The gamma5-problem of dimensional regularization - the HVBM scheme for the electroweak Standard Model at the 2-loop level

存在违反宇称的弱电相互作用的自然基本事实(本质上是左右对称)。它的技术描述使用了所谓的Gamma5矩阵。自1972年Hooft和Veltman的开创性工作以来，维正则化(DREG)为基本粒子理论中的高精度提供了一个在数学上一致且极其成功的框架。然而，Hooft和Veltman已经指出了Gamma5的一个问题。这个问题实质上意味着DREG不允许对Gamma5进行处理，这在数学上是一致的，在计算上也是简单的。在治疗Gamma5的众多建议中，只有一个得到了严格的证明和数学上的一致性：t Hooft/Veltman和Breitenlohner/Maison(HVBM方案)提出的原始建议。然而，在电弱相互作用中，伽马5无处不在，并且HVBM破坏了一个重要的规范不变性，在这种情况下，HVBM方案很难实际应用。因此，从业者传统上采用技术上更容易使用的替代方案，但也有其他缺点，如有效范围有限(有时不清楚)和/或缺乏数学一致性(可能导致错误或不明确的结果)。未来对精确预测的需求增加了人们对游戏问题的兴趣。最近的所有讨论都侧重于暖通弹道导弹的替代方案，并确认了替代方案的现状和局限性，突出了需要进一步开展工作和取得进展。因此，直接关注HVBM计划的互补性、不妥协的研究似乎是有希望的、及时的和有价值的。在此，我们提出了这样一项研究。我们将使用HVBM方案，并将其应用于双回路水平的电弱标准模型，大大超出当前状态。我们的目标是建立如何在现实理论中进行HVBM方案多回路计算，并促进未来这种类型的两回路和三回路计算。该研究计划包括五个步骤的系统序列，这些步骤首先应用于较简单的模型，然后应用于完整的弱电标准模型。一项主要成果是确定所谓的规范不变性恢复和消逝反项-这些是通用的构建块，将以计算机代码的形式发布，并允许以直接的方式进行未来的HVBM计算。此外，该项目还将回答几个关键的概念性问题，这些问题涉及基于暖通弹道管理的计算与更传统的计算之间的关系，以及与暖通弹道导弹计划内各种选择的利弊有关的问题。这样，该项目还将提供对传统方案的重要反馈，这些反馈可以通过与严格的HVBM结果进行比较来验证和改进。

A fundamental fact of nature of the existence of electroweak interactions which violate parity (essentially left-right symmetry). Its technical description uses the so-called gamma5-matrix. Since the seminal work of 't Hooft and Veltman in 1972, dimensional regularization (DREG) provides a mathematically consistent and extremely successful framework for high-precision in elementary particle theory. However, already 't Hooft and Veltman pointed out a problem with gamma5. The problem means in essence that DREG allows no treatment of gamma5 which is simultaneously mathematically consistent and computationally straightforward. Among the many proposals to treat gamma5, there is only one for which rigorous proofs and mathematical consistency have been established: the original one by 't Hooft/Veltman and Breitenlohner/Maison (HVBM scheme). However the HVBM scheme is difficult to apply in practice to the electroweak interactions where gamma5 is ubiquitous and where HVBM breaks an important gauge invariance. Therefore, practioners have traditionally applied alternative schemes which are technically easier to use but have other drawbacks such as limited (sometimes unclear) range of validity and/or lack of mathematical consistency (possibly leading to wrong or ambiguous results). The future need for precise predictions has increased the interest in the gamma5-problem. All recent discussions have focused on alternatives to HVBM and have confirmed the unsatisfactory status and the limitations of alternative schemes, highlighting the need for further work and progress. Hence a complementary, no-compromise study focusing directly on the HVBM scheme seems promising, timely and valuable. Here we propose such a study. We will use the HVBM scheme and apply it to the electroweak Standard Model at the two-loop level, significantly beyond the current status. The goal is to establish how to do HVBM-scheme multi-loop computations in realistic theories and facilitate future two- and three-loop computations of this kind. The research plan consists of a systematic sequence of five steps which are applied at the one-loop and two-loop level first to simpler models and then to the full electroweak Standard Model. A major deliverable is the determination of so-called gauge invariance-restoring and evanescent counterterms --- these are universal building blocks which will be published as computer codes and which will allow to carry out future HVBM computations in a straightforward way. In addition the project will answer several crucial conceptual questions, related to the relationship between HVBM-based and more traditional calculations and related to the pros and cons of various options within the HVBM scheme. In this way the project will also provide important feedback on the traditional schemes, which can be verified and improved by comparing with the rigorous HVBM results.