Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders

Abstract

We introduce a method to compute one-loop soft functions for exclusive $N$-jet processes at hadron colliders, allowing for different definitions of the algorithm that determines the jet regions and of the measurements in those regions. In particular, we generalize the $N$-jettiness hemisphere decomposition of [Jouttenus 2011] in a manner that separates the dependence on the jet boundary from the observables measured inside the jet and beam regions. Results are given for several factorizable jet definitions, including anti-$k_T$, XCone, and other geometric partitionings. We calculate explicitly the soft functions for angularity measurements, including jet mass and jet broadening, in $pp\to L+1$ jet and explore the differences for various jet vetoes and algorithms. This includes a consistent treatment of rapidity divergences when applicable. We also compute analytic results for these soft functions in an expansion for a small jet radius $R$. We find that the small-$R$ results, including corrections up to $\mathcal{O}(R^2)$, accurately capture the full behavior over a large range of $R$.

33 pages + appendices, 17 figures, v2: journal version, v3: fixed typo in eq.(4.37)

References in corpus (13)

• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• Toward a NNLO calculation of the B-->X_s+gamma decay rate with a cut on photon energy: II. Two-loop result for the jet function
• The Quark Beam Function at NNLL
• C-parameter Distribution at N${}^3$LL${}^{\prime }$ including Power Corrections
• The gluon jet function at two-loop order
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
• On jet mass distributions in Z+jet and dijet processes at the LHC
• Glauber Gluons and Multiple Parton Interactions
• Precision Jet Substructure from Boosted Event Shapes
• The Gluon Beam Function at Two Loops
• Dissecting Soft Radiation with Factorization
• Factorization for Jet Radius Logarithms in Jet Mass Spectra at the LHC

Cited by in corpus (10)

• A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO
• Electroweak Logarithms in Inclusive Cross Sections
• Joint Two-Dimensional Resummation in $q_T$ and $0$-Jettiness at NNLL
• Factorization for Jet Radius Logarithms in Jet Mass Spectra at the LHC
• Jet angularity measurements for single inclusive jet production
• Transverse Vetoes with Rapidity Cutoff in SCET
• Exploring slicing variables for jet processes
• Transverse Momentum-Dependent Heavy-Quark Fragmentation at Next-to-Leading Order
• Consistent treatment of rapidity divergence in soft-collinear effective theory
• N-jettiness in electroweak high-energy processes