标题： 有效场论中截断误差的量化 显示英文标题

标题： Quantifying truncation errors in effective field theory

摘要： 用于量化量子色动力学可观测量微扰计算中截断误差的贝叶斯过程被适应于有效场理论（EFT）展开。 在贝叶斯方法中，这些截断误差是从EFT预测的信念程度（DOB）区间推导出来的。 计算这些区间需要指定展开系数的先验概率分布（“先验”）。 通过编码对这些系数自然性的期望，该框架提供了对标准EFT程序的统计解释，其中截断误差是通过展开的逐阶收敛性来估计的。 它还允许探索这些误差条在何种情况下以及在何种情况下不敏感于EFT系数自然性的假设。 我们首先在一些代表性例子中演示EFT截断误差的贝叶斯概率分布的计算，然后专注于手征EFT在中子-质子散射中的应用。 Epelbaum、Krebs和 Mei{\ss }ner 最近提出了估算此类EFT计算中少核系统性质截断误差的明确规则。 我们发现，他们的基本程序从所考虑的一类自然性先验中普遍出现，并且所有这些先验都导致68% DOB区间的定量预测一致。 然后我们探讨了几种方法，通过这些方法可以利用一组可观测量的EFT收敛特性来检查EFT展开参数的统计一致性。 显示英文摘要

摘要： Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions ("priors") for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We first demonstrate the calculation of Bayesian probability distributions for the EFT truncation error in some representative examples, and then focus on the application of chiral EFT to neutron-proton scattering. Epelbaum, Krebs, and Mei{\ss}ner recently articulated explicit rules for estimating truncation errors in such EFT calculations of few-nucleon-system properties. We find that their basic procedure emerges generically from one class of naturalness priors considered, and that all such priors result in consistent quantitative predictions for 68% DOB intervals. We then explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter.