arXiv subjects

Antoine Gérardin

Publications and source records attributed to Antoine Gérardin.

At least 19 recordsLinked to original sources

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

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

Physics Briefing Book: Input for the 2026 update of the European Strategy for Particle Physics

The European Strategy for Particle Physics (ESPP) reflects the vision and presents concrete plans of the European particle physics community for advancing human knowledge in fundamental physics. The ESPP is updated every five-to-six years through a community-driven process. It commences with the submission of specific proposals and other input from the community at large, outlining projects envisioned for the near-, mid-, and long-term future. All submitted contributions are evaluated by the Physics Preparatory Group (PPG), and a preliminary analysis is presented at a Symposium meant to foster a broad community discussion on the scientific value and feasibility of the various ideas proposed. The outcomes of the analysis and the deliberations at the Symposium are synthesized in the current Briefing Book, which provides an important input in the deliberations of the Strategy recommendations by the European Strategy Group (ESG).

hep-ex↗

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

Lattice calculation of the $π^0$, $η$ and $η^{\prime}$ transition form factors and the hadronic light-by-light contribution to the muon $g-2$

In this paper we present a first ab-initio calculation of the $π^0$, $η$ and $η^{\prime}$ transition form factors performed with physical light-quark masses. We provide a complete parametrization of the form factors that includes both single and double-virtual kinematics. Our results are compared with experimental measurements of the form factors in the space-like region and with the measured two-photon decay widths. In a second step, our parametrizations of the transition form factors are used to compute the dominant pseudoscalar-pole contributions to the hadronic light-by-light scattering in the muon $g-2$. Our final result reads $a_μ^{\rm hlbl, ps-pole} = (85.1 \pm 5.2) \times 10^{-11}$. Although the pion-pole is dominant, we confirm that, together, the $η$ and $η^{\prime}$ provide roughly half of its contribution.

hep-lat↗

arXiv2024

The hadronic light-by-light contribution to the muon $g{-}2$ using staggered fermions at the physical point

Hadronic contributions dominate the uncertainty of the Standard Model prediction for the anomalous magnetic moment of the muon. In this work, we present results on the hadronic light-by-light contribution obtained from the evaluation of the hadronic four-point function of electromagnetic currents using the position-space formalism developed by the Mainz group. The simulations are performed with staggered fermions directly at the physical point. Several physical volumes are used to estimate finite volume effects. This direct lattice study is supplemented by considering the contribution of the light pseudoscalar pole in both finite and infinite volumes, where we reuse the pseudoscalar transition form factors that have been evaluated in previous simulations on the same ensembles.

hep-lat↗

arXiv2023

A strategy for B-physics observables in the continuum limit

In a somewhat forgotten paper [1] it was shown how to perform interpolations between relativistic and static computations in order to obtain results for heavy-light observables for masses from, say, $m_{\rm charm}$ to $m_{\rm bottom}$. All quantities are first continuum extrapolated and then interpolated in $1/m_h=1/m_{\rm heavy}$. Large volume computations are combined with finite volume ones where a relativistic bottom quark is accessible with small $am_{\rm bottom}$. We discuss how this strategy is extended to semi-leptonic form factors and other quantities of phenomenological interest. The essential point is to form quantities where the limit $m_h\to\infty$ is approached with power corrections O$(1/m_h)$ only. Perturbative corrections $\simα_s(m_h)^{γ+n}$ are cancelled in the construction of the observables. We also point out how such an approach can help to control systematics in semi-leptonic decays with just large volume data. First numerical results with $N_f = 2 + 1$ and lattice spacings down to 0.039 fm are presented in [2].

hep-lat↗

arXiv2023

$m_B$ and $f_{B^{(\star)}}$ in $2+1$ flavour QCD from a combination of continuum limit static and relativistic results

We present preliminary results for B-physics from a combination of non-perturbative results in the static limit with relativistic computations satisfying $am_{\mathrm{heavy}}\ll 1$. Relativistic measurements are carried out at the physical b-quark mass using the Schrödinger Functional in a $0.5 \ \mathrm{fm}$ box. They are connected to large volume observables through step scaling functions that trace the mass dependence between the physical charm region and the static limit, such that B-physics results can be obtained by interpolation; the procedure is designed to exactly cancel the troublesome $α_s(m_{\mathrm{heavy}})^{n+γ}$ corrections to large mass scaling. Large volume computations for both static and relativistic quantities use CLS $N_f=2+1$ ensembles at $m_u=m_d=m_s$, and with five values of the lattice spacing down to $0.039$ fm. Our preliminary results for the b-quark mass and leptonic decay constants have competitive uncertainties, which are furthermore dominated by statistics, allowing for substantial future improvement. Here we focus on numerical results, while the underlying strategy is discussed in a companion contribution.

hep-lat↗

arXiv2023

Investigation of the hadronic light-by-light contribution to the muon $g{-}2$ using staggered fermions

