arXiv subjects

G. Gagliardi

Publications and source records attributed to G. Gagliardi.

At least 19 recordsLinked to original sources

arXiv2026

Charmonium radiative transitions to dileptons from lattice QCD: The case of $h_c \to η_c \ell^+\ell^-$ and $χ_{c1} \to J/ψ\,\ell^+\ell^-$

We present a lattice QCD study of dilepton production in charmonium transitions, specifically focusing on the $1^{+-} \to 0^{-+}$ and $1^{++} \to 1^{--}$ processes: $h_c \to η_c \ell^+ \ell^-$ and $χ_{c1} \to J/ψ\ell^+ \ell^-$, where $\ell = e, μ$. The relevant hadronic matrix elements are computed using gauge field configurations generated by the Extended Twisted Mass Collaboration with $N_f = 2+1+1$ dynamical Wilson--Clover twisted-mass fermions at four lattice spacings. Simulations are performed at physical dynamical $u$, $d$, $s$, and $c$ quark masses, except for the coarsest lattice, where the lightest sea quark mass corresponds to a slightly heavier pion mass. A controlled continuum extrapolation is carried out. In the continuum limit for the $h_c$ decays, we obtain $Γ(h_c \to η_c e^+ e^-) = 5.45(19)~\mathrm{keV}$, and $Γ(h_c \to η_c μ^+ μ^-) = 0.635(22)~\mathrm{keV}$. For the $χ_{c1}$ decays, we find: $Γ(χ_{c1} \to J/ψe^+ e^-)= 2.869(90)~\mathrm{keV}$, and $Γ(χ_{c1} \to J/ψμ^+ μ^-) = 0.1993(72)~\mathrm{keV}$. Our results for the $χ_{c1}$ decays show good compatibility with experimental data. However, our prediction for the $h_c \to η_c e^+ e^- $ decay rate is approximately $3σ$ larger than the BESIII result. We also present predictions for the differential decay widths as functions of the dilepton invariant mass, $q^2$, and for angular observables sensitive to longitudinal transition form factors, which are inaccessible in radiative decays with real photon emission. These results constitute the first fully dynamical lattice QCD predictions for dilepton decay rates in $h_c$ and $χ_{c1}$ charmonium transitions, including their differential distributions and angular observables. They provide benchmark predictions for future experimental studies.

hep-lat↗

arXiv2026

Rare kaon decays $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$: Standard Model predictions from lattice QCD

Weak decays of charged kaons with an additional lepton-antilepton pair, $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$ ($K_{\ell2\ell'}$), are suppressed at order $O(G_{F}^{2}α_{\rm em}^{2})$ in the Standard Model (SM) and provide sensitive probes of its flavour structure, as well as independent determinations of the Cabibbo angle $|V_{us}|$. In this Letter we present the SM predictions for all four channels with $\ell,\ell' =e,μ$, based on the first complete lattice QCD calculation of the structure-dependent form factors reported in a companion paper [1]. Using the PDG value [2] $|V_{us}|^{\rm PDG}=0.22431(85)$, we obtain branching fractions with controlled uncertainties and precisions ranging from $2\%$ to $7\%$, depending on the channel. For the three modes with published measurements, our results agree with experiment. For the $K_{\mu2μ}$ mode, for which no published experimental result is available, we compare our prediction with the preliminary NA62 result, finding agreement at the $1.4σ$ level. Conversely, the measured decay rates can be used together with our results to extract $|V_{us}|$ from these modes. A weighted average over the two most precise channels, $K_{\mu2e}$ and $K_{\mu2μ}$, yields $|V_{us}|=0.2283(42)$, corresponding to a $1.8\%$ determination. These results pave the way for using $K_{\ell2\ell'}$ decays as precision probes of the SM.

hep-ph↗

arXiv2026

Complete lattice QCD calculation of $K^{-}\to \ell^{-}\barν_{\ell}\ell^{'+}\ell^{'-}$ form factors

