论文标题
贝叶斯对手性有效野外理论的核子核子扇区中低能常数的估计最高第四阶
Bayesian estimation of the low-energy constants up to fourth order in the nucleon-nucleon sector of chiral effective field theory
论文作者
论文摘要
We use Bayesian methods and Hamiltonian Monte Carlo (HMC) sampling to infer the posterior probability density function (PDF) for the low-energy constants (LECs) up to next-to-next-to-next- to-leading order (N3LO) in a chiral effective field theory ($χ$EFT) description of the nucleon-nucleon interaction.第一步，我们调节对中子 - 普罗顿和质子 - 普罗顿散射数据的推断，并解释不相关的$χ$ eft截断错误。我们演示了如何使用修订后的HMC推理方案成功地在N3LO上成功采样LEC的31维空间。在第二步中，我们通过重要性抽样的途径扩展分析，并对中子中子中的散射长度进行经验确定，以推断$^{1} S_0 $中子中子 - 中子之间的相互作用通道中领先的电荷依赖性接触LEC的后验PDF。在这样做的同时，我们通过共轭物处理$χ$ eft截断错误。我们使用所得的后PDF对$^{1} S_0 $波中的有效范围参数的后验预测分布进行采样，以及电荷对称断裂和与电荷独立破坏的强度。 We conclude that empirical point-estimate results of isospin breaking in the $^{1}S_0$ channel are consistent with the PDFs obtained in our Bayesian analysis and that, when accounting for $χ$EFT truncation errors, one must go to next-to-next-to-leading order to confidently detect isospin breaking effects.
We use Bayesian methods and Hamiltonian Monte Carlo (HMC) sampling to infer the posterior probability density function (PDF) for the low-energy constants (LECs) up to next-to-next-to-next- to-leading order (N3LO) in a chiral effective field theory ($χ$EFT) description of the nucleon-nucleon interaction. In a first step, we condition the inference on neutron-proton and proton-proton scattering data and account for uncorrelated $χ$EFT truncation errors. We demonstrate how to successfully sample the 31-dimensional space of LECs at N3LO using a revised HMC inference protocol. In a second step we extend the analysis by means of importance sampling and an empirical determination of the neutron-neutron scattering length to infer the posterior PDF for the leading charge-dependent contact LEC in the $^{1}S_0$ neutron-neutron interaction channel. While doing so we account for the $χ$EFT truncation error via a conjugate prior. We use the resulting posterior PDF to sample the posterior predictive distributions for the effective range parameters in the $^{1}S_0$ wave as well as the strengths of charge-symmetry breaking and charge-independence breaking. We conclude that empirical point-estimate results of isospin breaking in the $^{1}S_0$ channel are consistent with the PDFs obtained in our Bayesian analysis and that, when accounting for $χ$EFT truncation errors, one must go to next-to-next-to-leading order to confidently detect isospin breaking effects.
