Theoretical Subatomic Physics

我未来五年的目标是完成一种算法，用于寻找束缚态性质的量子修正。介子的能级等性质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。改进任何这些效应的理论都需要筛选各种能量尺度上产生的贡献。在一定的精确度上，复杂性阻碍了理论的进步。我的小组专门从事理论预测，以支持精确的实验。多环费曼幅值通常作为某些参数的展开来计算。所涉及的数学称为渐近展开，在高能物理学中得到了极大的发展。由此产生的大型公式是用符号计算处理的，我们很幸运在阿尔伯塔省有一个专用的大内存计算机集群。我们现在想把这个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，还涉及相对动量或扰动势等运算符。从期望值的角度来看，它们也很小。我们设想的算法将生成所需精度的表达式，就像给定循环顺序的费曼图可以由计算机程序生成一样。这种对束缚状态的自动化方法是不平凡的。它需要将已知的积分展开的数学扩展到被积函数依赖于非交换算子（动量和位置相关的势）的情况。我们还不能全面地解决这个问题，并建议把重点放在三个具体的案例上，这是实验迫切需要的。我们希望这些努力将使一般方法具体化。从现在起的五年内，这三个方面的实验都将取得进展。对彗星和Mu2e轻子类违逆的搜索将获得它们的第一批数据。由于我们在束缚介子衰变方面的结果，它们的背景将得到控制。他们将绘制电子谱图并验证我们的预测。我们关于束缚电子g-2的理论，加上预期的测量进展，将会得到更精确的电子质量，也有希望得到更好的精细结构常数alpha值。很有可能，对自由电子g-2的测量将得到改进，用新的α将检查当前μ子g-2的差异是否是由于新的物理。我们对兰姆位移的改进预测将有助于解释另一个低能难题，即质子半径。我的梦想是，到那时，我们将有一个成熟的算法来研究束缚状态。

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.