arXiv subjects

Simon Kuberski

Publications and source records attributed to Simon Kuberski.

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

Precision renormalisation and improvement of $N_{\rm f}=3$ lattice QCD with Wilson fermions

We renormalise (and improve) the flavour non-singlet axial current, pseudo-scalar density, vector current and tensor current, as well as quark masses, in O(a) improved lattice QCD with three massless flavours and lattice spacings down to 0.01 fm. To this end, we tune a number of lattices with Schrödinger functional boundary conditions and resolutions $8\leq L/a\leq 64$ to lines of constant physics with massless quarks and fixed gradient flow coupling $\bar{g}_\mathrm{GF}^2(L_i),\; i=0,1,2$, corresponding to $L_0 \approx 0.25$ fm, $L_1=2L_0$ and $L_2=4L_0$. We further renormalise and improve the quark mass of additional heavy quarks for use in the B-physics programme of the collaboration (arXiv:2312.09811). Our somewhat technical results enable first-principles strategies for solving multi-scale problems involving, e.g., the b-quark mass (arXiv:2312.10017) or a large temperature (arXiv:2501.11603). Comparing also to other determinations of the axial current renormalisation constant $Z_{\rm A}$, we have a precise confirmation of how renormalisation and the restoration of chiral symmetry work out with Wilson fermions at small $a$. In particular, the accurate restoration of chiral symmetry and the exact flavour symmetry lead to practically negligible uncertainties in observables determined from Ward identities: four to five significant digits are achieved for $Z_{\rm A},Z_{\rm V}$. We provide an explanation for the strong suppression of their statistical variances.

hep-lat↗

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

Heavy quark masses from step-scaling

We present a determination of the charm- and bottom-quark masses using the heavy-quark step-scaling strategy. Renormalization is performed in small volumes where relativistic bottom quarks can be simulated directly. A sequence of finite-volume simulations connects this calculation to large-volume CLS ensembles, where simulations at physical light and strange quark masses provide reliable control over low-energy hadronic physics. In all but the smallest volume, the B-scale is reached by interpolating between relativistic heavy-quark data and the static limit. The resulting quark masses are obtained with good precision, with subdominant systematic uncertainties that differ from, and thus complement, those of standard large-volume determinations.

hep-lat↗

arXiv2026

A first study of strong isospin breaking effects in lattice QCD using truncated polynomials

Computing derivatives of observables with respect to parameters of the theory is a powerful tool in lattice QCD, as it allows the study of physical effects not directly accessible in the original Monte Carlo simulation. Prominent examples of this include the impact of the up-down quark mass difference and electromagnetic corrections. In this work, we present a new approach based on automatic differentiation to evaluate such derivatives to arbitrarily high orders, where particular emphasis will be placed on strong isospin-breaking effects and on the propagation of derivatives through the conjugate gradient algorithm in the computation of correlation functions.

hep-lat↗

arXiv2026

Ground-State Extraction of Heavy-Light Meson Semileptonic Decay Form Factors

We discuss the extraction of heavy-light pseudo-scalar to light pseudo-scalar decay form factors from finite time correlation functions. We place particular emphasis on the contamination from excited states employing summed ratios and input from chiral perturbation theory. The analysis is performed on four CLS ensembles with $N_f = 2+1$ flavours of $\mbox{O}(a)$-improved Wilson fermions (presently) at the $\mathrm{SU}(3)$-symmetric point with relativistic heavy-quark masses in the charm region and above. The study presented here is part of the analysis aimed at the computation of the $B \to π\ell ν$ and $B_s \to K \ell ν$ semileptonic form factors, combining the continuum-limit relativistic results with static-limit calculations.

hep-lat↗

arXiv2025

Kaon Physics: A Cornerstone for Future Discoveries

The kaon physics programme, long heralded as a cutting-edge frontier by the European Strategy for Particle Physics, continues to stand at the intersection of discovery and innovation in high-energy physics (HEP). With its unparalleled capacity to explore new physics at the multi-TeV scale, kaon research is poised to unveil phenomena that could reshape our understanding of the Universe. This document highlights the compelling physics case, with emphasis on exciting new opportunities for advancing kaon physics not only in Europe but also on a global stage. As an important player in the future of HEP, the kaon programme promises to drive transformative breakthroughs, inviting exploration at the forefront of scientific discovery.

hep-ph↗

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↗

arXiv2025

The hadronic contribution to the running of $α$ and the electroweak mixing angle

We report on our update to [1] on the hadronic running of electroweak couplings from $O(a)$-improved Wilson fermions with $N_f=2+1$ flavours. The inclusion of additional ensembles at very fine lattice spacings together with a number of techniques to split the different contributions for a better control of cutoff effects allows us to substantially improve the precision. We employ two different discretizations of the vector current to compute the subtracted Hadronic Vacuum Polarization (HVP) functions $\bar{\mathitΠ}^{γγ}$ and $\bar{\mathitΠ}^{Zγ}$ for Euclidean time momenta up to $Q^2\leq 9 \ \mathrm{GeV}^2$ . To reduce cutoff effects in the short distance region we apply a suitable subtraction to the TMR kernel function, which cancels the leading $x_0^4$ behaviour. The subtracted term is then computed in perturbative QCD using the Adler function and added back to compensate for the subtraction. Chiral-continuum extrapolations are performed with five values of the lattice spacing and several pion masses, including its physical value, and several fit ansätze are explored to estimate the systematics arising from model selection. Our results show excellent prospects for high-precision estimates of $Δα_{\mathrm{had}}^{(5)}(M_Z^2)$ at the Z-pole.

