Reexamining the proton-radius problem using constrained Gaussian processes
Reexamining the proton-radius problem using constrained Gaussian processes
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DOI：
10.1103/physrevc.99.055202
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发表时间：
2018-08
影响因子：
3.1
通讯作者：
Shuang Zhou;P. Giulani;J. Piekarewicz;A. Bhattacharya;D. Pati
中科院分区：
文献类型：
--
作者：
Shuang Zhou;P. Giulani;J. Piekarewicz;A. Bhattacharya;D. Pati
背景资料："质子半径之谜“是指一个8年前的问题，它突出了从μ介子兰姆位移实验中提取质子电荷半径与使用弹性电子散射的实验相比的主要不一致性。对于后一种方法，电荷半径的确定涉及到外推的实验形状因子为零momentumtransfer.Purpose：为了估计质子半径，一种新的和强大的非参数方法的基础上的约束高斯过程。受约束的高斯过程模型的电气形状因子作为一个功能的动量transfer.Methods：在贝叶斯范式，我们开发了一个模型，足够灵活，适合的数据，没有任何参数假设的形状因子。贝叶斯估计通过对形状因子仅施加两个物理约束来指导：（a）其在零动量传递（归一化）时的值和（B）其整体形状，假定为动量传递的单调递减函数。这些假设的变体进行了探讨，以评估其impacts.Results：通过采用这两个约束条件，并结合整个范围内的实验数据，我们提取的电荷半径${r}_{p}=0.845\ifmmode\pm\else\textpm\fi{}0.001\phantom{\rule{0.16em}{0 ex}}\mathrm{fm}$，符合μ子实验。然而，我们表明，在我们的模型中，提取的半径取决于假设的约束条件和用于拟合高斯过程的实验数据的范围。例如，如果只使用低动量传递数据，放松归一化约束提供了一个值兼容较大的电子value.Conclusions：我们提出了一种新的技术来估计质子半径的电子散射数据的基础上约束高斯过程。我们证明了对形状因子施加合理的物理约束的影响是巨大的。外推法中使用的实验数据的范围也很关键。我们希望，随着这项技术的完善，再加上PRad实验的预期新结果，我们将更接近于解决这个难题。
Background: The ``proton radius puzzle'' refers to an 8-year-old problem that highlights major inconsistencies in the extraction of the charge radius of the proton from muonic Lamb-shift experiments as compared against experiments using elastic electron scattering. For the latter approach, the determination of the charge radius involves an extrapolation of the experimental form factor to zero momentum transfer.Purpose: To estimate the proton radius, a novel and powerful nonparametric method based on a constrained Gaussian process is introduced. The constrained Gaussian process models the electric form factor as a function of the momentum transfer.Methods: Within a Bayesian paradigm, we develop a model flexible enough to fit the data without any parametric assumptions on the form factor. The Bayesian estimation is guided by imposing only two physical constraints on the form factor: (a) its value at zero momentum transfer (normalization) and (b) its overall shape, assumed to be a monotonically decreasing function of the momentum transfer. Variants of these assumptions are explored to assess their impact.Results: By adopting both constraints and incorporating the whole range of experimental data available we extracted a charge radius of ${r}_{p}=0.845\ifmmode\pm\else\textpm\fi{}0.001\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$, consistent with the muonic experiment. Nevertheless, we show that within our model the extracted radius depends on both the assumed constraints and the range of experimental data used to fit the Gaussian process. For example, if only low-momentum-transfer data are used, relaxing the normalization constraint provides a value compatible with the larger electronic value.Conclusions: We have presented a novel technique to estimate the proton radius from electron-scattering data based on a constrained Gaussian process. We demonstrated that the impact of imposing sensible physical constraints on the form factor is substantial. Also critical is the range of the experimental data used in the extrapolation. We are hopeful that as the technique gets refined, together with the anticipated new results from the PRad experiment, we will get closer to a resolution of the puzzle.