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Dalibor Djukanovic

Publications and source records attributed to Dalibor Djukanovic.

At least 19 recordsLinked to original sources
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.

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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.

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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.

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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.

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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 isoscalar non-singlet axial form factor of the nucleon from lattice QCD

We present our progress on the computation of the axial form factor of the nucleon with flavour structure $u+d-2s$ from lattice QCD. We employ a set of $N_f=2+1$ CLS ensembles with $O(a)$-improved Wilson fermions and the Lüscher-Weisz gauge action, with lattice spacings ranging from $0.05\,\text{fm}$ to $0.086\,\text{fm}$ and pion masses spanning between $130\,\text{MeV}$ and $350\,\text{MeV}$. We employ multiple source-sink separations and use the summation method to suppress the contamination from excited states. We use a $z$-expansion on each ensemble to parametrize the $Q^2$-dependence of the form factor and simultaneously fit the available source-sink separations for all $Q^2\leq 0.7 \,{\rm GeV}^2$. We outline our analysis of the stability of the fits varying the ansätze and different estimations of the covariance matrix and report on our strategy for a comprehensive determination of the physical form factor.

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arXiv2024

Zemach and Friar radii of the proton and neutron from lattice QCD

We present the first lattice-QCD result for the Zemach and Friar radii of the proton and neutron. Our calculation includes both quark-connected and -disconnected diagrams and assesses all sources of systematic uncertainties arising from excited-state contributions, finite-volume effects and the continuum extrapolation. At the physical point, we obtain for the proton $r_Z^p = ( 1.013 \pm 0.010\ (\mathrm{stat}) \pm 0.012\ (\mathrm{syst}) )~\mathrm{fm}$ and $r_F^p = ( 1.301 \pm 0.012\ (\mathrm{stat}) \pm 0.014\ (\mathrm{syst}) )~\mathrm{fm}$. These numbers suggest small values of the Zemach and Friar radii of the proton, but are compatible with most of the experimental studies.

hep-lat↗
arXiv2024

Electromagnetic form factors of the nucleon from $N_f = 2 + 1$ lattice QCD

There is a long-standing discrepancy between different measurements of the electric and magnetic radii of the proton. Lattice QCD calculations are a well-suited tool for theoretical investigations of the structure of the nucleon from first principles. However, all previous lattice studies of the proton's electromagnetic radii have either neglected quark-disconnected contributions or were not extrapolated to the continuum and infinite-volume limit. Here, we present results for the electromagnetic form factors of the proton and neutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS) ensembles including both quark-connected and -disconnected contributions. From simultaneous fits to the $Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of the form factors, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain as our final values $\langle r_E^2 \rangle^p = (0.672 \pm 0.014$ (stat)${} \pm 0.018$ (syst)$)$ fm${}^2$, $\langle r_M^2 \rangle^p = (0.658 \pm 0.012$ (stat)${} \pm 0.008$ (syst)$)$ fm${}^2$, and $μ_M^p = 2.739 \pm 0.063$ (stat)${} \pm 0.018$ (syst). The magnetic moment is in good agreement with the experimental value, as is the one of the neutron. On the one hand, our result for the electric (charge) radius of the proton clearly points towards a small value, as favored by muonic hydrogen spectroscopy and the recent $ep$-scattering experiment by PRad. Our estimate for the magnetic radius, on the other hand, is well compatible with that inferred from the A1 $ep$-scattering experiment.

hep-lat↗
arXiv2024

Precision calculation of the electromagnetic radii of the proton and neutron from lattice QCD

We present lattice-QCD results for the electromagnetic form factors of the proton and neutron including both quark-connected and -disconnected contributions. The parametrization of the $Q^2$-dependence of the form factors is combined with the extrapolation to the physical point. In this way, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain at the physical pion mass and in the continuum and infinite-volume limit $\sqrt{\langle r_E^2 \rangle^p} = 0.820(14)$ fm, $\sqrt{\langle r_M^2 \rangle^p} = 0.8111(89)$ fm, and $μ_M^p = 2.739(66)$, where the errors include all systematics.

hep-lat↗
arXiv2024

Improved analysis of isovector nucleon matrix elements with $N_f=2+1$ flavors of $\mathcal{O}(a)$ improved Wilson fermions

We present an update of our determination of the isovector charges $g_A^{u-d}$, $g_S^{u-d}$ and $g_T^{u-d}$, and the isovector twist-2 forward matrix elements $\langle x\rangle_{u-d}$, $\langle x\rangle_{Δu-Δd}$ and $\langle x\rangle_{δu-δd}$ on the $N_\mathrm{f}=2+1$ gauge ensembles generated by the Coordinated Lattice Simulations (CLS) effort. We have significantly extended our coverage of the parameter space by adding ensembles at the physical pion mass and fine lattice spacing, at nearly-physical pion masses and very fine lattice spacings, and at very large physical lattice volumes, enabling a well-controlled extrapolation to the physical point. Another major improvement is achieved owing to the extended range of source-sink separations, which allows us to perform two-state fits to summed correlator ratios, leading to a much higher level of control over excited-state effects. Systematic uncertainties from the chiral, continuum and infinite-volume extrapolations are incorporated via model averages based on the Akaike Information Criterion. Our final results at the physical point are $g_A^{u-d} = 1.254(19)_\mathrm{stat}(15)_\mathrm{sys}[24]_\mathrm{total}$, $g_S^{u-d} = 1.203(77)_\mathrm{stat}(81)_\mathrm{sys}[112]_\mathrm{total}$, $g_T^{u-d} = 0.993(15)_\mathrm{stat}(05)_\mathrm{sys}[16]_\mathrm{total}$, $\langle x\rangle_{u-d} = 0.153(15)_\mathrm{stat}(10)_\mathrm{sys}[17]_\mathrm{total}$, $\langle x\rangle_{Δu - Δd} = 0.207(15)_\mathrm{stat}(06)_\mathrm{sys}[16]_\mathrm{total}$, and $\langle x\rangle_{δu - δd} = 0.195(17)_\mathrm{stat}(15)_\mathrm{sys}[23]_\mathrm{total}$. While our results for the isovector charges are in excellent agreement with the FLAG\,21 averages, we note that our error for the tensor charge $g_T^{u-d}$ is considerably smaller.

hep-lat↗
arXiv2024

Nucleon Sigma Terms with $N_f = 2 + 1$ O($a$)-improved Wilson fermions

We present a lattice-QCD based analysis of the nucleon sigma terms using gauge ensembles with $N_f = 2 + 1$ flavors of ${\cal O}(a)$-improved Wilson fermions, with a complete error budget concerning excited-state contaminations, the chiral interpolation as well as finite-size and lattice spacing effects. We compute the sigma terms determined directly from the matrix elements of the scalar currents. The chiral interpolation is based on SU(3) baryon chiral perturbation theory using the extended on-mass shell renormalization scheme. For the pion nucleon sigma term, we obtain $σ_{πN} = (43.7\pm3.6)$ MeV, where the error includes our estimate of the aforementioned systematics. The tension with extractions based on dispersion theory persists at the 2.4-$σ$ level. For the strange sigma term, we obtain a non-zero value, $σ_s=(28.6\pm9.3)$ MeV.

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arXiv2023

Proton and neutron electromagnetic radii and magnetic moments from lattice QCD

We present results for the electromagnetic form factors of the proton and neutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS) ensembles including both quark-connected and -disconnected contributions. The $Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of our form factor data is fitted simultaneously to the expressions resulting from covariant chiral perturbation theory including vector mesons amended by models for lattice artefacts. From these fits, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron, as well as the Zemach radius of the proton. To assess the influence of systematic effects, we average over various cuts in the pion mass and the momentum transfer, as well as over different models for the lattice-spacing and finite-volume dependence, using weights derived from the Akaike Information Criterion (AIC).

hep-lat↗
arXiv2023

Proton and neutron electromagnetic radii and magnetic moments from $N_f = 2 + 1$ lattice QCD

