Practical methods for a direct calculation of $\Delta I=1/2$ $K$ to $\pi\pi$ Decay
Practical methods for a direct calculation of $\Delta I=1/2$ $K$ to $\pi\pi$ Decay
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直接计算 $Delta I=1/2$ $K$ 到 $pipi$ 衰减的实用方法
DOI：
10.22323/1.139.0287
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Qi Liu
中科院分区：
文献类型：
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作者：
Qi Liu
直接计算复杂的$\Delta I=1/2$介子衰减幅度是出了名的困难，因为存在不连贯的图。在这里，我们描述并演示了解决这个问题的两种实用方法：egcg算法和使用时间分离$\pi-\pi$源。通过对域壁费米子进行微调的egcg实现，光夸克传播子的计算在从小（$16^3\times32\times16$）到大（$32^3\times64\times32$）的各种晶格上被加速了5-10倍。此外，通过将两个介子的每个源在时间方向上隔2-5个晶格间隔来实现噪声的大幅降低。这些方法结合使用$24^3\times64\times16$体积和329 MeV介子计算$K$到$\pi\pi$的阈值衰减。这些方法会产生来自138个仪表配置的Re（$A_0$）和Im（$A_0$）的非零信号。
A direct calculation of the complex $\Delta I=1/2$ kaon decay amplitude is notoriously difficult because of the presence of disconnected graphs. Here we describe and demonstrate two practical methods to defeat this problem: the EigCG algorithm and the use of time-separated $\pi-\pi$ sources. With a fine tuned EigCG implementation for domain wall fermions, the calculation of light quark propagators is accelerated by a factor of 5-10 on a variety of lattices from small ($16^3\times32\times16$) to large ($32^3\times64\times32$). In addition, a substantial reduction in noise is achieved by separating each of the sources for the two pions in the time direction by 2-5 lattice spacings. These methods are combined in a calculation of $K$ to $\pi\pi$ threshold decay using a $24^3\times64\times16$ volume and 329 MeV pions. These methods result in non-zero signals for both Re($A_0$) and Im($A_0$) from 138 gauge configurations.