arXiv subjects

Harvey B. Meyer

Publications and source records attributed to Harvey B. Meyer.

At least 19 recordsLinked to original sources

arXiv2026

Higher-order hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD

We present the first lattice QCD calculation of the next-to-leading order hadronic vacuum polarization contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation for the space-like kernel, which is combined with the spatially summed vector correlator computed on CLS ensembles with $N_{\mathrm{f}}=2+1$ flavors of $\mathrm{O}(a)$-improved Wilson fermions, covering six lattice spacings between $0.039$ and $0.097\,$fm and a range of pion masses including the physical value. After accounting for finite-size corrections and isospin-breaking effects, we obtain as our final, continuum-extrapolated result $a_μ^{\mathrm{hvp,\,nlo}}=-101.57(26)_{\mathrm{stat}}(54)_{\mathrm{syst}}\times10^{-11}$. It lies below the estimate provided by the 2025 White Paper of the Muon $(g-2)$ Theory Initiative by $1.4σ$ but is two times more precise. It also exhibits a strong tension of $4.6σ$ with data-driven evaluations based on hadronic cross section measurements excluding the recent result by CMD-3.

hep-lat↗

arXiv2026

Precision lattice calculation of the hadronic contribution to the running of the electroweak gauge couplings

We present an update of our lattice QCD determination of the hadronic contribution to the running of the electromagnetic coupling, $Δα_{\mathrm{had}}^{(5)}(-Q^2)$, and of the electroweak mixing angle in the space-like momentum region up to $Q^2=12\ \mathrm{GeV}^2$. The calculation is based on CLS ensembles with $N_f=2+1$ flavours of $O(a)$-improved Wilson fermions, covering five lattice spacings between $0.039$ and $0.085$ fm and a range of pion masses, including the physical point. A refined analysis employing a telescopic window strategy allows for a clean separation of systematic effects across Euclidean distance scales. Statistical precision is further enhanced through low-mode averaging, combined with a spectral reconstruction of the vector-vector correlator at long distances on the most chiral ensembles. We confirm significant tensions of up to $7σ$ at space-like virtualities around $Q^2= 1\ \mathrm{GeV}^2$ between our lattice results for $Δα_{\mathrm{had}}^{(5)}(-Q^2)$ and the corresponding data-driven estimates based on $e^+e^-$ cross section data. Combining our lattice data with perturbative QCD via the Euclidean split technique, we obtain at the $Z$-pole $Δα_{\mathrm{had}}^{(5)}(M_Z^2) = 0.027813(33)_{\mathrm{lat}}(35)_{\mathrm{pQCD}}$, which is more than two times more precise than recent data-driven estimates. Our result deviates slightly, by $1-2σ$, from the value produced by global electroweak fits. For the electroweak mixing angle, we present the hadronic contribution to its running and provide a precise determination of the octet-singlet mixing component $\barΠ^{(0,8)}$, in good agreement with phenomenological models but with significantly higher precision.

hep-lat↗

arXiv2026

Running of the Electroweak Gauge Couplings from First Principles

We present a high-precision calculation of the hadronic running of electroweak gauge couplings from first principles. Employing lattice QCD in the low-energy regime, we achieve permille precision for virtualities $Q^2 \lesssim 12\;\mathrm{GeV}^2$. At $Q^2 \simeq 1\;\mathrm{GeV}^2$, our determination deviates by up to $7σ$ from estimates based on $e^+e^-$ measurements. Combining lattice QCD with perturbative QCD via the Euclidean split technique, we obtain for the electromagnetic coupling $Δα^{(5)}_{\mathrm{had}}(M_Z^2) = 0.027821(34)_{\mathrm{lat}}(35)_{\mathrm{pQCD}}$, which is more than twice as precise as recent phenomenological determinations. We assess improvement scenarios by which the precision target for next-generation electroweak measurements could be reached.

hep-lat↗

arXiv2026

Electromagnetic pion mass splitting using a Pauli-Villars-regulated photon propagator

We present a lattice QCD calculation of the charged-neutral pion mass splitting $M_{π^+} - M_{π^0}$ at $\mathcal{O}(α_\mathrm{em})$ using a recently proposed framework based on a Pauli-Villars (PV) regulated photon propagator defined in the continuum and infinite-volume limit, with $Λ$ acting as an additional UV cutoff scale. The use of this propagator avoids power-law finite-volume effects, allowing for a straightforward treatment of the infinite-volume limit. We perform the calculation using CLS ensembles, studying finite-volume effects, the continuum limit and the extrapolation to the physical point for several values of the scale $Λ$. By means of the Cottingham formula, we further decompose the result into elastic and inelastic contributions at fixed $Λ$. Our final result, after removing the cutoff scale $Λ$, is $M_{π^+} - M_{π^0} = 4.56(22)$ MeV, in good agreement with the experimental measurement. This calculation serves as a validation of the formalism in a well-controlled setting and offers useful insights into the application of electromagnetic corrections to other observables.

