Standard Model and Beyond · Problem 3.19

Gauge Theories

Physics — Particle Physics · su3-meson-hyperon-couplings

Problem

The interactions of pseudoscalar mesons with hyperons can be described by

\mathcal{L} = g_{\pi^+ pn}\, \pi^+ \bar{p}\, i\gamma^5 n + g_{K^+ p\Lambda}\, K^+ \bar{p}\, i\gamma^5 \Lambda + g_{K^+ n\Sigma^-}\, K^+ \bar{n}\, i\gamma^5 \Sigma^- + \cdots + h.c., \tag{3.194}

where the dots refer to other mesons and hyperons. Show that

g_{K^+ n \Sigma^-}

can be expressed in terms of

g_{\pi^+ pn}

and

g_{K^+ p\Lambda}

in the

SU(3)

limit, and find the expression.