Nucleon-sigma coupling constant in QCD sum rules

The external-field QCD sum rules method is used to evaluate the coupling constant of the light isoscalar-scalar meson (“σ” or ɛ) to the nucleon. The contributions that come from the excited nucleon states and the response of the continuum threshold to the external field are calculated. The obtained value of the coupling constant is compatible with the large value required in one-boson exchange potential models of the two-nucleon interaction.

Figure 1

The diagrams that were used to calculate the Wilson coefficients of the correlation functions ${\Pi }_{\sigma }^q$ and ${\Pi }_{\sigma }^1$. The solid, wavy, and the dashed lines represent the quark, gluon, and the external scalar field, respectively.

Figure 2

(Color online) The Borel mass dependence of LHS and the fitted RHS of Eq. (24) for $s_0^q=2.3{\mathrm{GeV}}^2$ and ${\chi }_G\equiv \chi =-10{\mathrm{GeV}}^{-1}$. We also present the terms on the RHS individually. Note that the LHS curve (solid) overlies the RHS curve (dashed).

Figure 3

(Color online) The four terms on the LHS of Eq. (24) individually, together with the summation of them for $s_0^q=2.3{\mathrm{GeV}}^2$ and ${\chi }_G\equiv \chi =-10{\mathrm{GeV}}^{-1}$. Here ${\mathcal{O}}_1$ denotes the first term, ${\mathcal{O}}_2$ denotes the second term, and so on.

Figure 4

(Color online) The dependence of $g_{NN\sigma }/g_q^{\sigma }$ on the susceptibility χ for three different values of $s_0^q=2.0$, 2.3, and $2.5{\text{GeV}}^2$; here we take $\chi \equiv {\chi }_G$.