Chiral quark model in a Tamm-Dancoff inspired approximation

Abstract

A procedure inspired by the Tamm-Dancoff method is applied to the chiral quark model. It is illustrated here by the chiral \ensuremath{\sigma} model embedded in the chiral bag environment. This simple model is used as an example and as the test for the Tamm-Dancoff inspired approximation (TDIA). Here the TDIA is employed in two ways: (i) a set of field operator equations of motion is solved between quark states and (ii) the Hamilton field operator is averaged between suitable hadron states, and the equations of motion are derived for these mean fields. The second approach is analogous to the usual one which employs hedgehog quarks, which is also reproduced here. It turns out that the energy minimum (i.e., hadron masses) can be found with the TDIA also. Model predictions for the axial-vector coupling constant and for the nucleon magnetic moment obtained in the TDIA are comparable to those obtained using the usual hedgehog-based approximation. The TDIA can be used in more complex models too.