  In this addendum we complement the remarks made in ref[1] constraining the
value of the cosmological constant $\Lambda_4$ in terms of neutrino masses.
Those were based on a sharpened version of the Weak Gravity Conjecture as
applied to compactifications of the SM to lower dimensions. We argue that the
same line of reasoning implies that for fixed values of $\Lambda_4$ and the
Yukawa coupling of the lightest neutrino $Y_{\nu_1}$, the EW scale is bounded
above. This is a trivial consequence of neutrino masses depending on the Higgs
vev. In the case of massive Majorana neutrinos with a see-saw mechanism
associated to a large scale $M\simeq 10^{10-14}$ GeV and $Y_{\nu_1}\simeq
10^{-3}$, one obtains that the EW scale cannot exceed $M_{EW}\lesssim
10^2-10^4$ GeV. From this point of view, the delicate fine-tuning required to
get a small EW scale would be a mirage, since parameters yielding higher EW
scales would be in the swampland and would not count as possible consistent
theories. This would bring a new perspective into the issue of the EW
hierarchy.
