Conformal Colliders Meet the LHC

• Published in: arXiv.org
• Main Authors: Lee, Kyle, Meçaj, Bianka, Moult, Ian
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 06.05.2022
• Subjects: Correlators; Density; Energy flow; Factorization; Field theory; Large Hadron Collider; Light; Operators (mathematics); Phenomenology; Quantum chromodynamics; Scaling; Solenoids; Theorems; Transverse momentum
• ISSN: 2331-8422

The remarkably high energies of the Large Hadron Collider (LHC) have allowed for the first measurements of the shapes and scalings of multi-point correlators of energy flow operators, \(\langle \Psi | \mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2) \cdots \mathcal{E}(\vec n_k) |\Psi \rangle\), 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, \(\rho= |\Psi\rangle \langle \Psi |\), inside high transverse momentum jets at the LHC. Using the light-ray operator product expansion, the scaling behavior of multi-point correlators can be computed from the expectation value of the twist-2 spin-\(J\) light-ray operators, \(\mathbb{O}^{[J]}\), in this state, \(\text{Tr}[ \rho ~\mathbb{O}^{[J]} ]\). 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.