arXiv 2408.084132024-08-15hep-phhep-thnucl-th

迈向泛函QCD的定量精度 I

Towards quantitative precision in functional QCD I

Friederike Ihssen, Jan M. Pawlowski, Franz R. Sattler, Nicolas Wink

AI总结：

本研究在QCD的fRG方法中构建了带可控系统误差的系统性展开方案，结合三项新进展以2+1味真空QCD为基准测试，结果与前沿方法吻合，首次提供π介子多散射等相关数据。

摘要：

泛函方法是唯一能够在有限密度下进行直接计算的第一性原理量子色动力学（QCD）框架。相关结果的预测能力与定量可靠性，只能在具备可控系统误差估计的系统性展开方案中才能获得。本文在QCD的泛函重整化群（fRG）方法框架下构建了这样一种方案，旨在实现完全的表观收敛。在本研究中，我们以2+1味真空QCD中的关联函数与可观测量作为天然基准，对该方案进行了测试。本工作整合了过去二十年间积累的诸多演化改进，同时还报告了三项重要的新进展：（i）基于fRG方法模块化特性的全面系统误差分析；（ii）引入全自动化计算框架，为QCD的fRG方法提供了前所未有的获取与改进途径；（iii）纳入手征序参量的完整有效势。这也使得我们能够获取π介子的全阶散射事件以及关联函数的完整动量依赖关系，这是自动化计算框架（ii）的首次应用。所得结果与来自泛函方法和格点模拟的其他最新结果吻合度极高，并且首次提供了π介子一般多散射事件及σ模式的相关数据。

英文摘要：

Functional approaches are the only first principle QCD setup that allow for direct computations at finite density. Predictive power and quantitative reliability of the respective results can only be obtained within a systematic expansion scheme with controlled systematic error estimates. Here we set up such a scheme within the functional renormalisation group (fRG) approach to QCD, aiming for full apparent convergence. In the current work we test this setup, using correlation functions and observables in 2+1 flavour vacuum QCD as a natural benchmark case. While the current work includes many evolutionary improvements collected over the past two decades, we also report on three novel important developments: (i) A comprehensive systematic error analysis based on the modular nature of the fRG approach. (ii) The introduction of a fully automated computational framework, allowing for unprecedented access and improvement of the fRG approach to QCD. (iii) The inclusion of the full effective potential of the chiral order parameter. This also gives access to all-order scattering events of pions and to the full momentum dependence of correlation functions, which is a first application of the automated computational framework (ii). The results compare very well to other state-of-the-art results both from functional approaches and lattice simulations, and provide data on general multi-scattering events of pions and the sigma mode for the first time.

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