The mass splittings within the SU(2) multiplets of pseudoscalar mesons (π, K, D, B) are used as a laboratory to determine the mass difference between d and u quarks (current), through the simplest (two-point) quark-loop diagrams for the self-energies of the corresponding hadrons, together with the associated quark-condensate diagrams within the loops. The second-order e.m. correction is also calculated with a photon line joining the two opposite quark lines in the self-energy loop. The basic ingredient is a hadron–quark-vertex function generated from a vector-exchange-like (chirally invariant) four-fermion Lagrangian (with current quarks) under dynamical symmetry breaking (DχSB), precalibrated to spectroscopy and other important low-energy amplitudes. The results which are expressed as proportional to the u−d mass difference δc, but are otherwise free from any adjustable parameters, reproduce in a rather accurate way all the SU(2) mass differences (from kaon to bottom) with δc = 4.0 MeV, when all the three self-energy diagrams are included. The pion receives only e.m. contributions with a value 5.24 MeV.
A quark loop model for heavy mesons