We present the first complete lattice QCD calculation of the four structure-dependent form factors governing the rare charged kaon decay $K^- \to \ell^- \barν_\ell \ell'^+ \ell'^-$, with fully controlled statistical and systematic uncertainties. Our calculation is based on gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ flavors of Wilson-clover twisted-mass fermions. Simulations are performed directly at the physical values of the light and strange quark masses, and include an estimate of the quark-disconnected contributions in which the virtual photon couples to sea quarks. All four form factors are determined across the kinematical region probed by experiments. The Spectral Function Reconstruction (SFR) method of Ref. [1] is employed to overcome the analytic continuation problem for dilepton invariant masses above the two-pion threshold. Finite-volume effects are investigated using ensembles with spatial extents $L\simeq [3.8,7.6]~\mathrm{fm}$, while the continuum limit is obtained from three lattice spacings in the range $a\in[0.057, 0.08]~\mathrm{fm}$. Our results for the form factors enable the evaluation of decay rates and differential observables for all four channels, $K^- \to e^- \barν_e e^+ e^-$, $K^- \to e^- \barν_e μ^+ μ^-$, $K^- \to μ^- \barν_μe^+ e^-$, and $K^- \to μ^- \barν_μμ^+ μ^-$, thereby providing first-principles Standard Model predictions against which existing and upcoming measurements can be directly compared. A detailed phenomenological analysis of the decay rates and associated observables is presented in a companion paper [2].

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arXiv2026

KATRIN Sensitivity to keV Sterile Neutrinos with the TRISTAN Detector Upgrade

Sterile neutrinos in the keV mass range are a well-motivated extension of the Standard Model and viable dark matter candidates. Their existence can be probed in laboratory experiments, as the admixture of a sterile state would induce a characteristic kink-like distortion in the $β$-decay electron energy spectrum. The KATRIN experiment is designed to measure the effective electron neutrino mass with sub-eV sensitivity by analyzing the endpoint region of the tritium $β$-decay spectrum. Following the completion of its neutrino mass program, KATRIN will extend its physics reach to the search for keV-scale sterile neutrinos. This effort will be enabled by the TRISTAN detector, a newly developed silicon drift detector array optimized for differential measurements at high rates and energies well below the endpoint. In this article, we present the projected sensitivity of KATRIN to keV-scale sterile neutrinos using a dedicated simulation framework. With four months of detector livetime, KATRIN has the statistical power to probe mixing amplitudes at the level of $|U_{e4}|^2 \sim 10^{-6}$ for sterile neutrino masses in the (4$-$13) keV range, significantly extending the reach of previous laboratory searches. The major experimental systematic uncertainties investigated in this work reduces the sensitivity by a factor of 10$-$50 over the same mass range.

hep-ex↗

arXiv2026

Theoretical framework for lattice QCD computations of $B\to K \ell^+ \ell^-$ and $\bar{B}_s\to \ell^+\ell^- γ$ decays rates, including contributions from charming penguin diagrams

We develop a strategy for computing the $B\to K\ell^+\ell^-$ and $\bar{B}_s\toγ\ell^+\ell^-$ decay amplitudes using lattice QCD (where $\ell^\pm$ are charged leptons). We focus on those terms which contain complex contributions to the amplitude, due to on-shell intermediate states propagating between the weak operator and electromagnetic current(s). Such terms, which are generally estimated using model calculations and represent significant uncertainties in the phenomenological predictions for these decays, cannot be computed using standard lattice QCD techniques. It has recently been shown that such contributions can be computed using spectral-density methods and our proposed strategy, which we discuss in detail, is built on this approach. The complex contributions include the ``charming penguins" (matrix elements of the current-current operators $O_1^{(c)}$ and $O_2^{(c)}$ defined in Eq. (6) below), in which the charm-quark loop can propagate long distances, particularly close to the region of charmonium resonances. They also include the contributions from the chromomagnetic operator ($O_8$ in standard notation, defined in Eq. (8) below). We discuss the renormalization of the ultra-violet divergences, and in particular those which arise due to ``contact" terms, and explain how those which appear as inverse powers of the lattice spacing can be subtracted non-perturbatively. We apply the spectral density methods in an instructive exploratory computation of the charming penguin diagram in $B\to K\ell^+\ell^-$ decays in which the virtual photon is emitted from the charm-quark loop (the diagram in Fig. 1(a) below) and discuss the prospects and strategies for the reliable determination of the amplitudes in future dedicated computations; computations which are however, beyond the scope of the present paper.

