Consistent Factorization of Jet Observables in Exclusive Multijet Cross-Sections

TL;DR

This paper proves the consistency of a factorization theorem for jet shape observables in multijet e+e- collisions at NLL accuracy, accounting for various jet algorithms, numbers, and configurations, with detailed anomalous dimension cancellations.

Contribution

It demonstrates the NLL-level consistency of a SCET-based factorization theorem for jet shapes in multijet final states, including complex cancellations across different jet algorithms and configurations.

Findings

Factorization theorem is consistent at NLL for any number of jets.

Anomalous dimensions cancel intricately across different jet types and algorithms.

Results enable calculation of diverse jet observables to NLL accuracy.

Abstract

We demonstrate the consistency at the next-to-leading-logarithmic (NLL) level of a factorization theorem based on Soft-Collinear Effective Theory (SCET) for jet shapes in e+e- collisions. We consider measuring jet observables in exclusive multijet final states defined with cone and k_T-type jet algorithms. Consistency of the factorization theorem requires that the renormalization group evolution of hard, jet, and soft functions is such that the physical cross-section is independent of the factorization scale mu. The anomalous dimensions of the various factorized pieces, however, depend on the color representation of jets, choice of jet observable, the number of jets whose shapes are measured, and the jet algorithm, making it highly nontrivial to satisfy the consistency condition. We demonstrate the intricate cancellations between anomalous dimensions that occur at the NLL level, so that, up to power corrections that we identify, our factorization of the jet shape distributions is consistent for any number of quark and gluon jets, for any number of jets whose shapes are measured or unmeasured, for any angular size R of the jets, and for any of the algorithms we consider. Corrections to these results are suppressed by the SCET expansion parameter lambda (the ratio of soft to collinear or collinear to hard scales) and in the jet separation measure 1/t^2 = tan^2(R/2)/tan^2(psi/2), where psi is the angular separation between jets. Our results can be used to calculate a wide variety of jet observables in multijet final states to NLL accuracy.