Unitarity Bounds on Effective Field Theories at the LHC

Abstract: Effective Field Theory (EFT) extensions of the Standard Model are tools to compute observables $\big(e.g.$ cross sections with partonic center-of-mass energy $\sqrt{\hat{s}}\,\big)$ as a systematically improvable expansion suppressed by a new physics scale $M$. If one is interested in EFT predictions in the parameter space where $M<\sqrt{\hat{s}}$, concerns of self-consistency emerge, which can manifest as a violation of perturbative partial-wave unitarity. However, when we search for the effects of an EFT at a hadron collider with center-of-mass energy $\sqrt{s}$ using an inclusive strategy, we typically do not have access to the event-by-event value of $\sqrt{\hat{s}}$. This motivates the need for a formalism that incorporates parton distribution functions into the perturbative partial-wave unitarity analysis. Developing such a framework and initiating an exploration of its implications is the goal of this work. Our approach opens up a potentially valid region of the EFT parameter space where $M \ll \sqrt{s}$. We provide evidence that there exist valid EFTs in this parameter space. The perturbative unitarity bounds are sensitive to the details of a given search, an effect we investigate by varying kinematic cuts.