Effective chiral lagrangians with baryons—the mass splitting of the spin 1/2 parity partners

Abstract

There are two inequivalent spin 1/2 baryon field operators that can be constructed directly out of three quark field operators. These are associated with a pair of parity partners. Their chiral transformation properties yield some unexpected results. In particular.U(1) axial transformations can mix the two operators. With these chiral transformation properties the spin 1/2 baryon parity partners are incorporated in an effective chiral lagrangian together with the spin 0 meson fields. The mass splitting of these parity partners is then found to be related to their coupling to the flavour singlet pseudoscalar, $$M_ - - M_ + \simeq F_\pi g_{\mathop {flavour}\limits_{singlet} N_ - N_ + } $$ The further selection rule, in the exact chiral limit, $$g_{\pi N_ + N_ - } = 0$$ is also found. Using these results, and their extension to the non-chiral limit, the enhancement of the decay ofN− intoN+ η, as opposed toN+ π, is elucidated even though it is suppressed by phase space. Two flavours is given principle consideration although three flavours is also briefly discussed.