$\Delta$ the larger the “theoretical uncertainty” which might allow one to make conclusions concerning the CP-violation of interest.

From here on, for the sake of simplicity, we assume that the “theoretical uncertainty” dominates over the experimental one and we neglect $\Delta$. If the computation of the nuclear matrix elements becomes sufficiently accurate and/or if $\Delta$ is relatively large, it would be necessary to take into account also the uncertainty due to the experimental error in the analysis which follows.

For the best fit value of [@Gonza3nu], $({\mbox{$\Delta  m^2_{\mathrm{atm}}$}})_{\mathrm{BF}} = 3.1 \times 10^{-3} \ {\rm eV}$, taking $(\cos 2 \theta_{\odot})_{\mathrm{BF}}= 
0.5, 0.4, 0.3$ and allowing for 10% (20%) uncertainty in the values of both parameters [^9], condition (\[invh:cond1a\]) (with negligible $\Delta$) implies $\zeta < 1.65, 2.05, 2.73~(1.33,~1.67,~2.22)$, respectively.

Condition (\[invh:cond1a\]) is obtained for the most favorable case in which the minimal allowed value of $\!\!$, $({\mbox{$\left|  < \! m  \! > \right| \ $}}_{\rm \!\!exp})_{\mbox{}_{\rm MIN}}$, is very close to the upper bound of the allowed range of values for in the CP-conserving case and opposite CP-parities for the two relevant neutrinos, e.g., for $({\mbox{$\left|  < \! m  \! > \right| \ $}}_{\rm \!\!exp})_{\mbox{}_{\rm MIN}} =
\sqrt{{\mbox{$(\Delta  m^2_{\mathrm{atm}})_{ \! \mbox{}_{\mathrm{MAX}}} \ 