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

References in corpus (11)

• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Dynamical Threshold Enhancement and Resummation in Drell-Yan Production
• Treating the b quark distribution function with reliable uncertainties
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory
• Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production
• Resummation and NLO Matching of Event Shapes with Effective Field Theory
• The Beam Thrust Cross Section for Drell-Yan at NNLL Order
• Resummation of Large Endpoint Corrections to Color-Octet J/psi Photoproduction
• On The Equivalence of Soft and Zero-Bin Subtractions
• Soft-Gluon Cancellation, Phases and Factorization with Initial-State Partons

Cited by in corpus (7)

• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• The Beam Thrust Cross Section for Drell-Yan at NNLL Order
• The Soft Function for Exclusive N-Jet Production at Hadron Colliders
• Parton Fragmentation within an Identified Jet at NNLL
• Transverse Momentum Distributions from Effective Field Theory with Numerical Results
• Transverse Momentum Distributions in the Non-Perturbative Region
• Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis)