arXiv subjects

Dominik Erb

Publications and source records attributed to Dominik Erb.

6 recordsLinked to original sources

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 $M_{\pi^+} - M_{\pi^0}$ at $\mathcal{O}(\alpha_\mathrm{em})$ using a recently proposed framework based on a Pauli-Villars (PV) regulated photon propagator defined in the continuum and infinite-volume limit, with $\Lambda$ 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 $\Lambda$. By means of the Cottingham formula, we further decompose the result into elastic and inelastic contributions at fixed $\Lambda$. Our final result, after removing the cutoff scale $\Lambda$, is $M_{\pi^+} - M_{\pi^0} = 4.56(22)$ 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

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

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

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., $e^+e^-\to\pi^0 \gamma$. Here we argue that such contributions are largely canceled by virtual electromagnetic corrections to the purely hadronic channels: $\pi^+ \pi^-$, $\pi^+ \pi^- \pi^0$, 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↗

arXiv2025

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

We compute the isospin-violating part $a_\mu^{\text{HVP}, 38}$ of the hadronic-vacuum-polarization (HVP) contribution to the muon $(g-2)$ in lattice QCD at the SU$(3)_{\rm f}$-symmetric point where $M_\pi=M_K\simeq 416$ MeV. All diagrams involving internal photons are evaluated in coordinate space, employing a Pauli-Villars-regulated photon propagator with a cutoff scale $\Lambda$ well below the lattice cutoff. The counterterm $(m_u-m_d)$, whose $\Lambda$ dependence is consistent with the expected logarithmic behaviour, is calibrated using the experimental kaon mass splitting as input. The bare electromagnetic contribution at fixed $\Lambda$ 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↗

arXiv2024

The isospin-violating part of the hadronic vacuum polarisation

We present our calculation of the isospin-violating part of the hadronic vacuum polarisation (HVP) contribution to muon $(g-2)$ in lattice QCD at the $SU(3)_{\mathrm{f}}$ symmetric point. The computation of the contributing fully connected diagrams with one internal photon as well as the computation of the only (mass) counterterm are shown. The latter is determined from the charged-neutral kaon mass splitting. We employ coordinate-space methods and a photon propagator which is regulated \`a la Pauli-Villars with a cutoff scale $\Lambda$ well below the lattice cutoff. This regularization makes it possible for us to do crosschecks of individual contributions with calculations in the continuum. Our continuum extrapolated results show little to no dependence on $\Lambda$. This makes our final limit $\Lambda \rightarrow \infty$ straightforward.

hep-lat↗