hep-lat↗

arXiv2025

The anomalous magnetic moment of the muon in the Standard Model: an update

We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, $a_μ$, updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the $e^+e^-\toπ^+π^-$ cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a_μ^\text{SM} = 116\,592\,033(62)\times 10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1-6 of E989 at Fermilab, one finds $a_μ^\text{exp} - a_μ^\text{SM} =38(63)\times 10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

hep-ph↗

arXiv2025

Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point

We present a lattice QCD calculation of the radiative leptonic decay rates of the kaon, improving upon our previous work, arXiv:2006.05358. Our analysis uses gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) with $N_{f} = 2 + 1 + 1$ flavors of Wilson-clover twisted mass fermions. For the first time, we go beyond the electroquenched approximation by including quark-disconnected contributions. Several key improvements have been implemented: (i) the simulations are now performed directly at physical light- and strange-quark masses, (ii) finite-size effects are carefully investigated using lattices with spatial extents ranging from $L \simeq 3.8\,\mathrm{fm}$ to $L \simeq 7.7\,\mathrm{fm}$, and (iii) the continuum extrapolation is based on three lattice spacings in the range $a \in [0.08, 0.058]\,\mathrm{fm}$. As a result of the high-precision determination of the relevant correlation functions, we reduce the uncertainties on both the axial and vector form factors by nearly a factor of two compared to our previous analysis. When compared to experimental measurements in the electron channel ($K^- \to e^- \barν_e γ$), our results show a tension -- at the level of $2.6$ standard deviations -- with respect to KLOE data. On the other hand, they are compatible with measurements from the E36 Collaboration at J-PARC. In the muonic decay channel ($K^- \to μ^- \barν_μγ$), we confirm the tensions, already observed in our previous study, between lattice QCD predictions and ISTRA+ and OKA data, which are both primarily sensitive to the value of the negative-helicity form factor $F^{-}$.

hep-lat↗

arXiv2025

Lattice QCD study of the $χ_{c1}\to J/ψ\, γ$ decay

We present the results of our lattice QCD computation of the electric ($E_{1}$) and magnetic $(M_{2})$ form factors relevant to the $χ_{c1}\to J/ψ\,γ$ decay by using the gauge field configurations produced by the Extended Twisted Mass Collaboration with $N_{f}=2+1+1$ dynamical Wilson-Clover twisted mass fermions at four different lattice spacings with physical dynamical $u$ , $d$, $s$ and $c$ quark masses (except for the coarsest lattice for which the lightest sea quark corresponds to a pion with $m_π\simeq 175~\mathrm{MeV}$). In the continuum limit, we obtain $Γ( χ_{c1}\to J/ψ γ) = 0.3265(79)~\mathrm{MeV}$, which agrees to $(1÷2) σ$ with the experimental results and disagrees with a previous (unquenched) lattice QCD calculation. Our result for the magnetic quadrupole fractional transition amplitude, $a_{2} =M_{2}/\sqrt{E_{1}^{2}+M_{2}^{2}} = -0.0666(22)$, is in agreement with the experiment and represents an improvement by a factor of about $30$ with respect to the only existing (quenched) lattice QCD result.

hep-lat↗

arXiv2025

Lattice QCD determination of the radiative decay rates $h_{c}\to η_{c}\, γ$ and $h_{b}\to η_{b}\, γ$

