The Transverse Energy-Energy Correlator in the Back-to-Back Limit

TL;DR

The paper develops an operator-based SCET factorization for the transverse energy-energy correlator (TEEC) in the hadron-collider back-to-back (dijet) limit, expressing the cross section as a convolution of a hard function, TMD beam and jet functions, and a new dijet soft function projected onto the scattering plane. The soft function’s simple structure enables analytic NNLO results and, together with RG evolution in $\mu$ and $\nu$, facilitates NNLL resummation of the TEEC, which is then matched to fixed-order calculations. Numerical results at 13 TeV demonstrate that the factorization reproduces the singular behavior and that NNLL+NLO predictions stabilize the distribution and reduce uncertainties in the dijet region. The work establishes TEEC as a precise, tractable probe of QCD at the LHC and a clean arena to study factorization and its possible violations, with clear avenues for future higher-order and nonperturbative extensions.

Abstract

We present an operator based factorization formula for the transverse energy-energy correlator (TEEC) hadron collider event shape in the back-to-back (dijet) limit. This factorization formula exhibits a remarkably symmetric form, being a projection onto a scattering plane of a more standard transverse momentum dependent factorization. Soft radiation is incorporated through a dijet soft function, which can be elegantly obtained to next-to-next-to-leading order (NNLO) due to the symmetries of the problem. We present numerical results for the TEEC resummed to next-to-next-to-leading logarithm (NNLL) matched to fixed order at the LHC. Our results constitute the first NNLL resummation for a dijet event shape observable at a hadron collider, and the first analytic result for a hadron collider dijet soft function at NNLO. We anticipate that the theoretical simplicity of the TEEC observable will make it indispensable for precision studies of QCD at the LHC, and as a playground for theoretical studies of factorization and its violation.

Figures (5)

• Figure 1: The TEEC measures the $E_T$ weighted angular correlation of pairs of particles as a function of the angle $\phi$ in the transverse plane. In the $\phi \rightarrow \pi$ limit, it measures the momentum in the direction $\hat{y}$ perpendicular to the scattering plane spanned by the beam and jet axes, outlined in dashed blue.
• Figure 2: The spatial structure of the TEEC soft function. Each set of Wilson lines lies in a scattering plane, and their relative displacement is perpendicular to these planes.
• Figure 3: The TEEC at LO and NLO in the dijet limit. Here $\delta$NLO denotes only the NLO corrections.
• Figure 4: Fixed order singular and non-singular terms for the TEEC in the dijet limit.
• Figure 5: The resummed TEEC distribution matched to fixed order at both NLL+LO and NNLL+NLO.