  We have previously calculated the pion-nucleon $\Sigma_{\pi N}$ term in the
chiral mixing approach with $u,d$ flavors only, and found the lower bound
$\Sigma_{\pi N} \geq \left(1 + \frac{16}{3} \sin^2 \theta \right){3 \over 2}
\left(m_{u}^{0} + m_{d}^{0}\right)$. The mixing angle $\theta$ can be
calculated as $\sin^2\theta = \frac{3}{8}\left(g_A^{(0)} + g_A^{(3)}\right)$.
With presently accepted values of current quark masses, this leads to
$\Sigma_{\pi N} \geq 58.0 \pm 4.5 \begin{array}{l} +11.4 \\ -6.5 \end{array}$
MeV, which is in agreement with the values extracted from experiments, and
substantially higher than most previous two-flavour calculations. The causes of
this enhancement are: 1) the large, ($\frac{16}{3}\simeq 5.3$), purely $SU_L(2)
\times SU_R(2)$ algebraic factor, 2) the admixture of the
$[(\mathbf{1},\mathbf{\frac12})\oplus (\mathbf{\frac12},\mathbf{1})]$ chiral
multiplet component in the nucleon, whose presence has been known for some
time, but that had not been properly taken into account, yet. We have now
extended these calculations of $\Sigma_{\pi N}$ to three light flavours, i.e.,
to $SU_L(3) \times SU_R(3)$ multiplet mixing. Phenomenology of chiral $SU_L(3)
\times SU_R(3)$ multiplet mixing demands the presence of three chiral $SU_L(3)
\times SU_R(3)$ multiplets in order to successfully reproduce the baryons'
flavor-octet and flavor-singlet axial currents, as well as the baryon anomalous
magnetic moments. The physical significance of these results lies in the fact
that they show no need for $q^4 {\bar q}$ components, and in particular, no
need for an $s \bar s$ component in the nucleon, in order to explain the large
"observed" $\Sigma_{\pi N}$ value. We also predict the experimentally unknown
kaon-nucleon sigma term $\Sigma_{K N}$.