We present the results of our lattice QCD computation of the hadronic matrix elements relevant to the $h_{c}\to η_{c}γ$ and $h_{b}\to η_{b}γ$ decays by using the gauge configurations produced by the Extended Twisted Mass Collaboration with $N_{f}=2+1+1$ dynamical Wilson-Clover twisted mass fermions at five different lattice spacings with physical dynamical $u$ , $d$, $s$ and $c$ quark masses (except for the the coarsest lattice for which the lightest sea quark corresponds to a pion with $m_π\simeq 175~\mathrm{MeV}$). While the hadronic matrix element for $h_{c}\to η_{c}γ$ is obtained directly, the one relevant to $h_{b}\toη_{b}γ$ is reached by working with heavy quark masses $m^{(n)}_{H} = λ^{n-1} m_{c}$, with $λ\sim 1.24$ and $n=1,2, \ldots ,6$, and then extrapolated to $m_{b}$ by several judicious ansätze. In the continuum limit we obtain $Γ( h_{c}\to η_{c} γ) = 0.604(24)~\mathrm{MeV}$, which is by a factor of $2.3$ more accurate than the previous lattice estimates, and in good agreement with the experimental measurement. In the $b$-quark case we obtain $Γ( h_{b}\to η_{b} γ) =46.0(4.8)~\mathrm{keV}$.

hep-lat↗

arXiv2025

Measurement of the inhomogeneity of the KATRIN tritium source electric potential by high-resolution spectroscopy of conversion electrons from $^{83m}$Kr

Precision spectroscopy of the electron spectrum of the tritium $β$-decay near the kinematic endpoint is a direct method to determine the effective electron antineutrino mass. The KArlsruhe TRItium Neutrino (KATRIN) experiment aims to determine this quantity with a sensitivity of better than 0.3$\,$eV (90$\,$% C.L.). An inhomogeneous electric potential in the tritium source of KATRIN can lead to distortions of the $β$-spectrum, which directly impact the neutrino-mass observable. This effect can be quantified through precision spectroscopy of the conversion-electrons of co-circulated metastable $^{83m}$Kr. Therefore, dedicated, several-weeks long measurement campaigns have been performed within the KATRIN data taking schedule. In this work, we infer the tritium source potential observables from these measurements, and present their implications for the neutrino-mass determination.

nucl-ex↗

arXiv2024

Strange and charm quark contributions to the muon anomalous magnetic moment in lattice QCD with twisted-mass fermions

We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon in isospin symmetric QCD. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks at five lattice spacings and at values of the quark mass parameters that are close and/or include the isospin symmetric QCD point of interest. After computing the small corrections necessary to precisely match this point, and carrying out an extrapolation to the continuum limit based on the data at lattice spacings $a \simeq 0.049, 0.057, 0.068, 0.080$~fm and spatial lattice sizes up to $L \simeq 7.6$~fm, we obtain $a_μ^{\rm HVP}(s) = (53.57 \pm 0.63) \times 10^{-10}$ and $a_μ^{\rm HVP}(c) = (14.56 \pm 0.13) \times 10^{-10}$, for the quark-connected strange and charm contributions, respectively. Our findings agree well with the corresponding results by other lattice groups.

hep-lat↗

arXiv2024

First constraints on general neutrino interactions based on KATRIN data

The precision measurement of the tritium $β$-decay spectrum performed by the KATRIN experiment provides a unique way to search for general neutrino interactions (GNI). All theoretical allowed GNI terms involving neutrinos are incorporated into a low-energy effective field theory, and can be identified by specific signatures in the measured tritium $β$-spectrum. In this paper an effective description of the impact of GNI on the $β$-spectrum is formulated and the first constraints on the effective GNI parameters are derived based on the 4 million electrons collected in the second measurement campaign of KATRIN in 2019. In addition, constraints on selected types of interactions are investigated, thereby exploring the potential of KATRIN to search for more specific new physics cases, including a right-handed W boson, a charged Higgs or leptoquarks.

nucl-ex↗

arXiv2024

Inclusive hadronic decay rate of the $τ$ lepton from lattice QCD: the $\bar u s$ flavour channel and the Cabibbo angle

