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arXiv 0809.0412hep-lat
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Wilson手征微扰理论中的π介子散射

Pion Scattering in Wilson Chiral Perturbation Theory

Sinya Aoki, Oliver Bar, Benedikt Biedermann

摘要:

我们计算了两种味道的Wilson手征微扰理论的散射振幅。由明确的手征对称性破缺引起的晶格间距效应在O(a^2)内保持不变,我们考虑夸克质量m为a^2 λ ^3的情况。给出了不同同位旋通道中散射长度的解析表达式。由于O(a^2)项的存在,散射长度在手征极限下不会为零。此外,在单回路结果中还存在与a^2 ln M_pi^2成比例的额外手性分子。这些贡献可以模糊的连续手征谱和低能量常数的确定从数值晶格模拟。

英文摘要:

We compute the scattering amplitude in Wilson Chiral Perturbation Theory for two flavors. The lattice spacing effects due to the explicit chiral symmetry breaking are kept through O(a^2), and we consider the regime where the quark mass m is of order a^2 Lambda_^3. Analytic expressions for the scattering lengths in different isospin channels are given. As a result of the O(a^2) terms the scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to a^2 ln M_pi^2 are present in the one-loop results. These contributions can obscure the continuum chiral logarithms and the determination of low-energy constants from numerical lattice simulations.

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