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.

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

References in corpus (22)

• The Color Glass Condensate
• A first unbiased global determination of polarized PDFs and their uncertainties
• Evidence for polarization of gluons in the proton
• Transverse-momentum distributions in a diquark spectator model
• Multiplicities of charged pions and kaons from semi-inclusive deep-inelastic scattering by the proton and the deuteron
• Parton distributions and lattice QCD calculations: toward 3D structure
• Parton Distributions in Nucleons and Nuclei
• Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering
• Transverse-momentum-dependent gluon distribution functions in a spectator model
• Kinematics of Current Region Fragmentation in Semi-Inclusive Deeply Inelastic Scattering
• 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
• Quasi-parton distribution functions: a study in the diquark spectator model
• Phenomenology of NNLO jet production at the LHC and its impact on parton distributions
• Isovector EMC effect from global QCD analysis with MARATHON data
• Improved formulation of global QCD analysis with zero-mass hard cross sections
• Accessing the nucleon transverse structure in inclusive deep inelastic scattering
• Interplay of Threshold Resummation and Hadron Mass Corrections in Deep Inelastic Processes
• Probing Nucleons and Nuclei in High Energy Collisions
• What does kinematical target mass sensitivity in DIS reveal about hadron structure?
• 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