A Conformal Bridge for the Light Transform of QCD Correlation Functions

TL;DR

This paper introduces a method to apply conformal field theory techniques to QCD correlation functions by using a conformal bridge via the Wilson-Fisher fixed point, enabling higher-loop light transform calculations.

Contribution

It develops a novel approach to evaluate the light transform of QCD correlation functions at higher loops using conformal techniques at the Wilson-Fisher fixed point.

Findings

Successfully computed the two-loop charge-charge correlation in QCD.

Reproduced recent theoretical predictions for collider correlators.

Demonstrated the utility of conformal methods in non-conformal gauge theories.

Abstract

Understanding the link between correlation functions (CFs) of local operators and measurable collider correlators has emerged as a new opportunity in the study of gauge theory dynamics at colliders. While in Conformal Field Theories (CFTs) this connection is established by the light transform, the non-conformal nature of QCD complicates its use beyond the lowest perturbative order. We show that a continuation of the CFs to the Wilson-Fisher fixed point can be used as a method to overcome these obstacles, serving as a conformal bridge for the evaluation of the light transform. At the fixed point, the renormalized CF of four local operators features a variable drop and only depends on two conformal cross ratios, in line with a genuine CFT quantity. This allows us to exploit CFT techniques to perform, for the first time, its light transform at higher loop orders. Remarkably, the resulting collider correlator in four dimensions can be recovered from this result simply by using lower-loop data. We demonstrate this method by computing the back-to-back limit of the charge-charge correlation (QQC) at two loops in QCD through the light transform of the CF of four vector currents in the sequential light-cone limit, reproducing a recent prediction.