Baryon fields with $U_{L}(3)\times U_{R}(3)$ chiral symmetry V: Pion-Nucleon and Kaon-Nucleon $Σ$ Terms

Abstract

We have previously calculated the pion-nucleon $Σ_{πN}$ term in the chiral mixing approach with $u,d$ flavors only, and found the lower bound $Σ_{πN} \geq \left(1 + \frac{16}{3} \sin^2 θ\right){3 \over 2} \left(m_{u}^{0} + m_{d}^{0}\right)$. The mixing angle $θ$ can be calculated as $\sin^2θ= \frac{3}{8}\left(g_A^{(0)} + g_A^{(3)}\right)$. With presently accepted values of current quark masses, this leads to $Σ_{πN} \geq 58.0 \pm 4.5 \begin{array}{l} +11.4 \\ -6.5 \end{array}$ 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 $Σ_{πN}$ 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" $Σ_{πN}$ value. We also predict the experimentally unknown kaon-nucleon sigma term $Σ_{K N}$.