K -> pi pi 衰变是研究CP对称性破缺的一个理想场所。尤其是衰变过程中的直接CP破缺效应，由于其尺度很小，对于高能标的新物理更加敏感。目前格点QCD计算得到的直接CP破缺与间接CP破缺的比值，与实验测量值相差了2.1个标准差。要从CP破缺中获得确定的关于新物理存在的信息，还有赖于格点计算进一步提高精度。而另一方面，K -> pi pi 衰变过程中的电磁修正效应，无论对格点计算还是对实验测量来讲，都是一个重要的系统误差。本项目将用格点QCD的方法去计算 K -> pi pi 衰变过程中的电磁修正。首先解决电磁相互作用效应下同位旋 I=0 和 I=2 道 pi pi 散射态的混合，以及长程电磁相互作用引起的有限体积效应等几个问题；然后在非物理的参数底下开展计算，测试计算程序，调整计算方案以及完善分析方法；并最终帮助我们在物理的参数下确定 O(alpha_e) 阶的电磁修正。

K -> pi pi decay is an ideal place to study the CP violation. Due to its small size, the direct CP violation observed in the K -> pi pi decay is very sensitive to the high-energy-scale new physics. The most recent lattice QCD calculation of the direct CP-violating ratio deviates from the experimental measurements by 2.1 sigma. To confirm the existence of new physics, one needs to reduce the uncertainty in the lattice QCD calculation. On the other hand, the electromagnetic corrections are important systematic effects for determining the CP-violating parameters. We propose to perform a lattice QCD calculation of these electromagnetic corrections. In our approach, we first tackle the problems for the mixing between the isospin I=0 and I=2 pi pi scattering states due to the isospin violation and determine finite volume effects introduced by the long-range electromagnetic interaction. As a second step, we will perform the calculation at an unphysical parameter to test the numerical code, design the computational strategy and implement the analysis. The final target is to determine the O(alpha_e) correction at the physical pion mass.