Maarten Golterman

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 − → 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 2 π − π + π 0 mode.

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 (nongauge) 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 vectorlike. 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.

Tau-based finite-energy sum-rule (FESR) analyses often assume that scales s_0\sim m_\tau^2 s 0 ∼ m τ 2 are large enough that (i) integrated duality violations (DVs) can be neglected, and (ii) contributions from non-perturbative OPE condensates of dimension D D scale as (\Lambda_{QCD}/m_\tau )^D ( Λ Q C D / m τ ) D , allowing the OPE series to be truncated at low dimension. The latter assumption is not necessarily valid since the OPE series is not convergent, while the former is open to question given experimental results for the electromagnetic, I=1 I = 1 vector ( V V ), I=1 I = 1 axial vector ( A A ) and I=1 I = 1 V+A V + A current spectral functions, which show DV oscillations with amplitudes comparable in size to the corresponding \alpha_s α s -dependent perturbative contributions at s\sim2-3 s ∼ 2 − 3 GeV ^2 2 . Here, we discuss recently introduced new tools for assessing the numerical relevance of omitted higher- D D OPE contributions. Applying these to the “truncated OPE” strategy used in Refs.[M. Davier et al., Eur. Phys. J. C 74, 2803 (2014); A. Pich and A. Rodríguez-Sánchez, Phys. Rev. D 94, 034027 (2016)] and earlier work by the same authors, we find that this strategy fails to yield reliable results for the strong coupling from hadronic \tau τ decays.

We perform a precise extraction of the QCD coupling at the \tau τ -mass scale, \alpha_s(m_\tau) α s ( m τ ) , from a new vector isovector spectral function which combines ALEPH and OPAL distributions for the dominant channels, \tau\to\pi \pi^0\nu_\tau τ → π π 0 ν τ , \tau\to 3\pi \pi^0\nu_\tau τ → 3 π π 0 ν τ and \tau\to \pi 3\pi^0\nu_\tau τ → π 3 π 0 ν τ , with estimates of sub-leading contributions obtained from electroproduction cross-sections using CVC, as well as BaBar results for \tau \to K^-K^0\nu_\tau τ → K − K 0 ν τ . The fully inclusive spectral function thus obtained is entirely based on experimental data, without Monte Carlo input. From this new data set, we obtain \alpha_s(m_\tau)=0.3077±0.0075 α s ( m τ ) = 0.3077 ± 0.0075 , which corresponds to \alpha_s(m_Z)=0.1171±0.0010 α s ( m Z ) = 0.1171 ± 0.0010 . This analysis can be improved on the experimental side with new measurements of the dominant \pi\pi^0 π π 0 , \pi 3\pi^0 π 3 π 0 , and 3\pi \pi^0 3 π π 0 \tau τ decay modes.

Nonperturbative effects have a small but nontrivial 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 Operator Product Expansion (OPE)” approach and “Duality Violation (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 investigate these criticisms and show 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 nonperturbative 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, nontrivial issues for the truncated OPE approach.

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.

In previous work we have combined the π − π 0 , 2 π − π + π 0 , and π − 3 π 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 data for the K K ¯ mode to construct an inclusive nonstrange 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 → π − π 0 ν τ high-statistics decay data to construct a new inclusive nonstrange vector spectral function that combines more of the world’s available data. As no Belle data are at present available for the two 4 π 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 − 3 π 0 decay mode.

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 − → 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.

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, 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. Published by the American Physical Society 2024