Abstract
Modified interactions in the electroweak sector may lead to scattering amplitudes that grow with energy compared to their Standard Model (SM) counterparts. We present a detailed study of all 2 → 2 scattering amplitudes involving at least one top quark and a pair of EW bosons. We analyse the high energy behaviour of the amplitudes using the Standard Model Effective Field Theory (SMEFT) to parametrise the departures from the SM. We discuss the origin of the energy growth that arise from effective contact interactions by appealing to the Goldstone equivalence theorem and find that the amplitudes obey expected patterns of (non-)interference. The results are connected to unitary-violating behaviour in the framework of anomalous SM interactions. Therein, we identify the appearance of additional growth due to the violation of SU(2) gauge symmetry that leads to substantial differences between the SMEFT and the anomalous couplings approaches. We also discuss the embeddings of the scattering amplitudes into physical collider processes, presenting the parametric SMEFT sensitivity to relevant top quark operators and paying special attention to the extent to which the high energy behaviour of the 2 → 2 amplitude is retained in the actual processes accessible at colliders. The effective W approximation is exploited to gain analytical insight into the embeddings of the 2 → 2 helicity amplitudes. Finally, we provide a compendium of processes detailing numerous directions in which the SMEFT parameter space can be accessed through high energy top quark processes in current and future colliders.
Highlights
One of the most fascinating aspects of spontaneously broken, non-Abelian gauge-Yukawa theories, such as the Standard Model (SM), is how the high-energy behaviour of scattering amplitudes seems to magically arise from a set of intricate cancellations between contributions that would otherwise display unacceptable energy growth
Therein, we identify the appearance of additional growth due to the violation of SU(2) gauge symmetry that leads to substantial differences between the Standard Model Effective Field Theory (SMEFT) and the anomalous couplings approaches
The impact of SMEFT operators in the Warsaw basis on the helicity amplitudes of 10 relevant scatterings is summarised in the appendix
Summary
One of the most fascinating aspects of spontaneously broken, non-Abelian gauge-Yukawa theories, such as the Standard Model (SM), is how the high-energy behaviour of scattering amplitudes seems to magically arise from a set of intricate cancellations between contributions that would otherwise display unacceptable energy growth. A natural strategy is to look for deviations from the precise structure of the SM predictions that may lead to the aforementioned anomalous energy growths in the amplitudes Such non-unitary behaviour in top quark scattering processes could be observed at high energy collider experiments and would indicate a limited range of validity of the SM description, implying the presence of new physics at higher scales. The Standard Model Effective Field Theory (SMEFT) is an appropriate framework to study these effects It describes deviations from SM interactions and the associated energy growth of scattering amplitudes with a minimal set of high-scale assumptions.
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