hep-lat↗

arXiv2025

Machine-learning techniques as noise reduction strategies in lattice calculations of the muon $g-2$

Lattice calculations of the hadronic contributions to the muon anomalous magnetic moment are numerically highly demanding due to the necessity of reaching total errors at the sub-percent level. Noise-reduction techniques such as low-mode averaging have been applied successfully to determine the vector-vector correlator with high statistical precision in the long-distance regime, but display an unfavourable scaling in terms of numerical cost. This is particularly true for the mixed contribution in which one of the two quark propagators is described in terms of low modes. Here we report on an ongoing project aimed at investigating the potential of machine learning as a cost-effective tool to produce approximate estimates of the mixed contribution, which are then bias-corrected to produce an exact result. A second example concerns the determination of electromagnetic isospin-breaking corrections by combining the predictions from a trained model with a bias correction.

hep-lat↗

arXiv2024

Theory Driven Evolution of the Weak Mixing Angle

We present the first purely theoretical calculation of the weak mixing angle in the MS scheme at low energies by combining results from lattice QCD with perturbation theory. We discuss its correlation with the hadronic contribution to the anomalous magnetic moment of the muon and to the energy dependence of the electromagnetic coupling. We also compare the results with calculations using cross-section data as input. Implications for the Standard Model prediction of the mass of the W boson are also discussed.

hep-ph↗

arXiv2024

$\mathrm{D}$ and $\mathrm{D_s}$ decay constants in $N_{\rm f}=2+1$ QCD with Wilson fermions

We present results for the leptonic decay constants of the D and D$_{\rm s}$ mesons from $N_{\rm f}=2+1$ lattice QCD. We employ a set of 49 high statistics gauge ensembles generated by the Coordinated Lattice Simulations (CLS) effort utilising non-perturbatively improved Wilson fermions and the tree-level Symanzik improved gauge action at six values of the lattice spacing in the range $a = 0.098\,$fm down to $a = 0.039\,$fm, with pion masses varying from around $420\,$MeV down to below the physical point. The ensembles lie on three trajectories in the quark mass plane, two trajectories intersecting close to the physical quark mass point and the third one approaching the SU(3) chiral limit, enabling tight control of the light and strange quark mass dependence. We obtain $f_{\mathrm{D_s}}=246.8(1.3)\,$MeV, $f_\mathrm{D}=208.4(1.5)\,$MeV and $f_{\mathrm{D_s}}/f_\mathrm{D}=1.1842(36)$, where the precision of our results is mostly limited by the determination of the scale.

hep-lat↗

arXiv2024

Low-mode deflation for twisted-mass and RHMC reweighting in lattice QCD

We propose improved estimators to compute the reweighting factors which are needed for lattice QCD calculations that rely on twisted-mass reweighting for the light quark contribution and the Rational Hybrid Monte Carlo (RHMC) algorithm for non-degenerate quark masses. This is the case for a number of modern large-scale simulations based on O(a) improved Wilson fermions. We find a significant reduction of uncertainties for the reweighting factors at similar computational cost compared to the conventional estimation. This leads to a significant increase in precision for phenomenologically relevant observables with high correlation to the low eigenmodes of the Wilson-Dirac operator in the presence of exceptionally small eigenvalues. Supplementary details regarding the spectral gap of the light quark Dirac operator on the 2+1 flavor large-volume ensembles explored in this study can be found in an accompanying appendix.

hep-lat↗

arXiv2024

Muon $g-2$: Lattice calculations of the hadronic vacuum polarization

The experimental uncertainty on the anomalous magnetic moment of the muon has been significantly reduced with the recent results of the Fermilab $g-2$ experiment, and a further reduction is expected in the near future. The precision of the Standard Model prediction needs to improve correspondingly to increase the sensitivity of tests for physics beyond the Standard Model. The largest uncertainty is due to contributions from the strong interaction, in particular the hadronic vacuum polarization (HVP) contribution. Lattice QCD calculations have the potential to provide precise ab initio predictions of the HVP contribution. We review the state of lattice QCD calculations, focusing on the dominant sources of uncertainty that need to be controlled to provide results with sub-percent precision.

hep-lat↗

arXiv2024

Hadronic vacuum polarization in the muon $g-2$: The short-distance contribution from lattice QCD

We present results for the short-distance window observable of the hadronic vacuum polarization contribution to the muon $g-2$, computed via the time-momentum representation (TMR) in lattice QCD. A key novelty of our calculation is the reduction of discretization effects by a suitable subtraction applied to the TMR kernel function, which cancels the leading $x_0^4$-behaviour at short distances. To compensate for the subtraction, one must substitute a term that can be reliably computed in perturbative QCD. We apply this strategy to our data for the vector current collected on ensembles generated with $2+1$ flavours of O($a$)-improved Wilson quarks at six values of the lattice spacing and pion masses in the range $130-420\,$MeV. Our estimate at the physical point contains a full error budget and reads $(a_μ^{\rm hvp})^{\rm SD}=68.85(14)_{\rm stat}\,(42)_{\rm syst}\cdot10^{-10}$, which corresponds to a relative precision of 0.7\%. We discuss the implications of our result for the observed tensions between lattice and data-driven evaluations of the hadronic vacuum polarization.

hep-lat↗