Hadronic contributions dominate the uncertainty of the standard model prediction for the anomalous magnetic moment of the muon. In this work, we describe an ongoing lattice calculation of the hadronic light-by-light contribution, performed with staggered fermions. The presence of quarks with different tastes complicates the analysis of the position-space correlation function. We present a suitable adaption of the "Mainz method". As a first numerical test, we reproduce the well-known lepton-loop contribution. Results at a single lattice spacing for the light quark contribution, using two volumes, are then discussed. Our study of the long distance behavior and finite-volume effects is supplemented by considering the contribution of the light pseudoscalar-pole. The corresponding transition form factors have been evaluated in previous simulations on the same ensembles.

hep-lat↗

arXiv2023

Status update: $π^0\to γ^\ast γ^\ast$ transition form factor on CLS ensembles

In this report we present the status of the Mainz group's lattice QCD calculation of the pion transition form factor, 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 a moving frame as well as in the pion rest 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. At the final stage of the analysis, the result on E250 will be combined with the previous work published in 2019 to extrapolate the form factor to the continuum and to physical quark masses.

hep-lat↗

arXiv2023

Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization

Lattice QCD calculations of the hadronic vacuum polarization (HVP) have reached a precision where the electromagnetic (e.m.) correction can no longer be neglected. This correction is both computationally challenging and hard to validate, as it leads to ultraviolet (UV) divergences and to sizeable infrared (IR) effects associated with the massless photon. While we precisely determine the UV divergence using the operator-product expansion, we propose to introduce a separation scale $Λ\sim400\;$MeV into the internal photon propagator, whereby the calculation splits into a short-distance part, regulated in the UV by the lattice and in the IR by the scale $Λ$, and a UV-finite long-distance part to be treated with coordinate-space methods, thereby avoiding power-law finite-size effects altogether. In order to predict the long-distance part, we express the UV-regulated e.m. correction to the HVP via the forward hadronic light-by-light (HLbL) scattering amplitude and relate the latter via a dispersive sum rule to $γ^*γ^*$ fusion cross-sections. Having tested the relation by reproducing the two-loop QED vacuum polarization (VP) from the tree-level $γ^*γ^*\to e^+e^-$ cross-section, we predict the expected lattice-QCD integrand resulting from the $γ^*γ^*\toπ^0$ process.

hep-lat↗

arXiv2023

Hadronic light-by-light scattering contribution to the muon $g-2$ from lattice QCD: semi-analytical calculation of the QED kernel

Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor $g$ of the muon to deviate from the value of two predicted by Dirac's theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon $(g-2)$. Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detail the semi-analytical calculation of the QED part of the amplitude, employing position-space perturbation theory in continuous, infinite four-dimensional Euclidean space. We also provide some useful information about a computer code for the numerical implementation of our approach that has been made public at https://github.com/RJHudspith/KQED.

hep-lat↗

arXiv2023

Window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD

Euclidean time windows in the integral representation of the hadronic vacuum polarization contribution to the muon $g-2$ serve to test the consistency of lattice calculations and may help in tracing the origins of a potential tension between lattice and data-driven evaluations. In this paper, we present results for the intermediate time window observable computed using O($a$) improved Wilson fermions at six values of the lattice spacings below 0.1\,fm and pion masses down to the physical value. Using two different sets of improvement coefficients in the definitions of the local and conserved vector currents, we perform a detailed scaling study which results in a fully controlled extrapolation to the continuum limit without any additional treatment of the data, except for the inclusion of finite-volume corrections. To determine the latter, we use a combination of the method of Hansen and Patella and the Meyer-Lellouch-Lüscher procedure employing the Gounaris-Sakurai parameterization for the pion form factor. We correct our results for isospin-breaking effects via the perturbative expansion of QCD+QED around the isosymmetric theory. Our result at the physical point is $a_μ^{\mathrm{win}}=(237.30\pm0.79_{\rm stat}\pm1.22_{\rm syst})\times10^{-10}$, where the systematic error includes an estimate of the uncertainty due to the quenched charm quark in our calculation. Our result displays a tension of 3.9$σ$ with a recent evaluation of $a_μ^{\mathrm{win}}$ based on the data-driven method.

hep-lat↗

arXiv2022

The hadronic running of the electroweak couplings from lattice QCD

The energy dependency (running) of the strength of electromagnetic interactions $α$ plays an important role in precision tests of the Standard Model. The running of the former to the $Z$ pole is an input quantity for global electroweak fits, while the running of the mixing angle is susceptible to the effects of Beyond Standard Model physics, particularly at low energies. We present a computation of the hadronic vacuum polarization (HVP) contribution to the running of these electroweak couplings at the non-perturbative level in lattice QCD, in the space-like regime up to $Q^2$ momentum transfers of $7\,\mathrm{GeV}^2$. This quantity is also closely related to the HVP contribution to the muon $g-2$. We observe a tension of up to $3.5$ standard deviation between our lattice results for $Δα^{(5)}_{\mathrm{had}}(-Q^2)$ and estimates based on the $R$-ratio for $Q^2$ in the $3$ to $7\,\mathrm{GeV}^2$ range. The tension is, however, strongly diminished when translating our result to the $Z$ pole, by employing the Euclidean split technique and perturbative QCD, which yields $Δα^{(5)}_{\mathrm{had}}(M_Z^2)=0.027\,73(15)$. This value agrees with results based on the $R$-ratio within the quoted uncertainties, and can be used as an alternative to the latter in global electroweak fits.

