fields. If one imposes the boundary condition given by $$\label{eq:fund45}
\psi(x+Le_j)=e^{2\pi i\theta_j}\psi (x), \qquad j=1,2,3,$$ on a valence quark field, the spatial momentum of that quark is quantized according to $$\label{eq:fund46}
p_j = \frac{2\pi n_j}{L} + \frac{2\pi \theta_j}{L}, \qquad j=1,2,3,$$ where $L$ denotes the spatial lattice size, $e_j$ the unit vector in the spatial $j$-th direction and $\theta_j$ real parameter. In this way one can explore arbitrarily small momentum on the lattice by adjusting the value of twist $\theta_j$.

For the meson two-point function consisting of quark and anti-quark propagators, we apply the twist only to quark and not to antiquark or vice versa. Similarly, for the three-point function, we twist only one or two out of the three quark propagators. In other words, we pretend that each valence quark line in the two- and three-point function quark diagrams carry a different flavor and select the appropriate flavor to apply twisting. In this way we can avoid a twist of a quark line cancelled by the opposite twist of the antiquark line carrying the same flavor [@boyle2007]. This procedure and the twisting of only valence quarks mean that we deal with partially quenched QCD with a different flavor symmetry content 