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arXiv 2202.00934hep-phhep-th
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功率抑制校正显示红外抵消的新特征

Power suppressed corrections show new features of infrared cancellations

Paolo Ciafaloni, Denis Comelli, Alfredo Urbano

摘要:

红外发散角的抵消是量子场论中的一个古老课题,其主要结果被浓缩为著名的Kinoshita-Lee-Nauenberg(KLN)定理。在本文中,我们考虑质量抑制的背景下自发破缺的规范理论的领先(即双对数)的红外发散的修正。我们工作在一个简化的理论设置的基础上自发破缺的$U'(1)\otimes U(1)$规范群。我们分析了,在单圈水平,包括质量抑制条款,双对数修正的衰变通道的一个假设的重$Z'$规范玻色子耦合到轻手征费米子和轻质量$Z$规范玻色子混合。限于这个理论框架,只有最终状态IR校正是相关的。我们发现,充分利用KLN定理需要非平凡的各种衰变通道的组合,以摆脱质量抑制IR校正。基于这一观察,我们表明,从重$Z'$规范玻色子的任何两体衰变开始,质量抑制的双对数修正的取消需要在整个衰变宽度上求和(从而强制包含与起始状态无关的最终状态)。在途中,我们证明了一些技术成果,是相关的质量抑制的IR原产地的双谱线的计算。我们的结果是相关的模型,扩大了标准模型,增加了沉重的$Z'$。

英文摘要:

The cancellation of infrared (IR) divergences is an old topic in quantum field theory whose main results are condensed into the celebrated Kinoshita-Lee-Nauenberg (KLN) theorem. In this paper, we consider mass-suppressed corrections to the leading (i.e. double-logarithmic) IR divergences in the context of spontaneously broken gauge theories. We work in a simplified theoretical set-up based on the spontaneously broken $U'(1)\otimes U(1)$ gauge group. We analyze, at the one-loop level and including mass-suppressed terms, the double-logarithmic corrections to the decay channels of a hypothetical heavy $Z'$ gauge boson coupled to light chiral fermions and mixed with a light massive $Z$ gauge boson. Limited to this theoretical framework, only final state IR corrections are relevant. We find that full exploitation of the KLN theorem requires non-trivial combinations of various decay channels in order to get rid of the mass-suppressed IR corrections. Based on this observation we show that, starting from any two-body decay of the heavy $Z'$ gauge boson, the cancellation of the mass-suppressed double-logarithmic corrections requires the sum over the full decay width (thus enforcing the inclusion of final states which are na\"ıvely unrelated to the starting one). En route, we prove a number of technical results that are relevant for the computation of mass-suppressed double-logarithms of IR origin. Our results are relevant for models that enlarge the Standard Model by adding a heavy $Z'$.

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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