow regions in $\sqrt{s}$, providing a tool to investigate emerging discrepancies between data-driven and lattice determinations of $a_μ^{\rm HVP}$. Alternatively, for a narrow region around the $ρ$ mass, they may allow for a comparison of the dispersive determination of $a_μ^{\rm HVP}$ with lattice deteruminations zooming in on the region of the well-known BaBar-KLOE discrepancy. Second, we show how such sum rules can in principle be used for carrying out precision comparisons of hadronic-$τ$-decay-based data and $e^+e^-\to\mbox{hadrons}(γ)$-based data, where lattice computations can provide the necessary isospin-breaking corrections.

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arXiv2022

The muon anomalous magnetic moment: is the lattice spacing small enough?

We present new results for the light-quark connected part of the leading order hadronic-vacuum-polarization (HVP) contribution to the muon anomalous magnetic moment, using $2+1+1$ staggered fermions. We have collected more statistics on previous ensembles, and we added two new ensembles. This allows us to reduce statistical errors on the HVP contribution and related window quantities significantly. We also calculated the current-current correlator to next-to-next-to-leading order (NNLO) in staggered chiralperturbation theory, so that we can correct to NNLO for finite-volume, pion-mass mistuning and taste-breaking effects. We discuss the applicability of NNLO chiral perturbation theory, emphasizing that it provides a systematic EFT approach to the HVP contribution, but not to short- or intermediate-distance window quantities. This makes it difficult to assess systematic errors on the standard intermediate-distance window quantity that is now widely considered in the literature. In view of this, we investigate a longer-distance window, for which EFT methods should be more reliable. Our most important conclusion is that new high-statistics computations at lattice spacings significantly smaller than 0.06 fm are indispensable. The ensembles we use have been generously provided by MILC and CalLat.

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