form factor for the renormalized current. The presence of ratios guarantee that statistical fluctuations are suppressed. Nonetheless, making simple choices such as $\vec{p}\ne 0$ and $\vec{p'}=0$, we have observed an increasingly larger fluctuation of the ratio as pion mass is reduced, and this trend worsens for larger momenta. With an interesting choice of momenta, $\vec{p'}\ne \vec{p}$ but $|\vec{p'}|=|\vec{p}|$, the ratio (\[eq:ratio\]) simplifies to $$\label{eq:ratio3ptOnly}
R'(\tau)=\frac{C^{3pt}(\vec{p'},t_f;\vec{p},0;\tau)}{C^{3pt}(\vec{p'},t_f;\vec{p'},0;\tau)}.$$ Since the two-point functions as well as the ratio of energies drop out, leaving just the ratio of three-point functions, we expect this choice to yield better signals than those choices for which all factors are present. Furthermore, one can choose 6 permutations in momentum directions while keeping $|\vec{p'}|=|\vec{p}|$, gaining more statistics.

Partially twisted boundary condition
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The minimum non-zero quark momentum $2\pi/La$ for the periodic boundary condition on a $32^3\times 64$ lattice with a 2 GeV inverse lattice spacing is about 0.4 GeV. To probe the region of smaller momentum transfer as well as to improve the resolution of four-momentum transfer, we apply the method of partially twisted boundary condition [@boyle2007; @sachrajda2005; @bedaque2005; @jian] in which valence quark fields are subjected to twisted boundary condition while periodic boundary condition is kept for sea quark 