Collinear Factorization at sub-asymptotic kinematics and validation in a diquark spectator model

Abstract

We revisit the derivation of collinear factorization for Deep Inelastic Scattering at sub-asymptotic values of the four momentum transfer squared, where the masses of the particles participating in the interaction cannot be neglected. By using an inclusive jet function to describe the scattered quark final state, we can restrict the needed parton kinematic approximations just to the four-momentum conservation of the hard scattering process, and explicitly expand the rest of the diagram in powers of the unobserved parton transverse momenta rather than neglecting those. This procedure provides one with more flexibility in fixing the virtuality of the scattered and recoiling partons than in the standard derivation, and naturally leads to scaling variables that more faithfully represent the partonic kinematic at sub-asymptotic energy than the Bjorken's xB variable. We then verify the validity of the obtained factorization formula by considering a diquark spectator model designed to reproduce the main features of electron-proton scattering at large $x_B$ in Quantum Chromo-Dynamics. In the model, the Deep Inelastic Scattering contribution to the cross section can be explicitly isolated and analytically calculated, then compared to the factorized approximation. Limiting ourselves to the leading twist contribution, we then show that use of the new scaling variables maximizes the kinematic range of validity of collinear factorization, and highlight the intrinsic limitations of this approach due to the unavoidably approximate treatment of four momentum conservation in factorized diagrams. Finally, we briefly discuss how these limitations may be overcome by including higher-twist corrections to the factorized calculation.

arXiv commentThoroughly rewritten for conceptual clarity, with theoretical discussion upfront and model validation following this. Expanded bibliography

References in corpus (66)

• The Color Glass Condensate
• New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC
• Semi-inclusive deep inelastic scattering at small transverse momentum
• The Spin Structure of the Nucleon
• Parton Distribution Functions, ${\alpha }_s$ and Heavy-Quark Masses for LHC Run II
• A Modification of the Saturation Model: DGLAP evolution
• A first unbiased global determination of polarized PDFs and their uncertainties
• Physics Opportunities with the 12 GeV Upgrade at Jefferson Lab
• Evidence for polarization of gluons in the proton
• Constraints on large-$x$ parton distributions from new weak boson production and deep-inelastic scattering data
• AKK Update: Improvements from New Theoretical Input and Experimental Data
• Transverse-momentum distributions in a diquark spectator model
• Parton distributions and lattice QCD calculations: a community white paper
• The Structure of the Proton in the LHC Precision Era
• Leptoproduction of Heavy Quarks I-- General Formalism and Kinematics of Charged Current and Neutral Current Production Processes
• Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data
• Multiplicities of charged pions and kaons from semi-inclusive deep-inelastic scattering by the proton and the deuteron
• A ZEUS next-to-leading-order QCD analysis of data on deep inelastic scattering
• Global parton distributions with nuclear and finite-Q^2 corrections
• Open Heavy Flavor Production in QCD -- Conceptual Framework and Implementation Issues
• Parton distributions and lattice QCD calculations: toward 3D structure
• Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum
• Quark-hadron duality in electron scattering
• Quark-Hadron Duality in Electron Scattering
• Parton Distributions in Nucleons and Nuclei
• A Review of Target Mass Corrections
• Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering
• Measurement of D^(*+-) Meson Production and F_2^c in Deep-Inelastic Scattering at HERA
• Quark Fragmentation within an Identified Jet
• Transverse-momentum-dependent gluon distribution functions in a spectator model
• Monte Carlo sampling variant of the DSSV14 set of helicity parton densities
• New parton distributions from large-x and low-Q^2 data
• Parton momentum and helicity distributions in the nucleon
• Target Mass Corrections to Electro-Weak Structure Functions and Perturbative Neutrino Cross Sections
• Kinematics of Current Region Fragmentation in Semi-Inclusive Deeply Inelastic Scattering
• Collinear factorization for deep inelastic scattering structure functions at large Bjorken xB
• Deep inelastic cross-section measurements at large y with the ZEUS detector at HERA
• Multiplicities of charged kaons from deep-inelastic muon scattering off an isoscalar target
• An estimate of higher twist at small x and low Q^2 based upon a saturation model
• Isospin Dependence of Power Corrections in Deep Inelastic Scattering
• Quasi-parton distribution functions: a study in the diquark spectator model
• Mapping the Kinematical Regimes of Semi-Inclusive Deep Inelastic Scattering
• Phenomenology of NNLO jet production at the LHC and its impact on parton distributions
• Isovector EMC effect from global QCD analysis with MARATHON data
• Challenges with Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering
• Study of HERA ep Data at Low Q^2 and Low x_Bj and the Need for Higher-Twist Corrections to Standard pQCD Fits
• Differential Top Quark Pair Production at the LHC: Challenges for PDF Fits
• Improved formulation of global QCD analysis with zero-mass hard cross sections
• Parton distributions in the presence of target mass corrections
• Impact of PDF uncertainties at large x on heavy boson production
• Accessing the nucleon transverse structure in inclusive deep inelastic scattering
• Hadron mass corrections in semi-inclusive deep-inelastic scattering
• Interplay of Threshold Resummation and Hadron Mass Corrections in Deep Inelastic Processes
• Infrared Scales and Factorization in QCD
• Higher-twist quark-mass contributions to deep-inelastic scattering
• Probing Nucleons and Nuclei in High Energy Collisions
• What does kinematical target mass sensitivity in DIS reveal about hadron structure?
• Hadron mass corrections in semi-inclusive deep inelastic scattering
• Quark fragmentation as a probe of dynamical mass generation
• K${}^{-}$ over K${}^{+}$ multiplicity ratio for kaons produced in DIS with a large fraction of the virtual-photon energy
• Gauge invariance and kaon production in deep inelastic scattering at low scales
• Virtuality and Transverse Momentum Dependence of Pion Distribution Amplitude
• Evidence of quasi-partonic higher-twist effects in deep inelastic scattering at HERA at moderate $Q^2$
• What are the low-$Q$ and large-$x$ boundaries of collinear QCD factorization theorems?
• Antiproton over proton and K${}^{-}$ over K${}^{+}$ multiplicity ratios at high $z$ in DIS
• Bayesian Monte Carlo extraction of sea asymmetry with SeaQuest and STAR data

Cited by in corpus (1)

• Basics of factorization in a scalar Yukawa field theory