The Quark Beam Function at Two Loops

Abstract

In differential measurements at a hadron collider, collinear initial-state radiation is described by process-independent beam functions. They are the field-theoretic analog of initial-state parton showers. Depending on the measured observable they are differential in the virtuality and/or transverse momentum of the colliding partons in addition to the usual longitudinal momentum fraction. Perturbatively, the beam functions can be calculated by matching them onto standard quark and gluon parton distribution functions. We calculate the inclusive virtuality-dependent quark beam function at NNLO, which is relevant for any observables probing the virtuality of the incoming partons, including N-jettiness and beam thrust. For such observables, our results are an important ingredient in the resummation of large logarithms at N3LL order, and provide all contributions enhanced by collinear t-channel singularities at NNLO for quark-initiated processes in analytic form. We perform the calculation in both Feynman and axial gauge and use two different methods to evaluate the discontinuity of the two-loop Feynman diagrams, providing nontrivial checks of the calculation. As part of our results we reproduce the known two-loop QCD splitting functions and confirm at two loops that the virtuality-dependent beam and final-state jet functions have the same anomalous dimension.

arXiv comment27 pages, 3 figures; v2: journal version

References in corpus (50)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Invariant Operators in Collinear Effective Theory
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• Hard Scattering Factorization from Effective Field Theory
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory
• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• N-Jettiness: An Inclusive Event Shape to Veto Jets
• JaxoDraw: A graphical user interface for drawing Feynman diagrams. Version 2.0 release notes
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone
• A precise determination of alpha_s from LEP thrust data using effective field theory
• Factorization at the LHC: From PDFs to Initial State Jets
• Universality of non-leading logarithmic contributions in transverse-momentum distributions
• Higgs Production with a Central Jet Veto at NNLL+NNLO
• Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions
• Vector boson production at hadron colliders: hard-collinear coefficients at the NNLO
• QCD transverse-momentum resummation in gluon fusion processes
• Jet p_T Resummation in Higgs Production at NNLL'+NNLO
• Universality of transverse-momentum resummation and hard factors at the NNLO
• The Quark Beam Function at NNLL
• Factorization and NNLL Resummation for Higgs Production with a Jet Veto
• Transverse parton distribution functions at next-to-next-to-leading order: the quark-to-quark case
• Factorization and N^3LL_p+NNLO Predictions for the Higgs Cross Section with a Jet Veto
• Higgs-Boson Production at Small Transverse Momentum
• Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering
• The Beam Thrust Cross Section for Drell-Yan at NNLL Order
• Jet Mass Spectra in Higgs + One Jet at NNLL
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
• Factorization and Resummation of Higgs Boson Differential Distributions in Soft-Collinear Effective Theory
• Resummation Properties of Jet Vetoes at the LHC
• Using 1-Jettiness to Measure 2 Jets in DIS 3 Ways
• The Gluon Beam Function at Two Loops
• Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k_T
• Resummation of Large Endpoint Corrections to Color-Octet J/psi Photoproduction
• Higgs boson production at hadron colliders: hard-collinear coefficients at the NNLO
• Resummation of jet-veto logarithms in hadronic processes containing jets
• Fragmentation in Jets: Cone and Threshold Effects
• The 1-Jettiness DIS event shape: NNLL + NLO results
• Transverse Momentum Distributions from Effective Field Theory with Numerical Results
• The evolution of parton distributions beyond leading order: the singlet case
• N-Jettiness as a probe of nuclear dynamics
• Transverse Momentum Distributions in the Non-Perturbative Region
• Probing nuclear dynamics in jet production with a global event shape
• Next-to-Leading Order Hard Scattering Using Fully Unintegrated Parton Distribution Functions
• Transverse Parton Distribution Functions at Next-To-Next-To-Leading-Order

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