The Pion Mass Formula

Abstract

The often used Gell-Mann–Oakes–Renner (GMOR) mass formula for Nambu-Goldstone (NG) bosons in QCD, such as the pions, involves the condensate ·q q Ò f_p and the quark current masses. Within the context of the Global Colour Model (GCM) for QCD a manifestly different formula was recently found. Remarkably, Langfeld and Kettner have shown the two formulae to be equivalent. Here we note that the above recent analyses refer to the constituent pion and not the exact pion, even within the GCM. Further we generalise the Langfeld-Kettner identity to include the full response of the constituent quark correlators to the presence of a non-zero (and momentum dependent) quark current mass. Results are reported using an effective gluon correlator from meson data fitting.