We study the all-line transverse (ALT) shift which we developed for on-shell recursion of amplitudes for particles of any mass. We discuss the validity of the shift for general theories of spin ≤1, and illustrate the connection between Ward identity and constructibility for massive spin-1 amplitude under the ALT shift. We apply the shift to the electroweak theory, and various four-point scattering amplitudes among electroweak gauge bosons and fermions are constructed. We show explicitly that the four-point gauge boson contact terms in massive electroweak theory automatically arise after recursive construction, independent of UV completion, and they automatically cancel the terms growing as (energy)4 at high energy. We explore UV completion of the electroweak theory that cancels the remaining (energy)2 terms and impose unitarity requirements to constrain additional couplings. The ALT shift framework allows consistent treatment in dealing with contact term ambiguities for renormalizable massive and massless theories, which we show can be useful in studying real-world amplitudes with massive spinors.

中文翻译：

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电弱理论的动量偏移和壳层递归关系


我们研究了全线横向 （ALT） 偏移，该偏移是我们为任何质量的粒子的壳层递归振幅而开发的。我们讨论了自旋 ≤1 的一般理论中移位的有效性，并说明了 ALT 移位下 Ward 恒等式与大质量自旋 1 振幅的可构造性之间的联系。我们将这种偏移应用于电弱理论，构建了电弱规范玻色子和费米子之间的各种四点散射振幅。我们明确表明，大质量电弱理论中的四点规范玻色子接触项是在递归构造后自动出现的，与 UV 完成无关，并且它们会自动抵消在高能量下增长为 （能量）4 的项。我们探讨了电弱理论的 UV 完成，该理论抵消了剩余的 （能量）2 项，并施加了幺正性要求来约束额外的耦合。ALT 移位框架允许在处理可重整化有质量和无质量理论的接触项歧义时进行一致的处理，我们证明这在研究具有大质量旋量的真实世界振幅时很有用。