Joint resummation of two angularities at next-to-next-to-leading logarithmic order

Abstract

Multivariate analyses are emerging as important tools to understand properties of hadronic jets which play a key role in the LHC experimental program. We take a first step towards precise and differential theory predictions by calculating the cross section for $e^{+}{e}^{-}\to$ 2 jets differential in the angularities $e_{\alpha }$ and $e_{\beta }$. The logarithms of $e_{\alpha }$ and $e_{\beta }$ in the cross section are jointly resummed to next-to-next-to-leading logarithmic accuracy, using the SCET+ framework we developed, and are matched to the next-to-leading order cross section. We perform analytic one-loop calculations that serve as input for our numerical analysis, provide controlled theory uncertainties, and compare our results to Pythia. We also obtain predictions for the cross section differential in the ratio $e_{\alpha }/e_{\beta }$, which cannot be determined from a fixed-order calculation. The effect of nonperturbative corrections is also investigated. Using Event2, we validate the logarithmic structure of the single angularity cross section predicted by factorization theorems at $\mathcal{O}({\alpha }_s^2)$, demonstrating that for specific angularities recoil must be taken into account when using the thrust axis, while it can be ignored if these are measured with respect to the winner-take-all axis.

arXiv comment40 pages, 13 figures. v3: fixed a few minor typos

References in corpus (27)

• An Introduction to PYTHIA 8.2
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Identifying Boosted Objects with N-subjettiness
• Resummation of non-global QCD observables
• Energy Correlation Functions for Jet Substructure
• Maximizing Boosted Top Identification by Minimizing N-subjettiness
• Jet Shapes and Jet Algorithms in SCET
• Gaining (Mutual) Information about Quark/Gluon Discrimination
• Jet Shapes with the Broadening Axis
• Parton showers with quantum interference
• Pileup subtraction for jet shapes
• Logarithmic accuracy of parton showers: a fixed-order study
• Jet Observables Without Jet Algorithms
• Comparing and Counting Logs in Direct and Effective Methods of Resummation
• Non-Global Logarithms, Factorization, and the Soft Substructure of Jets
• Unsafe but Calculable: Ratios of Angularities in Perturbative QCD
• Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions
• NNLL Resummation for Jet Broadening
• Implementing NLO DGLAP evolution in Parton Showers
• Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k_T
• Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions
• Toward Multi-Differential Cross Sections: Measuring Two Angularities on a Single Jet
• Parton shower evolution with subleading color
• Factorization and Resummation for Generic Hierarchies between Jets
• The Fully-Differential Quark Beam Function at NNLO
• On the dependence of QCD splitting functions on the choice of the evolution variable
• Calculating Soft Radiation at One Loop

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