and $L'_j = L_{\mu}, L_{\tau} = (1,
\mathbf{2})$ under $SU(2)_A \times SU(2)_B$, then the matrix of couplings $\lambda_T$ is (to leading order) $$%
\lambda_T = \lambda_0 \(\begin{array}{ccc} 0 & a & b \\ a & 0 & 0
\\ b & 0 & 0 \end{array} \) .
%
\label{lambdaT1}$$ It is natural to assume that the overall coefficient $\lambda_0$ in (\[lambdaT1\]) is of order unity. In fact if we now return to a string theory context, particularly that of the heterotic string with orbifold compactification, then the fact that the two generations of $L'_j$ in (\[WT\]) arise from the same sector of the string Hilbert space (i.e., the same fixed point location under the orbifold action) suggests that we should identify the coupling strengths: $a=b$.

Neutrino mass matrices based on the texture in (\[lambdaT1\]) with $a=b$ are not new to this work, but were in fact considered not long ago as a starting point for the bimaximal mixing scenario [@Barger:1998ta; @Barbieri:1998mq; @Altarelli:1998nx; @Jezabek:1998du]. In fact, the form of (\[lambdaT1\]) can be derived from a bottom-up point of view by first postulating a new symmetry based on the modified lepton number combination $L_e - L_{\mu} -
L_{\tau}$ [@Mohapatra:1999zr; @Babu:2002ex]. Indeed, the 