arXiv 1911.123662019-11hep-phhep-th

Goldstone等价性与高能电弱物理

Goldstone Equivalence and High Energy Electroweak Physics

Gabriel Cuomo, Luca Vecchi, Andrea Wulzer

备注：: 50 pages + appendices, 7 figures, v2 fixed typos, added fig. 5
发表信息：: SciPost Phys. 8 (2020) 5, 078
DOI：: 10.21468/SciPostPhys.8.5.078

摘要：

质量规范理论的破缺相和不破缺相之间的过渡，即高能时纵向自由度和戈德斯通自由度的重新排列，在标准形式主义中显然不是平滑的。光滑性的缺乏具体表现为纵向极化矢量随能量的异常增长，因为它们出现在费曼规则中，对于真实的壳层外粒子和来自规范场传播子分解的虚粒子都是如此。这使得费曼振幅在高能极限的表征非常麻烦，这反过来又对研究远高于电弱尺度的能量的电弱过程提出了特殊的挑战。我们开发了一个洛伦兹协变的形式主义，其中偏振矢量是良好的行为，因此，能量功率计数是明显的个人费曼图的水平。这使我们能够证明有效的W近似的有效性，更一般地说，共线发射的因式分解，并计算相应的分裂函数在树级顺序。我们的形式主义适用于在微扰理论的所有订单，为任意的规范群和一般的线性规范固定泛函。它可以用来简化标准模型回路计算，直接在费曼图上进行高能展开。这是通过计算顶夸克衰变的辐射修正来说明的。

英文摘要：

The transition between the broken and unbroken phases of massive gauge theories, namely the rearrangement of longitudinal and Goldstone degrees of freedom that occurs at high energy, is not manifestly smooth in the standard formalism. The lack of smoothness concretely shows up as an anomalous growth with energy of the longitudinal polarization vectors, as they emerge in Feynman rules both for real on-shell external particles and for virtual particles from the decomposition of the gauge field propagator. This makes the characterization of Feynman amplitudes in the high-energy limit quite cumbersome, which in turn poses peculiar challenges in the study of Electroweak processes at energies much above the Electroweak scale. We develop a Lorentz-covariant formalism where polarization vectors are well-behaved and, consequently, energy power-counting is manifest at the level of individual Feynman diagrams. This allows us to prove the validity of the Effective W Approximation and, more generally, the factorization of collinear emissions and to compute the corresponding splitting functions at the tree-level order. Our formalism applies at all orders in perturbation theory, for arbitrary gauge groups and generic linear gauge-fixing functionals. It can be used to simplify Standard Model loop calculations by performing the high-energy expansion directly on the Feynman diagrams. This is illustrated by computing the radiative corrections to the decay of the top quark.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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