Unitarity bounds on effective field theories at the LHC

Abstract

A bstract Effective Field Theory (EFT) extensions of the Standard Model are tools to compute observables (e.g. cross sections with partonic center-of-mass energy $$ \sqrt{\hat{s}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> </mml:msqrt> </mml:math> ) 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 &lt; $$ \sqrt{\hat{s}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> </mml:msqrt> </mml:math> , 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 $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> using an inclusive strategy, we typically do not have access to the event-by-event value of $$ \sqrt{\hat{s}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mover> <mml:mi>s</mml:mi> <mml:mo>̂</mml:mo> </mml:mover> </mml:msqrt> </mml:math> . 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 ≪ $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> . 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.

Topics & Concepts