We present a lattice determination of the inclusive decay rate of the process $τ\mapsto X_{us} ν_τ$ in which the $τ$ lepton decays into a generic hadronic state $X_{us}$ with $\bar u s$ flavour quantum numbers. Our results have been obtained in $n_f=2+1+1$ iso-symmetric QCD with full non-perturbative accuracy, without any OPE approximation and, except for the presently missing long-distance isospin-breaking corrections, include a solid estimate of all sources of theoretical uncertainties. This has been possible by using the Hansen-Lupo-Tantalo method [1] that we have already successfully applied in [2] to compute the inclusive decay rate of the process $τ\mapsto X_{ud} ν_τ$ in the $\bar u d$ flavour channel. By combining our first-principles theoretical results with the presently-available experimental data we extract the CKM matrix element $\vert V_{us}\vert$, the Cabibbo angle, with a $0.9$\% accuracy, dominated by the experimental error.

hep-lat↗

arXiv2024

Lattice QCD determination of the normalization of the leading-twist photon distribution amplitude and susceptibility of the quark condensate

The normalization of the leading-twist photon distribution amplitude (DA), $f_γ^{\perp}$, is an important ingredient in the study of exclusive processes involving the photon emission by means of QCD sum-rules. In this paper we determine the up- , down- and strange-quark contribution to $f_γ^{\perp}$ by exploiting its relation to the zero-momentum two-point correlation function of the electromagnetic current $J_{\rm em}^μ$ and the electric component of the tensor current $T^{μν}$. To that end we employ the gauge ensembles obtained by using $N_{f}=2+1+1$ Wilson-Clover twisted-mass quark flavors, generated by the Extended Twisted Mass (ETM) Collaboration, and after adding all sources of systematic uncertainties, we obtain a total error of $1.5\%$ and $3.5\%$, respectively, for the light- ($u$ and $d$) and strange-quark contribution to $f_γ^{\perp}(2~{\rm GeV})$ in the $\overline{\mathrm{MS}}$ scheme, thus improving their accuracy by a factor of $2.3$ and $2.8$, respectively. For the strange-quark contribution $f_{γ,s}^{\perp}(2~{\rm GeV})$, we observe a discrepancy with respect to previous lattice calculations. By combining our result with the world average lattice value of the chiral condensate, we obtain for the susceptibility of the quark condensate $χ_d^{\overline{\mathrm{MS}}} (2\, {\rm GeV}) \simeq χ_u^{\overline{\mathrm{MS}}} (2\, {\rm GeV}) =2.17(12)~{\rm GeV^{-2}}$.

hep-lat↗

arXiv2024

The $B_{s}\to μ^{+}μ^{-}γ$ decay rate at large $q^{2}$ from lattice QCD

We determine, by means of lattice QCD calculations, the local form factors describing the $B_{s}\to μ^{+}μ^{-}γ$ decay. For this analysis we make use of the gauge configurations produced by the ETM Collaboration with $N_{f}=2+1+1$ flavour of Wilson-Clover twisted-mass fermions at maximal twist. To obtain the $B_{s}$ meson form-factors, we perform simulations for several heavy-strange meson masses $m_{H_{s}}$ in the range $m_{H_{s}} \in [ m_{D_{s}}, 2 m_{D_{s}} ]$, and extrapolate to the physical $B_{s}$ meson point $m_{B_{s}}\simeq 5.367~{\rm GeV}$ making use of the HQET scaling laws. We cover the region of large di-muon invariant masses $\sqrt{q^{2}} > 4.16\,{\rm GeV}$, and use our results to determine the branching fraction for $B_{s}\to μ^{+}μ^{-}γ$, which has been recently measured by LHCb in the region $\sqrt{q^{2}} > 4.9\,{\rm GeV}$. The largest contribution to the uncertainty in the partial branching fractions at values of $\sqrt{q^{2}} < 4.8\,{\rm GeV}$ is now due to resonance and other long-distance effects, including those from "charming penguins", which we estimate by summing over the contributions from the $J_P=1^-$ charmonium resonances.

