we twisted one quark with a twist angle $\vec{\theta}=(\theta, \theta, \theta)$ and left the other untwisted. In Fig. \[fig:checkTBC13700\](a) we plot the effective energy for the ground state, two values of the twist angle and their combination with the first integer momenta at the hopping parameters $\kappa_{s}=0.1364$, $\kappa_{ud}=0.13700$ where $M_\pi \approx 702$ MeV. The propagator is fitted over $t=7-27$ to extract the energy $E(\vec p)$. Errors are estimated by the jackknife method with the bin size of 100 trajectories. The results are plotted in Fig. \[fig:checkTBC13700\](b), together with the expected behavior, $$\label{eq:DispersionRel}
E\left(\vec p \right)^2 = \left( aM_\pi \right)^2 + \left( \frac{2\pi}{L}\vec n + \frac{2\pi}{L}\vec\theta \right)^2,$$ which demonstrates clearly that the term $\frac{2\pi \theta_j}{L}$ acts as true physical momentum. The two data points on the right represent combinations of an integer momentum $(1,0,0)$ and a twist. The energy-momentum relation is correctly reproduced in this case as well.

Random wall source
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At light quark masses the computing cost for inversion of Dirac operator becomes very expensive. Thus we have employed some improvements for obtaining the form factor with acceptable statistical errors at reasonable computing time. The first improvement is to utilize the random wall source. This method has a long 