with the form of (\[WT\]) and implies a triplet mass of order $$%
M_T = 2.0 \times \lambda_2 \lambda_T \(\frac{v_2 v'_2}{(100
\GeV)^2}\) \times 10^{14} \GeV
%
\label{MT}$$ where we have defined $v_2 = \lang (h_2)^0 \rang$ and $v'_2 =
\lang (h'_2)^0 \rang$. The solar mass difference (\[dm12\]) can be restored in this case by taking $\epsilon \simeq \frac{1}{43}$ in the mass matrix given by $$%
m_{\nu} = \sqrt{\frac{|\Delta m^2_{23}|}{2}} \(
\begin{array}{ccc} 0 & -1 & -1 \\ -1 & 0 & \epsilon
\\ -1 & \epsilon & 0 \end{array} \) .
%
\label{perturb}$$ This value is particularly encouraging for theories motivated by the weakly coupled heterotic string compactified on orbifolds. Such theories generally give rise to an Abelian gauge factor with non-vanishing trace anomaly. This anomaly is cancelled by the Green-Schwarz mechanism, which involves a Fayet-Iliopoulos (FI) term $\xi_{\rm FI}$ in the 4D Lagrangian [@Dine:1987xk; @Dine:1987gj; @Atick:1987gy]. In general, at least one field $X$ of the massless spectrum, charged under this anomalous $U(1)$ factor, will receive a vev $X \simeq
\sqrt{\xi_{\rm FI}}$ so as to ensure $\lang D_X \rang = 0$ below the scale $\xi_{\rm FI}$. Explicit orbifold constructions suggest that $0.09 \leq r_{\rm FI} = \sqrt{|\xi_{\rm FI}|}/M_{\PL} \leq
0.14$ 