hep-lat↗

arXiv2026

The strange and flavor-singlet axial form factors of the nucleon from lattice QCD

The singlet axial form factor of the nucleon provides essential input for a complete understanding of the nucleon axial structure. Together with the isovector and isoscalar octet channels, in the forward limit it forms the basis for a full flavor decomposition of the proton spin. In this work we present a lattice QCD determination of the singlet axial form factor $G^{u+d+s}_A(Q^2)$ and related strange contribution $G^{s}_A(Q^2)$ using a set of $N_f = 2 + 1$ CLS gauge ensembles with $O(a)$-improved Wilson fermions, with a full error budget for the extrapolation to the chiral, continuum and infinite-volume limits. Particular focus is placed on the treatment of the disconnected contributions, which constitute the crucial element for the extraction of the strange component. Together with determinations of the isovector and isoscalar octet axial form factors, this work provides a comprehensive lattice QCD determination of the nucleon axial structure across different flavor channels.

hep-lat↗

arXiv2026

Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $(g-2)_μ$

The Standard Model prediction of the muon $g-2$ increasingly depends on lattice QCD computations of the hadronic vacuum polarization (HVP), where the isospin-breaking (IB) effects remain a significant source of uncertainty. To complement the lattice QCD evaluations, the data-driven approach to HVP has been used to assess some of the electromagnetic IB effects, in particular from the channels with a photon in the final state, e.g., $e^+e^-\toπ^0 γ$. Here we argue that such contributions are largely canceled by virtual electromagnetic corrections to the purely hadronic channels: $π^+ π^-$, $π^+ π^- π^0$, etc. We identify these leading corrections by performing a field-theoretical calculation in a vector-meson dominance model, thereby reconciling the timelike and spacelike approaches to electromagnetic effects. Although these virtual corrections are more difficult to extract in a systematic manner, addressing them is essential for the data-driven method to consistently complement the lattice QCD program.

hep-ph↗

arXiv2026

Lattice determination of the higher-order hadronic vacuum polarization contribution to the muon $g-2$

We present the first lattice QCD calculation of the next-to-leading order (NLO) hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation combined with the spatially summed vector correlator computed on CLS ensembles with $N_{\mathrm{f}}=2+1$ flavors of $\mathrm{O}(a)$-improved Wilson fermions, spanning six lattice spacings ($0.039$-$0.097\,$fm) and a range of pion masses including the physical value. After accounting for finite-size corrections and isospin-breaking effects, we obtain in the continuum limit $a_μ^{\mathrm{hvp,\,nlo}} = (-101.57 \pm 0.26_{\rm stat} \pm 0.54_{\rm syst}) \times 10^{-11}$, corresponding to a total relative error of 0.6$\%$. Our result lies 1.4$σ$ below the estimate of the 2025 White Paper update and is two times more precise. It also shows a tension of $4.6σ$ with data-driven evaluations based on hadronic cross section measurements prior to the CMD-3 result.

hep-lat↗

arXiv2026

The hadronic contribution to the running of the electroweak gauge couplings

We present an updated determination of the hadronic vacuum polarization contribution to the running of the electromagnetic coupling $Δα_{\mathrm{had}}^{(5)}(-Q^2)$, and of the electroweak mixing angle in the space-like momentum range up to $12 \ \mathrm{GeV}^2$. Using $N_f=2+1$ CLS ensembles at five values of the lattice spacing and several pion masses, including the physical point, we achieve a significantly enhanced precision over our previous result. A refined analysis strategy based on telescopic series and a new family of kernel functions enables a clean separation of distinct Euclidean regions, disentangling strong cutoff effects at short distances from the pronounced chiral dependence at larger ones. Employing the Euclidean split technique, we convert our lattice results into an ab initio estimate of $Δα_{\mathrm{had}}^{(5)}(M_Z^2)$. A comparison with results from other lattice calculations and phenomenology is performed. We also analyze improvement scenarios required to match the projected precision of future electroweak measurements at next-generation colliders.

hep-lat↗

arXiv2026

Factorizing the position-space photon propagator in QED corrections to lattice QCD correlators

Electromagnetic corrections to the $n$-point functions of lattice QCD can be evaluated using a position-space photon propagator defined in infinite volume. Here we address the computational challenge arising from the volume-squared sum over the endpoints of the photon propagator. We consider a class of integral representations of the photon propagator that lead to a factorization of the two volume-sums, the Fourier representation being one instance thereof. An alternative choice is based on expressing the free scalar propagator as the autoconvolution of the corresponding five-dimensional propagator. We compare the performance of three different choices in the context of electromagnetic corrections to the hadronic vacuum polarization, on a gauge ensemble of size $48^3\times128$ with a pion mass of 286 MeV. As an outlook, we discuss more generally the factorization of sums over internal vertices, taking as an example the hadronic light-by-light contribution to the muon $(g-2)$.

