The QCD rotator with a light quark mass

Abstract

The low-lying energy excitations of 2-flavour QCD in the chiral limit confined to a small spatial box ($\delta$-regime) are that of an $O(4)$ rotator. In this work, we calculate the corrections due to the presence of a nonzero quark mass up to NNL order by means of dimensional regularised chiral perturbation theory. The final result for the energy gap of the system only involves the low-energy constants $F$, $\Lambda_1$, $\Lambda_2$ and $B$.