Constraints on effective field theory parameters for the $\Lambda N\to NN$ transition

The relation between the low-energy constants appearing in the effective field theory description of the $\Lambda N\to NN$ transition potential and the parameters of the one-meson-exchange model previously developed is obtained. We extract the relative importance of the different exchange mechanisms included in the meson picture by means of a comparison to the corresponding operational structures appearing in the effective approach. The ability of this procedure to obtain the weak baryon-baryon-meson couplings for a possible scalar exchange is also discussed.

Figure 1

(a) Nonstrange and (b) strange meson-exchange contributions to the $\Lambda N\to NN$ weak transition potential. A weak insertion is indicated by an empty square, while a filled square stands for a strong interaction vertex.

Figure 2

Lowest-order contribution to the weak $\Lambda N\to NN$ diagram. Empty symbols represent weak vertices while solid ones represent strong vertices. A circle stands for a nonderivative operator.

Figure 3

Hypernuclear decay observables (total and partial decay rates and asymmetry for ${}_5^{\Lambda }\mathrm{He}$, ${}_{11}^{\Lambda }\mathrm{B}$ and ${}_{12}^{\Lambda }\mathrm{C}$), including their error bars and their fitted values. The total decay rates are in units of the $\Lambda$ decay rate in free space (${\Gamma }_{\Lambda }=3.8\times {10}^9$s${}^{-1}$). All the quantities are adimensional.

Figure 4

Contribution of each experimental point included in the fit to the total ${\chi }^2$ for the four different fits discussed in the text.

Figure 5

Comparison between $C_0^0$ and $C_0^{0\left(\sigma \right)}$ for the Nijmegen minimum. The shaded blue area represents the dependence of $C_0^{0\left(\sigma \right)}$ on $A_{\sigma }$ given by Eq. (5.3), while the fitted EFT $C_0^0$ value is represented by the solid orange area. See text for details.

Figure 6

Same as Fig. 5 but for the Jülich minimum.