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.
Highlights
Introduction.—Event shape observables, which measure the flow of radiation in a scattering event, play a central role in QCD
Many interesting effects, namely nontrivial color evolution and amplitude level factorization violation, first occur for dijet event shapes, for which complete results are only available at NLL [13,14,15,16,17,18]
Apart from a brief comment on the anomalous dimension of the soft function at N3LO, we leave the study of violations of this factorization formula to future work, and restrict ourselves to next-to-next-to-leading logarithm (NNLL) accuracy where Eq (3) holds
Summary
Introduction.—Event shape observables, which measure the flow of radiation in a scattering event, play a central role in QCD. The singular behavior of the observable is described by a dijet configuration, with collinear radiation along the beam and jet axes, as well as low energy soft radiation. The relationship in Eq (2) allows us to derive a factorization formula for the TEEC in the dijet limit in terms of standard transverse momentum dependent (TMD)
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