The Quark Beam Function at NNLL

Abstract

In hard collisions at a hadron collider the most appropriate description of the initial state depends on what is measured in the final state. Parton distribution functions (PDFs) evolved to the hard collision scale Q are appropriate for inclusive observables, but not for measurements with a specific number of hard jets, leptons, and photons. Here the incoming protons are probed and lose their identity to an incoming jet at a scale μ_B << Q, and the initial state is described by universal beam functions. We discuss the field-theoretic treatment of beam functions, and show that the beam function has the same RG evolution as the jet function to all orders in perturbation theory. In contrast to PDF evolution, the beam function evolution does not mix quarks and gluons and changes the virtuality of the colliding parton at fixed momentum fraction. At μ_B, the incoming jet can be described perturbatively, and we give a detailed derivation of the one-loop matching of the quark beam function onto quark and gluon PDFs. We compute the associated NLO Wilson coefficients and explicitly verify the cancellation of IR singularities. As an application, we give an expression for the next-to-next-to-leading logarithmic order (NNLL) resummed Drell-Yan beam thrust cross section.

54 pages, 9 figures; v2: notation simplified in a few places, typos fixed; v3: journal version

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Cited by in corpus (111)

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• An Effective Field Theory for Forward Scattering and Factorization Violation
• Subleading Power Corrections for N-Jettiness Subtractions
• Higgs-Boson Production at Small Transverse Momentum
• Matching the Quasi Parton Distribution in a Momentum Subtraction Scheme
• The Quark Beam Function at Two Loops
• Introduction to GPDs and TMDs
• Factorization and Resummation for Dijet Invariant Mass Spectra
• The Beam Thrust Cross Section for Drell-Yan at NNLL Order
• Jet Mass Spectra in Higgs + One Jet at NNLL
• Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation
• Resummation of Transverse Momentum Distributions in Distribution Space
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
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• Resummation of Double-Differential Cross Sections and Fully-Unintegrated Parton Distribution Functions
• Parton Fragmentation within an Identified Jet at NNLL
• Rapidity renormalized TMD soft and beam functions at two loops
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• Collinear and TMD Quark and Gluon Densities from Parton Branching Solution of QCD Evolution Equations
• Fragmentation in Jets at NNLO
• Glauber Gluons and Multiple Parton Interactions
• Resummation Properties of Jet Vetoes at the LHC
• The Gluon Beam Function at Two Loops
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• Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k_T
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• N-Jettiness Subtractions for $gg\to H$ at Subleading Power
• An Explanation of the WW Excess at the LHC by Jet-Veto Resummation
• The Three-loop Quark Jet Function
• Power Corrections for N-Jettiness Subtractions at $\mathcal{O}({\alpha }_s)$
• Momentum Broadening in Weakly Coupled Quark-Gluon Plasma (with a view to finding the quasiparticles within liquid quark-gluon plasma)
• Higgsstrahlung at NNLL${}^{\prime }+$NNLO Matched to Parton Showers in GENEVA
• XCone: N-jettiness as an Exclusive Cone Jet Algorithm
• The Nucleon Energy Correlators
• Single-top-quark production in the $t$-channel at NNLO
• Forward Jets and Energy Flow in Hadronic Collisions
• A Toolbox for $q_T$ and $0$-Jettiness Subtractions at N${}^3$LO
• The Energy-Energy Correlation in the back-to-back limit at N${}^3$LO and N${}^3$LL${}^{\prime }$
• Factorization and Resummation for Generic Hierarchies between Jets
• Factorization connecting continuum and lattice TMDs
• Next-to-leading power corrections to $V+1$ jet production in $N$-jettiness subtraction
• Transverse Momentum Distributions from Effective Field Theory with Numerical Results
• Factorization and Resummation for Massive Quark Effects in Exclusive Drell-Yan
• Rapidity-Dependent Jet Vetoes
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• N-jettiness beam functions at N3LO
• Transverse Momentum Distributions in the Non-Perturbative Region
• Factorization for Jet Radius Logarithms in Jet Mass Spectra at the LHC
• Two-Loop Radiative Jet Function for Exclusive $B$-Meson and Higgs Decays
• Jet Vetoes Interfering with H->WW
• Heavy Quark Fragmenting Jet Functions
• Employing Helicity Amplitudes for Resummation
• Probing nuclear dynamics in jet production with a global event shape
• Zero-jettiness resummation for top-quark pair production at the LHC
• The Fully-Differential Quark Beam Function at NNLO
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• Underlying event sensitive observables in Drell-Yan production using GENEVA
• Jet Veto Resummation with Jet Rapidity Cuts
• Extending the MINLO method
• Two-Loop Beam and Soft Functions for Rapidity-Dependent Jet Vetoes
• Next-to-Next-to-Leading Order $N$-Jettiness Soft Function for One Massive Colored Particle Production at Hadron Colliders
• Collinear expansion for color singlet cross sections
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• N-jettiness Subtractions for NNLO QCD Calculations
• The spin-dependent quark beam function at NNLO
• Lattice QCD calculation of the pion distribution amplitude with domain wall fermions at physical pion mass
• Final state interactions in single- and multi-particle inclusive cross sections for hadronic collisions
• Variable Flavor Number Scheme for Final State Jets in DIS
• Double-real contribution to the quark beam function at N${}^3$LO QCD
• Leading jets and energy loss
• The Fully-Differential Gluon Beam Function at NNLO
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• Coulomb gluons will generally destroy coherence
• Power Counting and Modes in SCET
• Collinear functions for QCD resummations
• Angularity in DIS at next-to-next-to-leading log accuracy
• Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders
• Jet energy drop
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• The NNLO quark beam function for jet-veto resummation
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• NNLO electron structure functions (PDFs) from SCET
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• Combining Fixed-Order Helicity Amplitudes With Resummation Using SCET
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• Effective Field Theories for the LHC
• Revisiting evolution equations for generalised parton distributions
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• N-jettiness in electroweak high-energy processes
• Nucleon Tomography with 0-jettiness
• Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis)
• Soft Integrals and Soft Anomalous Dimensions at N${}^3$LO and Beyond
• Jet Charge with Global Event Shapes: Probing Quark Flavor Dynamics