& 0 &1 \end{array}\right) ,
%$$ leads to $$%
\frac{\pi}{4} - \theta_{12} \simeq \frac{\sin\theta_{12}^e}{\sqrt{2}},%$$ which is satisfied for $\sin\theta_{12}^e\simeq
0.27^{+0.07}_{-0.08}$. This mixing also leads to the prediction of a large $$%
\sin^2 \theta_{13}\simeq \frac{\sin^2\theta_{12}^e}{{2}}
\simeq(0.017-0.059)
%$$ (the range is $\pm 2\sigma$), close to the current experimental upper limit of 0.032. Finally, this model implies $$%
m_{\beta\beta} \simeq m_2 (\cos^2 \theta_{12}-\sin^2
\theta_{12})\simeq 0.018 {\rm \ eV}
%$$ for the effective mass relevant to neutrinoless double beta decay. This is the standard result for the inverted hierarchy, with the minus sign due to the opposite signs of $m_1$ and $m_2$. Such a value should be observable in planned experiments [@DeGouvea:2005gd; @Langacker:2004xy; @Altarelli:2004za; @Mohapatra:2004vr].

Realization in Heterotic String Models {#sec:string}
======================================

Having outlined in a broad manner the elementary requirements for phenomenological viability of any triplet-based model with a structure dictated by the superpotential in (\[Wfull\]), we might now wish to ask whether such a set of fields and couplings really does arise in explicit string constructions as we have been assuming. Rather than build all possible constructions of a certain type for a dedicated scan – an undertaking that would undoubtedly produce interesting results in many areas, but which we reserve for 