Theoretical Subatomic Physics

理论亚原子物理

• 批准号: SAPIN-2016-00034
• 负责人: Czarnecki, Andrzej
• 金额: $ 7.29万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762437
• 关键词: Theoretical; Subatomic; Physics

My goal in the next five years is to finalize an algorithm for finding quantum corrections to properties of bound states. Properties such as energy levels of muonium are determined by the interaction between the electron and the muon, their self-interactions, and their relative motion. Improving the theory of any of these effects requires sifting through contributions arising at various energy scales. At a certain level of precision, complications prohibit the theoretical progress.My group specializes in theoretical predictions to support precise experiments. Multi-loop Feynman amplitudes are evaluated, usually as an expansion in some parameter. The mathematics involved is known as asymptotic expansions, greatly developed in high-energy physics. Resulting large formulas are handled with symbolic computation and we are fortunate to have a cluster of dedicated, large-memory computers in Alberta.We now want to generalize this successful approach to bound states. The challenge is that the amplitudes involve not only small numerical parameters but also operators like the relative momentum or a perturbing potential. They are also small, in the sense of expectation values.The algorithm we envision will generate expressions needed for the desired precision, much like Feynman diagrams in a given loop order can be produced by computer programs.Such an automated approach to bound states is nontrivial. It requires an extension of the known mathematics of expansion of integrals to the situation where an integrand depends on non-commuting operators (momentum and a position-dependent potential). We have not yet been able to solve this problem in all generality, and propose to focus on three specific cases, urgently needed by experiments. We hope that the general method will crystallize out of these efforts.Five years from now, experiments will have progressed on all three fronts. Searches for lepton-flavor violation, COMET and Mu2e, will have taken their first data. Their background will be under control thanks to our results on the bound muon decay. They will map the electron spectrum and test our predictions. Our theory of the bound-electron g-2, together with the anticipated progress in measurements, will result in a more accurate electron mass, and hopefully also a better value of the fine structure constant alpha. Very likely, the measurement of the free-electron g-2 will be improved, and with the new alpha will check whether the current muon g-2 discrepancy is due to new physics. Our improved prediction of the Lamb shift will help interpret the other low-energy conundrum, that of the proton radius.My dream is that by then we will have a fully-fledged algorithm for bound state studies.

我在未来五年的目标是最终确定一个算法，用于找到对束缚态性质的量子修正。介子的性质，如能级，是由电子和介子之间的相互作用、它们的自相互作用和它们的相对运动决定的。要改进这些效应的理论，就需要对不同能量尺度下的贡献进行筛选。在一定的精度水平上，复杂性阻碍了理论的进步，我的团队专门从事理论预测，以支持精确的实验。多回路费曼振幅的评估，通常作为一些参数的扩展。所涉及的数学被称为渐近展开，在高能物理学中得到了很大的发展。我们很幸运地在阿尔伯塔有一群专用的大内存计算机，现在我们想把这种成功的方法推广到束缚态。挑战在于振幅不仅涉及小的数值参数，还涉及相对动量或微扰势等算子。从期望值的意义上说，它们也很小，我们设想的算法将生成所需的表达式，以达到所需的精度，就像计算机程序可以生成给定循环顺序的费曼图一样。它需要将已知的积分展开数学扩展到被积函数依赖于非对易算子（动量和位置相关势）的情况。我们还没有能够解决这个问题在所有的一般性，并建议集中在三个具体情况下，迫切需要的实验。我们希望，通过这些努力，一般方法将具体化，五年后，所有三个方面的试验都将取得进展。 探测轻子味破坏的彗星和μ 2 e将获得它们的第一批数据。由于我们对束缚μ介子衰变的研究结果，它们的背景将得到控制。他们将绘制电子光谱图并检验我们的预测。我们的束缚电子g-2理论，加上预期的测量进展，将导致更准确的电子质量，并希望也是一个更好的精细结构常数α值。很有可能，对自由电子g-2的测量将得到改进，并且用新的α将检查当前μ介子g-2的差异是否是由于新的物理学。我们对兰姆位移的改进预测将有助于解释另一个低能难题，即质子半径。我的梦想是，到那时我们将有一个完全成熟的束缚态研究算法。