Scalar-meson–baryon coupling constants in QCD sum rules

The external-field QCD sum rules method is used to evaluate the coupling constants of the light isoscalar-scalar meson (“σ” or ɛ) to the $\Lambda ,\Sigma$, and Ξ baryons. It is shown that these coupling constants as calculated from QCD sum rules are consistent with SU(3) flavor relations, which leads to a determination of the $F/(F+D)$ ratio of the scalar octet assuming ideal mixing: we find ${\alpha }_s\equiv F/(F+D)=0.55$. The coupling constants with SU(3) breaking effects are also discussed.

Figure 1

Borel mass dependence of LHS and fitted RHS of the sum rule for $\Lambda \Lambda \sigma$ coupling in Eq. (25) for $s_0^{\Lambda }=2.3$ GeV${}^2$ and ${\chi }_G\equiv \chi =-10$ GeV${}^{-1}$. We also present the RHS terms individually. Note that the LHS curve overlies the RHS curve.

Figure 2

Same as Fig. 1, but for the sum rule for $\Xi \Xi \sigma$ coupling in Eq. (30).

Figure 3

Same as Fig. 1, but for the sum rule for $\Sigma \Sigma \sigma$ coupling in Eq. (31).

Figure 4

Dependence of $g_{\Lambda \Lambda \sigma }/g_q^{\sigma }$ on susceptibility χ for three different values of $s_0^q$; here $\chi \equiv {\chi }_G$.

Figure 5

Same as Fig. 4, but for the dependence of $g_{\Sigma \Sigma \sigma }/g_q^{\sigma }$.

Figure 6

Borel mass dependence of LHS and fitted RHS of the sum rule for $\Lambda \Lambda \sigma$ coupling in Eq. (25) with SU(3) breaking effects; ${\chi }_G\equiv \chi =-10$ GeV${}^{-1}$. We also present the RHS terms individually. Note that the LHS curve overlies the RHS curve.

Figure 7

Same as Fig. 6, but for the sum rule for $\Xi \Xi \sigma$ coupling in Eq. (30).

Figure 8

Same as Fig. 6, but for the sum rule for $\Sigma \Sigma \sigma$ coupling in Eq. (31).