Zero-jettiness soft function to third order in perturbative QCD

Abstract

We present the high-precision result for the zero-jettiness soft function at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. At this perturbative order, the soft function is the last missing ingredient required for the computation of a hadronic colour singlet production or a colour singlet decay into two jets using the zero-jettiness variable as the slicing parameter. Furthermore, the knowledge of the N3LO soft function enables the re-summed description of the thrust distribution in the process $e^{+}{e}^{-}\to \text{hadrons}$ through next-to-next-to-next-to-leading logarithmic order, which is important for the extraction of the strong coupling constant using this shape variable. On the methodological side, the complexity of the zero-jettiness variable forced us to develop a new semi-analytic method for phase-space integration in the presence of constraints parameterized through Heaviside functions which, hopefully, will be useful for further development of the $N$-jettiness slicing scheme.

arXiv comment6 pages, attached results in computer readable form

References in corpus (52)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Higgs boson production at hadron colliders in NNLO QCD
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• An automatized algorithm to compute infrared divergent multi-loop integrals
• N-Jettiness: An Inclusive Event Shape to Veto Jets
• Kira - A Feynman Integral Reduction Program
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Integral Reduction with Kira 2.0 and Finite Field Methods
• Structure functions for large $x$ and renormalization of Wilson loops
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• $W$-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD
• Factorization at the LHC: From PDFs to Initial State Jets
• Color singlet production at NNLO in MCFM
• Three-Loop Results for Quark and Gluon Form Factors
• Numerical evaluation of multi-loop integrals by sector decomposition
• Virtual corrections to gg -> H to two loops in the heavy top limit
• The Quark Form Factor at Higher Orders
• Two-Loop Quark and Gluon Form Factors in Dimensional Regularisation
• Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region
• The two-loop hemisphere soft function
• Subleading Power Corrections for N-Jettiness Subtractions
• Collider Physics at the Precision Frontier
• Higgs boson production at the LHC using the $q_T$ subtraction formalism at N${}^3$LO QCD
• The N-jettiness soft function at next-to-next-to-leading order
• The two-loop soft current in dimensional regularization
• The Quark Beam Function at Two Loops
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
• EERAD3: Event shapes and jet rates in electron-positron annihilation at order ${\alpha }_s^3$
• The Gluon Beam Function at Two Loops
• The Three-loop Quark Jet Function
• Fiducial Drell-Yan production at the LHC improved by transverse-momentum resummation at N${}^4$LL+N${}^3$LO
• Third order fiducial predictions for Drell-Yan at the LHC
• A Composite Higgs with a Heavy Composite Axion
• A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO
• Triple (and quadruple) soft-gluon radiation in QCD hard scattering
• Transverse Mass Distribution and Charge Asymmetry in W Boson Production to Third Order in QCD
• Gluon jet function at three loops in QCD
• N-jettiness beam functions at N3LO
• The NNLO QCD soft function for 1-jettiness
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• Third order QCD predictions for fiducial W-boson production
• Collinear expansion for color singlet cross sections
• Next-to-Next-to-Leading Order $N$-Jettiness Soft Function for One Massive Colored Particle Production at Hadron Colliders
• NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter $\epsilon$
• Tree-level soft emission of a quark pair in association with a gluon
• The spin-dependent quark beam function at NNLO
• Same-hemisphere three-gluon-emission contribution to the zero-jettiness soft function at N3LO QCD
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• The NNLO soft function for N-jettiness in hadronic collisions
• Transverse momentum resummation at N3LL+NNLO for diboson processes
• Two-loop $N$-jettiness soft function for $pp\to 2j$ production
• One-loop corrections to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD

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• Precision $e^{+}{e}^{-}$ Hemisphere Masses in the Dijet Region with Power Corrections
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