hep-lat↗

arXiv2022

The hadronic running of the electromagnetic coupling and electroweak mixing angle

We present results for the hadronic running of the electromagnetic coupling and the weak mixing angle from simulations of lattice QCD with $N_f=2+1$ flavours of $O(a)$-improved Wilson fermions. Using two different discretisations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarisation (HVP) functions $\barΠ^{γγ}$ and $\barΠ^{Zγ}$ for spacelike squared momenta $Q^2\leq 7$ $\mathrm{GeV}^2$. Our results are extrapolated to the physical point using ensembles at four lattice spacings, with pion masses ranging from 130 to 420 MeV. We observe a tension of up to 3.5 standard deviations between our lattice results for $Δα_{\rm had}^{(5)}(-Q^2)$ and estimates based on the $\textit{R}$-ratio for space-like momenta in the range $Q^2=3-7\,\rm GeV^2$. To obtain an estimate for $Δα_\mathrm{had}^{(5)}(M_Z^2)$, we employ the Euclidean split technique. The implications for comparison with global electroweak fits are assessed.

hep-lat↗

arXiv2022

Intermediate window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from O$(a)$ improved Wilson quarks

Following the publication of the new measurement of the anomalous magnetic moment of the muon, the discrepancy between experiment and the theory prediction from the $g-2$ theory initiative has increased to $4.2\,σ$. Recent lattice QCD calculations predict values for the hadronic vacuum polarization contribution that are larger than the data-driven estimates, bringing the Standard Model prediction closer to the experimental measurement. Euclidean time windows in the time-momentum representation of the hadronic vacuum polarization contribution to the muon $g-2$ can help clarify the discrepancy between the phenomenological and lattice predictions. We present our calculation of the intermediate distance window contribution using $N_\mathrm{f}=2+1$ flavors of O$(a)$ improved Wilson quarks. We employ ensembles at six lattice spacings below $0.1\,$fm and pion masses down to the physical value. We present a detailed study of the continuum limit, using two discretizations of the vector current and two independent sets of improvement coefficients. Our result at the physical point displays a tension of $3.9\,σ$ with a recent evaluation of the intermediate window based on the data-driven method.

hep-lat↗

arXiv2022

Pseudoscalar transition form factors and the hadronic light-by-light contribution to the muon $g-2$

We report on our progress toward the computation of the $π^0$, $η$ and $η^{\prime}$ transition form factors using staggered quarks on $N_f=2+1+1$ gauge ensembles generated by the Budapest-Marseille-Wuppertal collaboration. These form factors are essential ingredients to evaluate the pseudoscalar-pole contributions to the hadronic light-by-light scattering in the muon $g-2$. Preliminary results for the pseudoscalar-pole contributions are presented, at finite lattice spacing, for all three light mesons.

hep-lat↗

arXiv2022

The hadronic running of the electromagnetic coupling and the electroweak mixing angle from lattice QCD

We compute the hadronic running of the electromagnetic and weak couplings in lattice QCD with $N_{\mathrm{f}}=2+1$ flavors of $\mathcal{O}(a)$ improved Wilson fermions. Using two different discretizations of the vector current, we compute the quark-connected and -disconnected contributions to the hadronic vacuum polarization (HVP) functions $\barΠ^{γγ}$ and $\barΠ^{γZ}$ for Euclidean squared momenta $Q^2\leq 7\,\mathrm{GeV}^2$. Gauge field ensembles at four values of the lattice spacing and several values of the pion mass, including its physical value, are used to extrapolate the results to the physical point. The ability to perform an exact flavor decomposition allows us to present the most precise determination to date of the $\mathrm{SU}(3)$-flavor-suppressed HVP function $\barΠ^{08}$ that enters the running of $\sin^2θ_{\mathrm{W}}$. Our results for $\barΠ^{γγ}$, $\barΠ^{γZ}$ and $\barΠ^{08}$ are presented in terms of rational functions for continuous values of $Q^2$ below $7 \,\mathrm{GeV}^2$. We observe a tension of up to $3.5$ standard deviation between our lattice results for $Δα^{(5)}_{\mathrm{had}}(-Q^2)$ and estimates based on the $R$-ratio for space-like momenta in the range $3$--$7\,\mathrm{GeV}^2$. The tension is, however, strongly diminished when translating our result to the $Z$ pole, by employing the Euclidean split technique and perturbative QCD, which yields $Δα^{(5)}_{\mathrm{had}}(M_Z^2)=0.027\,73(15)$ and agrees with results based on the $R$-ratio within the quoted uncertainties.

hep-lat↗