hep-lat↗

arXiv2026

Electromagnetic pion mass splitting using PV-regulated photon propagator

Several hadronic observables are nowadays computed in lattice QCD with a sub-percent precision which requires the inclusion of strong isospin-breaking and electromagnetic effects. Most of the methods that implement the photon propagator in finite-volume lead to power-law suppressed finite-size effects and do not allow for a straightforward crosscheck against phenomenology and other calculations. Both issues can be avoided by working with a Pauli-Villars regulated photon propagator defined directly in the continuum and infinite volume. This methodology can be profitably exploited to improve the determination of leading-order electromagnetic corrections to several observables such as the HVP or nucleon masses. In this work we apply the strategy to the charged/neutral pion mass difference using CLS ensembles.

hep-lat↗

arXiv2025

Euclidean coordinate-space perturbation theory with a single mass scale

We develop elements of coordinate-space perturbation theory for massive quantum field theories in general $d$-dimensional Euclidean space. Using the expansion in Gegenbauer polynomials, we provide analytic expressions for several three-point correlation functions in theories with one massive and one massless field. To this end, a class of antiderivatives of products of two Bessel functions multiplied by a power of their common argument are studied systematically. We expect these results to be useful in perturbative calculations involving vertices of high degree, at finite temperature and/or in finite volume, as well as in auxiliary perturbative computations for a lattice QCD treatment of hadronic effects in precision observables. As an illustration, we compute the one-loop coordinate-space propagator of a massive particle coupled to a massless one, both in the vacuum and at finite temperature.

hep-lat↗

arXiv2025

Non-singlet vector current in lattice QCD: $\mathrm{O}(a)$-improvement from large volumes

In previous work, we determined the improvement coefficients $c_\mathrm{V}$ and $c_{\tilde{\mathrm{V}}}$ required for the massless $\mathrm{O}(a)$-improvement of the local and point-split discretizations of the non-singlet vector current for $N_\mathrm{f}=3$ non-perturbatively $\mathrm{O}(a)$-improved Wilson fermions and the Lüscher-Weisz gauge action, using ensembles of large-volume configurations generated by the Coordinated Lattice Simulations (CLS) initiative. A new estimate for the mass-dependent improvement coefficient $\bar{b}_{\mathrm{A}}^\mathrm{eff}$ has recently become available, differing from the one used in our earlier study, and on which our implementation via a massive axial Ward identity relied. Here, we update our analysis of the mass-independent vector improvement coefficients based on the new axial current improvement coefficient, and analyse additional ensembles with a different chiral trajectory in order to validate our results at two values of the bare coupling. We find that using the new estimate of $\bar{b}_{\mathrm{A}}^\mathrm{eff}$ improves the consistency between the two chiral trajectories, as well as with a previous determination of the improvement coefficients directly in the massless limit on small volumes.

hep-lat↗

arXiv2025

Isospin-violating vacuum polarization in the muon $(g-2)$ with SU(3) flavour symmetry from lattice QCD

We compute the isospin-violating part $a_μ^{\text{HVP}, 38}$ of the hadronic-vacuum-polarization (HVP) contribution to the muon $(g-2)$ in lattice QCD at the SU$(3)_{\rm f}$-symmetric point where $M_π=M_K\simeq 416$ MeV. All diagrams involving internal photons are evaluated in coordinate space, employing a Pauli-Villars-regulated photon propagator with a cutoff scale $Λ$ well below the lattice cutoff. The counterterm $(m_u-m_d)$, whose $Λ$ dependence is consistent with the expected logarithmic behaviour, is calibrated using the experimental kaon mass splitting as input. The bare electromagnetic contribution at fixed $Λ$ is compared to a phenomenological estimate based on the kaon-loop and pseudoscalar-pole contributions to the forward light-by-light amplitude. An extension of these calculations to physical pion and kaon masses appears promising.

hep-lat↗

arXiv2025

The isoscalar octet axial form factor of the nucleon from lattice QCD

The isoscalar axial-vector form factor of the nucleon plays a key role in understanding the electroweak interaction of nucleons. For the interpretation of the spin structure of the nucleon the non-singlet isoscalar axial charge is indispensable. Moreover, $G_A^{u+d-2s}(Q^2)$ together with the isovector and singlet isoscalar form factors are needed for the flavor-decomposition of the axial-vector form factor. Detailed knowledge of the flavor decomposition facilitates extractions of Standard Model (SM) parameters from low energy experiments such as the electroweak charge of the proton in the P2 experiment. Here we present a lattice determination of $G_A^{u+d-2s}(Q^2)$ on $N_f=2+1$ $\mathcal{O}(a)$ improved Wilson fermions, with a full error budget concerning extrapolations and interpolations to the continuum and infinite volume and physical quark masses.