We present results for the electromagnetic form factors of the proton and neutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS) ensembles including both quark-connected and -disconnected contributions. The $Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of our form factor data is fitted simultaneously to the expressions resulting from covariant chiral perturbation theory including vector mesons amended by models for lattice artefacts. From these fits, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron, as well as the Zemach radius of the proton. To assess the influence of systematic effects, we average over various cuts in the pion mass and the momentum transfer, as well as over different models for the lattice-spacing and finite-volume dependence, using weights derived from the Akaike Information Criterion (AIC). Our results for the magnetic moments of the proton and neutron are in good agreement with the experimental values and have a relative precision of about $2.4\,\%$ and $3.7\,\%$, respectively. For the electromagnetic radii of the proton, we achieve a precision at the $1.5\,\%$ level.

hep-lat↗
arXiv2022

The pion-nucleon sigma term with $N_f=2+1$ $\mathcal{O}(a)$-improved Wilson fermions

We present an analysis of the pion-nucleon sigma term on the CLS ensembles with $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions. We perform a chiral interpolation based on ensembles with pion masses ranging from 130 MeV to roughly 350 MeV. The analysis covers four lattice spacings between $a\approx [0.05 \, \rm{fm}\ldots 0.09\, \rm{fm}]$, allowing for an estimate of systematics associated with lattice artefacts.

hep-lat↗
arXiv2022

Mass and isovector matrix elements of the nucleon at zero-momentum transfer

We present the current status of our analysis of nucleon structure observables including isovector charges and twist-2 matrix elements as well as the nucleon mass. Results are computed on a large set of CLS $N_f=2+1$ gauge ensembles with $M_π\approx0.130\mathrm{MeV}\ldots 350\mathrm{MeV}$, four values of the lattice spacing $a=0.05\mathrm{fm}\ldots 0.09\mathrm{fm}$ and covering a large range of physical volumes. Compared to the results presented at last year's conference we have added data on a very fine and large box at small light quark mass ($T\times L^3=192 \times 96^3$, $M_π=172\mathrm{MeV}$, $a=0.05\mathrm{fm}$). Additional (intermediate) source-sink separations have been computed on the coarser ensembles, further increasing effective statistics and allowing for a more fine-grained control in the treatment of the excited-state contamination. Excited states in the nucleon matrix elements are tamed by a simultaneous, two-state fit ansatz using the summation method.

hep-lat↗
arXiv2022

Electromagnetic form factors of the proton and neutron from $N_f = 2 + 1$ lattice QCD

We present results for the electromagnetic form factors of the proton and neutron computed on the Coordinated Lattice Simulations (CLS) ensembles with $N_f = 2 + 1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved conserved vector current. In order to estimate the excited-state contamination, we employ several source-sink separations and apply the summation method. The quark-disconnected diagrams entering the isoscalar quantities are computed explicitly. For this purpose, a stochastic estimation based on the one-end trick is performed, in combination with a frequency-splitting technique and the hopping-parameter expansion. By these means, we obtain a clear signal for the form factors including the quark-disconnected contributions, which have a statistically significant effect on our results. From the $Q^2$-dependence of the form factors, we determine the electric and magnetic charge radii and the magnetic moments of the proton and neutron. The chiral interpolation is carried out by simultaneously fitting the pion mass and $Q^2$-dependence of our form factor data directly to the expressions resulting from covariant chiral perturbation theory including vector mesons. To assess the influence of systematic effects, we average over various cuts in the pion mass and the momentum transfer, as well as over different models for the lattice spacing and finite volume dependence.

hep-lat↗
arXiv2022

Isovector Axial Form Factor of the Nucleon from Lattice QCD

The isovector axial form factor of the nucleon plays a key role in interpreting data from long-baseline neutrino oscillation experiments. We present a lattice QCD calculation of this form factor, introducing a new method to directly extract its z-expansion from lattice correlators. Our final parameterization of the form factor, which extends up to spacelike virtualities of 0.7 GeV^2 with fully quantified uncertainties, agrees with previous lattice calculations but is significantly less steep than neutrino-deuterium scattering data suggests.

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