the deviation of the solar mixing angle from its TB mixing value[^7] \[sbound\] |s|   . This translates into $0.29 \lesssim \sin^2 \theta_{12}^l \lesssim 0.38$. The lower bound is tighter than the $3 \, \sigma$ bound found in [@fogli], whereas the upper bound is a bit weaker than the bound achieved with a global fit analysis of the experimental data. One should notice that these bounds are given for mixing angles evaluated at a scale close to the scale of grand unification, i.e. corrections coming from renormalisation group running have not yet been included, and also contributions resulting, for example, from a non-canonical Kähler potential have been neglected. As has been argued, these effects can be small [@RGnoncanon]. We remark that identical sum rule bounds also arise in the case of a SUSY $A_4 \times SU(5)$ model [@Cooper:2012wf]. This is clear, since also in this model lepton mixing is TB at LO, $\theta_{13}^l$ is generated in the neutrino sector by a suitable breaking of one of the two $Z_2$ symmetries and the leading corrections from the charged lepton sector are of the same form as in this model.

Note that the contribution to the light neutrino mass matrix $m^{eff}_\nu$ originating from 