Electromagnetic pion mass splitting using PV-regulated photon propagator

Abstract

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.

Figures (5)

• Figure 1: Left plot: ratio between the PV-regulated photon propagator and the unregulated one ($\Lambda=\infty$) for different values of the photon mass. Right plot: comparison between the PV-regulated photon propagator and the unregulated one.
• Figure 2: The connected (left) and disconnected (right) diagrams relevant to the determination of $\Delta M_\pi$ at leading-order in $\alpha_\mathrm{em}$. See deDivitiis:2013xla for the derivation.
• Figure 3: Comparison between the lattice data and the analytical infinite volume contribution assuming only single-pion states are propagating. The plots refer to the D450 (left) and J303 (right) ensembles respectively, both at the PV-mass $\Lambda=16\,m_\mu$. The shaded area represents the region where $f_\Lambda^\pi$ replaces $f^\mathrm{latt}_\Lambda$ in evaluating the pion mass splitting.
• Figure 4: Example of the chiral-continuum extrapolation at $\Lambda=20\,m_\mu$. The dependence on $a^2$ and on $M_\pi^2$ are shown in the left and right plot respectively. In both the plots the gray squares correspond to the original lattice data, while the blue dots correspond to the ones corrected by the fit ansatz using $M_\pi=M_\pi^\mathrm{phys}$ (left plot) and $a=0$ (right plot). In the left plot the blue points corresponding to the same lattice spacing are slightly misplaced to improve the visibility. The black square is the result of the extrapolation.
• Figure 5: Left: our lattice determination for $\Delta M_\pi(\Lambda)$ (black dots) after chiral-continuum extrapolation for different values of the photon mass compared to the elastic contribution (solid red line) determined from the forward Compton amplitude. Right: inelastic contribution and $\Lambda$ dependence.