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arXiv 1506.02466nucl-thnucl-exphysics.comp-ph
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手性核相互作用的不确定性分析与逐级优化

Uncertainty analysis and order-by-order optimization of chiral nuclear interactions

B. D. Carlsson, A. Ekström, C. Forssén, D. Fahlin Strömberg, G. R. Jansen, O. Lilja, M. Lindby, B. A. Mattsson, K. A. Wendt

摘要:

手征有效场论(chiEFT)提供了一种描述低能核力的系统方法。此外,chiEFT能够提供统计和系统不确定性的有根据的估计-尽管这种独特的优势尚未得到充分利用。我们通过对所有低能常数(LEC)进行优化和统计分析来填补这一空白,直到下一个到下一个到领先的顺序。我们的优化协议对应于一个同时适合散射和束缚态可观的π-核子,核子-核子,和几个核子部门,从而利用chiEFT的完整模型功能。我们研究了其他观测量的影响,通过演示误差传播的方法,可以很容易地通过未来的作品。我们采用数学优化和实现自动微分,以获得高效和机器精确的一阶和二阶导数的目标函数相对于LEC。我们使用功率计数参数来估计chiEFT固有的系统不确定性,我们构建了不同数量的不确定性的手性相互作用。统计误差传播与蒙特卡洛抽样相比,统计误差一般较小的系统相比。总之,我们发现,同时拟合不同的数据集对于(i)识别最佳LEC集,(ii)捕获所有相关性,(iii)减少统计不确定性,以及(iv)在chiEFT中实现逐阶收敛至关重要。此外,某些系统的不确定性,在几个核子部门被示出得到实质上放大的多体部门,特别是当不同的手征势的截止。本文的方法和结果为从头算核理论中的不确定性量化开辟了新的领域。

英文摘要:

Chiral effective field theory (chiEFT) provides a systematic approach to describe low-energy nuclear forces. Moreover, chiEFT is able to provide well-founded estimates of statistical and systematic uncertainties -- although this unique advantage has not yet been fully exploited. We fill this gap by performing an optimization and statistical analysis of all the low-energy constants (LECs) up to next-to-next-to-leading order. Our optimization protocol corresponds to a simultaneous fit to scattering and bound-state observables in the pion-nucleon, nucleon-nucleon, and few-nucleon sectors, thereby utilizing the full model capabilities of chiEFT. We study the effect on other observables by demonstrating error-propagation methods that can easily be adopted by future works. We employ mathematical optimization and implement automatic differentiation to attain efficient and machine-precise first- and second-order derivatives of the objective function with respect to the LECs. We use power-counting arguments to estimate the systematic uncertainty that is inherent to chiEFT and we construct chiral interactions at different orders with quantified uncertainties. Statistical error propagation is compared with Monte Carlo sampling showing that statistical errors are in general small compared to systematic ones. In conclusion, we find that a simultaneous fit to different sets of data is critical to (i) identify the optimal set of LECs, (ii) capture all relevant correlations, (iii) reduce the statistical uncertainty, and (iv) attain order-by-order convergence in chiEFT. Furthermore, certain systematic uncertainties in the few-nucleon sector are shown to get substantially magnified in the many-body sector; in particlar when varying the cutoff in the chiral potentials. The methodology and results presented in this Paper open a new frontier for uncertainty quantification in ab initio nuclear theory.

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