Why is the positive pion heavier than the neutral one?

Physicists used lattice QCD simulations to calculate why a positively charged pion weighs about 4.56 MeV more than its neutral counterpart—a difference driven by electromagnetic forces. They deployed a new technique using a Pauli-Villars regulated photon propagator that avoids messy finite-volume artifacts, then tested the result against known measurements to validate the method for use on other particles.