\gamma^\nu (1-\gamma_5)]\\
&\frac{1}{2} \, {\rm Tr} [({\ensuremath{\mathrlap{\!\not{\phantom{p}}}p}}^\prime+m_e) \gamma_\mu (C_V-C_A \gamma_5) ({\ensuremath{\mathrlap{\!\not{\phantom{p}}}p}}+m_e) \gamma_\nu (C_V-C_A\gamma_5)] \, \, \,\end{aligned}$$ where the factor $1/2$ in front of the second trace takes account of the averaging of the spin orientations in the initial state (target electron). The application of the first trace operator yields the projectile-related tensor of Eq. (\[eq:EQ110\]). The application of the second trace yields the target-related tensor, which (owing to the fact that the electron NC is not purely $V-A$ in character) is now of a more complex form. $$P_{\mu \nu} = 4 \left( c_1 \left( p^\prime_\mu p_\nu + p^\prime_\nu p_\mu + \left( \frac{q^2}{2} - m_e^2 \right) g_{\mu\nu} \right) - i c_2 \epsilon_{\mu \nu c d} p^c p^{\prime \, d} + c_3 m_e^2 g_{\mu\nu} \right) \, \, \, ,$$ where $c_1=C_V^2+C_A^2$, $c_2=2 C_V C_A$, and $c_3=C_V^2-C_A^2$.

As in Section \[sec:D1\], an effective target-related tensor may be constructed on the basis of the properties: $q_\mu K^{\mu \nu} = q_\nu K^{\mu \nu} = 0$. $$(P_{\mu \nu})_{\rm eff} = 4 \left( c_1 \left( 2 p_\mu p_\nu + \left( \frac{q^2}{2} - m_e^2 \right) g_{\mu\nu} \right) - i c_2 \epsilon_{\mu \nu c d} p^c q^d + c_3 m_e^2 g_{\mu\nu} \right) \, \, \, .$$ The contraction of 