Calculating Soft Radiation at One Loop

Abstract

We present an efficient way to calculate the effect of soft QCD radiation at one loop, which is needed for predictions at next-to-next-to-leading logarithmic accuracy. We use rapidity coordinates and isolate the divergences in the integrand. By performing manipulations with cumulative variables, we avoid complications from plus distributions. We address rapidity divergences, divergences with an azimuthal dependence, complicated jet boundaries and multi-differential measurements. The process and measurements can be easily adjusted, as we demonstrate by reproducing many existing soft functions. The results for a general LHC process with multiple Wilson lines are obtained by treating Wilson lines that are not back-to-back using a boost. We also obtain, for the first time, the N-jettiness soft function for generic jet angularities, and the collinear-soft function for the measurement of two angularities.

arXiv comment21 pages, 1 figure; v2: references added

References in corpus (21)

• A General Algorithm for Calculating Jet Cross Sections in NLO QCD
• Invariant Operators in Collinear Effective Theory
• The Dipole Formalism for the Calculation of QCD Jet Cross Sections at Next-to-Leading Order
• An automatized algorithm to compute infrared divergent multi-loop integrals
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• N-Jettiness: An Inclusive Event Shape to Veto Jets
• The Rapidity Renormalization Group
• Jet Shapes with the Broadening Axis
• Universal structure of subleading infrared poles in gauge theory amplitudes
• Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions
• Analytic Regularization in Soft-Collinear Effective Theory
• NLL+NNLO predictions for jet-veto efficiencies in Higgs-boson and Drell-Yan production
• Resummed event shapes at hadron-hadron colliders
• Infrared divergences and non-lightlike eikonal lines in Sudakov processes
• 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
• 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
• XCone: N-jettiness as an Exclusive Cone Jet Algorithm

Cited by in corpus (12)

• The transverse momentum distribution of hadrons within jets
• The Energy Distribution of Subjets and the Jet Shape
• A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO
• Joint transverse momentum and threshold resummation beyond NLL
• Generic dijet soft functions at two-loop order: correlated emissions
• Factorization for Jet Radius Logarithms in Jet Mass Spectra at the LHC
• Joint resummation of two angularities at next-to-next-to-leading logarithmic order
• Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders
• The NNLO soft function for N-jettiness in hadronic collisions
• Consistent treatment of rapidity divergence in soft-collinear effective theory
• N${}^3$LL + $\mathcal{O}({\alpha }_s^2)$ predictions of lepton-jet azimuthal angular distribution in deep-inelastic scattering
• One-loop Jet Functions by Geometric Subtraction