# Why does the Walecka model not include pions?

The Walecka or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?

• Er ... isn't the $\sigma$ a stand in for all the light scalar mesons? I certainly don't recall him addressing this question when I took his class at W&M back in the late 90's (he generously threw it open to all JLAB grad-students and even intervened with the W&M parking office to get us permits). – dmckee --- ex-moderator kitten Jul 15 '14 at 0:11
• No. I see that this does not answer the question as the pion is a pseudoscalar. So I have nothing to offer. – dmckee --- ex-moderator kitten Jul 15 '14 at 0:13
• I haven't read it fully (not much of a particle physicist), but this review of QHD (co-authored by Walecka) seems to introduce the pion alongside the sigma and omega mesons. – Kyle Kanos Jul 15 '14 at 2:48
• To clarify the situation, QHD was an attempt to go beyond the mean field approximation in this effective interaction model. There are no symmetry arguments for excluding the pion from these higher order terms. – Lewis Miller Dec 6 '15 at 14:23