Nuclear electric dipole moment in the cluster model with a triton: $^7$Li and $^{11}$B

We calculate the electric dipole moment (EDM) of the nuclei $^7$Li and $^{11}$B in the cluster model with $\alpha$ ($^4$He) and triton ($^3$H) clusters as degrees of freedom. The $^7$Li and $^{11}$B nuclei are treated in the two- and three-body problem, respectively, using the Gaussian expansion method, assuming the one-meson exchange P, CP-odd nuclear forces. We find that $^7$Li and $^{11}$B have larger sensitivity to the CP violation than the deuteron. It is also suggested that the EDMs of $^7$Li and $^{11}$B, together with those of $^6$Li, $^9$Be and the $1/2^+_1$ excited state of $^{13}$C, obey an approximate counting rule accounting for the EDM of the cluster and the $\alpha -N $ polarization. We show their sensitivity on the hadronic level CP violation in terms of the chiral effective field theory, and discuss their role in probing new physics beyond the standard model.