On the Edge of Safety: Charge-Charge Correlation in the Back-to-Back Limit

Abstract

We investigate the Charge-Charge Correlation (QQC) in electron-positron annihilation as a probe of charge dynamics in Quantum Chromodynamics. While generally divergent beyond leading order, we show that the QQC is infrared and collinear safe in the back-to-back limit, a property that we dub leading-power safety. This enables an analytic perturbative treatment that bypasses the reliance on non-perturbative track or fragmentation functions. Using Soft-Collinear Effective Field Theory, we derive a factorization theorem and determine its logarithmic behavior analytically up to four loops in QCD, uncovering remarkable connections with the Energy-Energy Correlation (EEC). Prior to this work, the behavior of the QQC beyond leading order was entirely unknown; we now establish its resummation to next-to-next-to-next-to-next-to-leading logarithmic (N$^4$LL) accuracy, placing it among the observables with the highest perturbative precision alongside the EEC. Our results are validated through a numerical analysis using Event2, exhibiting excellent agreement with the predicted singular terms. This work establishes the QQC as a novel, calculable probe of charge dynamics and unveils a new window into the inner workings of non-Abelian gauge theories.