Theoretical Subatomic Physics

我在未来五年的目标是完成一种算法，找到对束缚态性质进行量子修正的算法。电子和Muon之间的相互作用、它们的自身相互作用以及它们的相对运动决定了Muon的性质，如能级。要改进任何这些效应的理论，都需要筛选各种能量尺度上的贡献。在一定的精确度上，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。多回路费曼幅度通常作为某些参数的展开式来计算。所涉及的数学被称为渐近展开，在高能物理中得到了极大的发展。由此产生的大型公式是用符号计算来处理的，我们很幸运地在艾伯塔省拥有一群专用的、大内存的计算机。*我们现在想将这种成功的方法推广到束缚态。挑战在于，振幅不仅涉及很小的数值参数，还涉及相对动量或微扰势等运算符。从期望值的意义上讲，它们也很小。*我们设想的算法将生成所需精度所需的表达式，就像给定循环顺序的费曼图可以由计算机程序生成一样。*这样一种自动处理束缚状态的方法不是微不足道的。它需要将已知的积分展开数学推广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的所有一般性，并建议集中在实验迫切需要的三个具体情况。我们希望通用的方法将在这些努力中具体化。*五年后，所有三个方面的实验都将取得进展。搜索轻子味道违规的彗星和Mu2e将获得他们的第一个数据。多亏了我们关于束缚介子衰变的结果，它们的背景将得到控制。他们将绘制电子光谱图，并测试我们的预测。我们的束缚电子g-2理论，加上在测量方面的预期进展，将导致更准确的电子质量，并有望得到更好的精细结构常数α的值。很有可能，自由电子g-2的测量将得到改进，新的阿尔法将检查目前的muon g-2差异是否源于新的物理。我们对兰姆位移的改进预测将有助于解释另一个低能量难题，质子半径的难题。*我的梦想是，到那时，我们将拥有一个全面的束缚态研究算法。

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.