Conformal collider physics meets LHC data

Abstract

The remarkably high energies of the Large Hadron Collider (LHC) have allowed for the first measurements of the shapes and scalings of multipoint correlators of energy flow operators, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo stretchy="false">⟨</a:mo> <a:mi mathvariant="normal">Ψ</a:mi> <a:mo stretchy="false">|</a:mo> <a:mi mathvariant="script">E</a:mi> <a:mo stretchy="false">(</a:mo> <a:msub> <a:mover accent="true"> <a:mi>n</a:mi> <a:mo stretchy="false">→</a:mo> </a:mover> <a:mn>1</a:mn> </a:msub> <a:mo stretchy="false">)</a:mo> <a:mi mathvariant="script">E</a:mi> <a:mo stretchy="false">(</a:mo> <a:msub> <a:mover accent="true"> <a:mi>n</a:mi> <a:mo stretchy="false">→</a:mo> </a:mover> <a:mn>2</a:mn> </a:msub> <a:mo stretchy="false">)</a:mo> <a:mo>⋯</a:mo> <a:mi mathvariant="script">E</a:mi> <a:mo stretchy="false">(</a:mo> <a:msub> <a:mover accent="true"> <a:mi>n</a:mi> <a:mo stretchy="false">→</a:mo> </a:mover> <a:mi>k</a:mi> </a:msub> <a:mo stretchy="false">)</a:mo> <a:mo stretchy="false">|</a:mo> <a:mi mathvariant="normal">Ψ</a:mi> <a:mo stretchy="false">⟩</a:mo> </a:math> , providing new insights into the Lorentzian dynamics of quantum chromodynamics (QCD). In this letter, we use recent advances in effective field theory to derive a rigorous factorization theorem for the light-ray density matrix, <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mi>ρ</x:mi> <x:mo>=</x:mo> <x:mo stretchy="false">|</x:mo> <x:mi mathvariant="normal">Ψ</x:mi> <x:mo stretchy="false">⟩</x:mo> <x:mo stretchy="false">⟨</x:mo> <x:mi mathvariant="normal">Ψ</x:mi> <x:mo stretchy="false">|</x:mo> </x:math> , inside high transverse momentum jets at the LHC. Using the light-ray operator product expansion, the scaling behavior of multipoint correlators can be computed from the expectation value of the twist-2 spin- <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mi>J</fb:mi> </fb:math> light-ray operators, <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:msup> <hb:mi mathvariant="double-struck">O</hb:mi> <hb:mrow> <hb:mo stretchy="false">[</hb:mo> <hb:mi>J</hb:mi> <hb:mo stretchy="false">]</hb:mo> </hb:mrow> </hb:msup> </hb:math> , in this state, <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi>Tr</mb:mi> <mb:mo stretchy="false">[</mb:mo> <mb:mi>ρ</mb:mi> <mb:msup> <mb:mi mathvariant="double-struck">O</mb:mi> <mb:mrow> <mb:mo stretchy="false">[</mb:mo> <mb:mi>J</mb:mi> <mb:mo stretchy="false">]</mb:mo> </mb:mrow> </mb:msup> <mb:mo stretchy="false">]</mb:mo> </mb:math> . We compute the light-ray density matrix at next-to-leading order, and combine this with results for the next-to-leading logarithmic scaling behavior of the correlators up to six-points, comparing with CMS open data. This theoretical accuracy allows us to resolve the quantum scaling dimensions of QCD light-ray operators inside jets at the LHC. Our factorization theorem for the light-ray density matrix at the LHC completes the link between recent developments in the study of energy correlators and LHC phenomenology, opening the door to a wide variety of precision jet substructure studies.

Topics & Concepts