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arXiv 2406.12656hep-lat
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在纯规范理论中使用两层算法实现胶球计算的指数误差降低

Exponential Error Reduction for Glueball Calculations Using a Two-Level Algorithm in Pure Gauge Theory

Lorenzo Barca, Francesco Knechtli, Sofie Martins, Michael Peardon, Stefan Schaefer, Juan Andrés Urrea-Niño

AI总结:

本文在四维 SU(3) 纯规范理论中采用两层算法计算胶球,证明其可在长距离指数降低统计误差,并通过 Wilson 圈变分基给出多个道的首态结果。

摘要:

本研究探索了应用两层算法来提高四维 SU(3) 纯规范理论中胶球计算的信噪比。我们的结果表明,统计误差呈现指数级降低,从而能够在当前标准方法需要指数级更多样本的距离上可靠地提取有效质量。然而,在较短距离上,由于多层方法的方差降低趋于饱和,标准方法被证明更有效。我们讨论了预期多层采样优于标准算法的物理距离,并有不同格距和胶球道的数值证据支持。此外,我们构建了一个变分基,它由长度至12、各有5种涂抹尺寸的35个 Wilson 圈组成,并给出了标量、赝标量和张量道能谱中第一个态的结果。

英文摘要:

This study explores the application of a two-level algorithm to enhance the signal-to-noise ratio of glueball calculations in four-dimensional $\mathrm{SU(3)}$ pure gauge theory. Our findings demonstrate that the statistical errors exhibit an exponential reduction, enabling reliable extraction of effective masses at distances where current standard methods would demand exponentially more samples. However, at shorter distances, standard methods prove more efficient due to a saturation of the variance reduction using the multi-level method. We discuss the physical distance at which the multi-level sampling is expected to outperform the standard algorithm, supported by numerical evidence across different lattice spacings and glueball channels. Additionally, we construct a variational basis comprising 35 Wilson loops up to length 12 and 5 smearing sizes each, presenting results for the first state in the spectrum for the scalar, pseudoscalar, and tensor channels.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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