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arXiv · 2605.29902

Electromagnetic pion mass splitting using a Pauli-Villars-regulated photon propagator

Alessandro De Santis·Dominik Erb·Harvey B. Meyer
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Abstract

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.

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Alessandro De Santis, Dominik Erb, Harvey B. Meyer. 2026-05-28. Electromagnetic pion mass splitting using a Pauli-Villars-regulated photon propagator. https://arxiv.org/abs/2605.29902

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