arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1808.08211nucl-th
收藏

利用核子-核子相移探索手征有效场论的贝叶斯参数估计

Exploring Bayesian parameter estimation for chiral effective field theory using nucleon-nucleon phase shifts

S. Wesolowski, R. J. Furnstahl, J. A. Melendez, D. R. Phillips

摘要:

最近,我们开发了一个贝叶斯框架参数估计一般有效场论。在这里,我们提出了选定的结果,使用该框架来估计参数与核子核子(NN)的潜力来自使用手征有效场论($χ$ EFT):Epelbaum,Krebs和Meißner(EKM)的半本地NN潜力。有许多NN散射数据,直到高能量,并且具有相当小的误差,因此对不自然的低能常数(LEC)施加惩罚通常对拟合有很小的影响。相比之下,我们发现,包括在$χ$ EFT估计高阶起着重要的作用,在鲁棒的参数estimation.We提出了两个案例研究,我们的贝叶斯机制阐明物理问题。第一个涉及EKM势在四阶的$χ$ EFT展开:二维后验概率密度函数(pdf)的四阶$s$波LEC从奈梅亨PWA 93相移表明,这些参数在NN潜力退化。我们跟踪PDF的这一功能的存在下,一个操作员在四阶NN潜在的壳上消失。第二个案例研究检查LEC提取的稳定性,因为在更高的能量下的更多数据被包括在拟合中。我们表明,只要$χ$ EFT截断误差是适当占在参数估计,LEC值提取使用我们的贝叶斯方法是不敏感的最大能量选择的fit.Uncorrelated和完全相关的截断误差模型进行比较,指向的方式使用高斯过程更普遍的相关结构建模。

英文摘要:

We recently developed a Bayesian framework for parameter estimation in general effective field theories. Here we present selected results from using that framework to estimate parameters with a nucleon-nucleon (NN) potential derived using chiral effective field theory ($χ$EFT): the semi-local NN potential of Epelbaum, Krebs, and Meißner (EKM). There are many NN scattering data, up to high energies, and with rather small errors, so imposing a penalty for unnatural low-energy constants (LECs) usually has a small effect on the fits. In contrast, we have found that including an estimate of higher orders in $χ$EFT plays an important role in robust parameter estimation.We present two case studies where our Bayesian machinery illuminates physics issues. The first involves the EKM potential at fourth order in the $χ$EFT expansion: the two-dimensional posterior probability density function (pdf) for the fourth-order $s$-wave LECs obtained from the Nijmegen PWA93 phase shifts indicates these parameters in the NN potential are degenerate. We trace this feature of the pdf to the presence of an operator in the fourth-order NN potential that vanishes on-shell. The second case study examines the stability of LEC extractions as more data at higher energies are included in the fit. We show that as long as $χ$EFT truncation errors are properly accounted for in the parameter estimation, the LEC values extracted using our Bayesian approach are not sensitive to the maximum energy chosen for the fit.Uncorrelated and fully correlated models for the truncation errors are compared, pointing the way to the use of Gaussian processes to more generally model the correlation structure.

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。

↑