hep-lat↗

arXiv2025

Probing how bright the quark-gluon plasma glows in lattice QCD

Determining the spectrum of photons emitted by the quark-gluon plasma non-perturbatively remains an open computational challenge. In this letter we calculate two moments of that spectrum at a temperature $T\approx 254\,$MeV, employing lattice QCD with two flavors of $\mathrm{O}(a)$-improved Wilson fermions, without facing an inverse problem. Our central value for the difference of these two moments, which is sensitive to photon energies $ω\gtrsim πT$, is lower than, but compatible with that obtained by integrating the leading-order weak-coupling photon spectrum. This study informs the $\textit{direct photon puzzle}$ in heavy-ion collision phenomenology, where it has proved difficult to simultaneously explain the yield and azimuthal anisotropy of photons not originating from final-state hadronic decays.

hep-lat↗

arXiv2025

Computing the UV-finite electromagnetic corrections to the hadronic vacuum polarization in the muon $(g-2)$ from lattice QCD

In order to reach a precision of $0.2\%$ on the hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon, $(g-2)_μ$, such that the full Standard-Model prediction matches in precision the direct experimental measurement, it is crucial to include the leading, O($α$) electromagnetic corrections to HVP. In this work, we determine an important contribution to the latter from a diagram comprised of two two-point quark-loops, connected by the internal photon and gluons. This ultraviolet-finite correction is calculated from lattice QCD using a coordinate-space formalism, where photons are treated in the continuum and infinite volume. Our result amounts to a $(-0.89\pm 0.18)\%$ correction to the leading-order HVP contribution to $(g-2)_μ$. To overcome the worsening statistical noise at large distances, our analysis is combined with phenomenological models featuring light pseudoscalar mesons with masses below 1 GeV. In particular, our data show a very steep mass dependence as dictated by the charged pion loop. Similarly, the other diagrams appearing in the O$(α)$-corrections to the HVP with the internal photon connecting two separate quark loops are also ultraviolet-finite and can be computed with the same formalism.

hep-lat↗

arXiv2025

The $π^0\to γ^\ast γ^\ast$ transition form factor and the pion pole contribution to $a_μ$ on CLS ensembles

We present the status of the Mainz group's lattice QCD calculation of the pion transition form factor $\mathcal{F}_{π^0γ^\astγ^\ast}$, which describes the interaction of an on-shell pion with two off-shell photons. This form factor is the main ingredient in the calculation of the pion-pole contribution to hadronic light-by-light scattering in the muon $g-2$. We use the $N_f = 2 + 1$ CLS gauge ensembles, and we update our previous work by including a physical pion mass ensemble (E250). We compute the transition form factor in the pion rest frame as well as in a moving frame in order to have access to a wider range of photon virtualities. In addition to the quark-line connected correlator we also compute the quark-line disconnected diagrams that contribute to the form factor. In this final stage of the analysis, we combine the result on E250 with the previous work published in 2019 to extrapolate the form factor to the continuum and to physical quark masses. Testing different ansätze for the fit, we explore the systematic uncertainties of the extrapolation. The contribution from the disconnected diagrams is also scrutinized.

hep-lat↗

arXiv2025

The hadronic vacuum polarization contribution to the muon $g-2$ at long distances

We present our lattice QCD result for the long-distance part of the hadronic vacuum polarization contribution, $(a_μ^{\rm hvp})^{\rm LD}$, to the muon $g-2$ in the time-momentum representation. This is the numerically dominant, and at the same time the most challenging part regarding statistical precision. Our calculation is based on ensembles with dynamical up, down and strange quarks, employing the O($a$)-improved Wilson fermion action with lattice spacings ranging from $0.035-0.099$ fm. In order to reduce statistical noise in the long-distance part of the correlator to the per-mille level, we apply low-mode averaging and combine it with an explicit spectral reconstruction. Our result is $(a_μ^{\rm hvp})^{\rm LD} = 423.2(4.2)_{\rm stat}(3.4)_{\rm syst}\times 10^{-10}$ in isospin-symmetric QCD, where the pion decay constant is used to set the energy scale. When combined with our previous results for the short- and intermediate-distance window observables and after including all sub-dominant contributions as well as isospin-breaking corrections, we obtain the total leading-order hadronic vacuum polarization contribution as $a_μ^{\rm hvp} = 724.5(4.9)_{\rm stat}(5.2)_{\rm syst}\times 10^{-10}$. Our result displays a tension of 3.9 standard deviations with the data-driven estimate published in the 2020 White Paper, but leads to a SM prediction for the total muon anomalous magnetic moment that agrees with the current experimental average.

hep-lat↗