hep-lat↗

arXiv2023

Spectral-function determination of complex electroweak amplitudes with lattice QCD

We present a novel method to determine on the lattice both the real and imaginary parts of complex electroweak amplitudes involving two external currents and a single hadron or the QCD vacuum in the external states. The method is based on the spectral representation of the relevant time-dependent correlation functions and, by extending the range of applicability of other recent proposals built on the same techniques, overcomes the difficulties related to the analytic continuation from Minkowskian to Euclidean time, arising when intermediate states with energies smaller than the external states contribute to the amplitude. In its simplest form, the method relies on the standard $i \varepsilon$ prescription to regularize the Feynman integrals and at finite $\varepsilon$ it requires to verify the condition $1/L \ll \varepsilon \ll Δ(E)$, where $L$ is the spatial extent of the lattice and, for any given energy $E$, $Δ(E)$ represents the typical size of the interval around $E$ in which the hadronic amplitude is significantly varying. In order to illustrate the effectiveness of this approach in a realistic case, we apply the method to evaluate non-perturbatively the hadronic amplitude contributing to the radiative leptonic decay $D_s \to\ellν_\ell\,γ^*$, working for simplicity with a single lattice ensemble at fixed volume and lattice spacing.

hep-lat↗

arXiv2023

Lattice calculation of the $D_{s}$ meson radiative form factors over the full kinematical range

We compute the structure-dependent axial and vector form factors for the radiative leptonic decays $D_s\to \ellν_\ellγ$, where $\ell$ is a charged lepton, as functions of the energy of the photon in the rest frame of the $D_s$ meson. The computation is performed using gauge-field configurations with 2+1+1 sea-quark flavours generated by the European Twisted Mass Collaboration and the results have been extrapolated to the continuum limit. For the vector form factor we observe a very significant partial cancellation between the contributions from the emission of the photon from the strange quark and that from the charm quark. The results for the form factors are used to test the reliability of various Anzätze based on single-pole dominance and its extensions, and we present a simple parametrization of the form factors which fits our data very well and which can be used in future phenomenological analyses. Using the form factors we compute the differential decay rate and the branching ratio for the process $D_s\to eν_eγ$ as a function of the lower cut-off on the photon energy. With a cut-off of 10 MeV for example, we find a branching ratio of Br$(E_γ>10\,\mathrm{MeV})=4.4(3)\times 10^{-6}$ which, unlike some model calculations, is consistent with the upper bound from the BESIII experiment Br$(E_γ>10\,\mathrm{MeV})<1.3\times 10^{-4}$ at 90% confidence level. Even for photon energies as low as 10 MeV, the decay $D_s\to eν_eγ$ is dominated by the structure-dependent contribution to the amplitude (unlike the decays with $\ell=μ$ or $τ$), confirming its value in searches for hypothetical new physics as well as in determining the Cabibbo-Kobayashi-Maskawa (CKM) parameters at $O(α_\mathrm{em})$, where $α_{\mathrm{em}}$ is the fine-structure constant.

hep-lat↗

arXiv2022

Time windows of the muon HVP from twisted-mass lattice QCD

We present a lattice determination of the leading-order hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_μ^{\rm HVP}$, in the so-called short and intermediate time-distance windows, $a_μ^{\rm SD}$ and $a_μ^{\rm W}$. We employ gauge ensembles produced by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavours of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavours tuned close to their physical values. The simulations are carried out at three values of the lattice spacing equal to $\simeq 0.057, 0.068$ and $0.080$ fm with spatial lattice sizes up to $L \simeq 7.6$~fm. For the short distance window we obtain $a_μ^{\rm SD} = 69.27\,(34) \cdot 10^{-10}$, in agreement with the dispersive determination based on experimental $e^+ e^-$ data. For the intermediate window we get instead $a_μ^{\rm W} = 236.3\,(1.3) \cdot 10^{-10}$, which is consistent with recent determinations by other lattice collaborations, but disagrees with the dispersive determination at the level of $3.6\,σ$.

hep-lat↗