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Semi-Inclusive Hadron Production at HERA: the Effect of QCD Gluon Resummation

P. Nadolsky, D. R. Stump, C. -P. Yuan

TL;DR

The paper extends the Collins-Soper-Sterman resummation formalism to semi-inclusive deep-inelastic scattering in the current region, addressing large logarithms that arise when the final-state transverse momentum q_T is small compared to the hard scale Q. It develops a general framework incorporating fragmentation functions, derives resummed and matched cross-sections, and applies the formalism to transverse energy flows and charged-particle multiplicities observed at HERA. The results show good agreement with H1 energy-flow data in the current region and illuminate the limitations of fixed-order perturbation theory at small q_T, while highlighting the role of nonperturbative Sudakov factors and fragmentation uncertainties. The work lays the groundwork for a broader analysis of hadron multiplicities and suggests avenues for constraining nonperturbative effects through combined DIS, Drell-Yan, and e+e- data, with future NNLO improvements and richer datasets needed for tighter constraints.

Abstract

We present a formalism that improves the applicability of perturbative QCD in the current region of semi-inclusive deep inelastic scattering. The formalism is based on all-order resummation of large logarithms arising in the perturbative treatment of hadron multiplicities and energy flows in this region. It is shown that the current region of semi-inclusive DIS is similar to the region of small transverse momenta in vector boson production at hadron colliders. We use this resummation formalism to describe transverse energy flows and charged particle multiplicity measured at the electron-proton collider HERA. We find good agreement between our theoretical results and experimental data for the transverse energy flows.

Semi-Inclusive Hadron Production at HERA: the Effect of QCD Gluon Resummation

TL;DR

The paper extends the Collins-Soper-Sterman resummation formalism to semi-inclusive deep-inelastic scattering in the current region, addressing large logarithms that arise when the final-state transverse momentum q_T is small compared to the hard scale Q. It develops a general framework incorporating fragmentation functions, derives resummed and matched cross-sections, and applies the formalism to transverse energy flows and charged-particle multiplicities observed at HERA. The results show good agreement with H1 energy-flow data in the current region and illuminate the limitations of fixed-order perturbation theory at small q_T, while highlighting the role of nonperturbative Sudakov factors and fragmentation uncertainties. The work lays the groundwork for a broader analysis of hadron multiplicities and suggests avenues for constraining nonperturbative effects through combined DIS, Drell-Yan, and e+e- data, with future NNLO improvements and richer datasets needed for tighter constraints.

Abstract

We present a formalism that improves the applicability of perturbative QCD in the current region of semi-inclusive deep inelastic scattering. The formalism is based on all-order resummation of large logarithms arising in the perturbative treatment of hadron multiplicities and energy flows in this region. It is shown that the current region of semi-inclusive DIS is similar to the region of small transverse momenta in vector boson production at hadron colliders. We use this resummation formalism to describe transverse energy flows and charged particle multiplicity measured at the electron-proton collider HERA. We find good agreement between our theoretical results and experimental data for the transverse energy flows.

Paper Structure

This paper contains 15 sections, 116 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Kinematic Variables
  3. Lorentz scalars
  4. Hadron frame
  5. Photon-hadron center-of-mass frame
  6. Parton kinematics
  7. The resummed NLO cross-section
  8. Hadronic multiplicities and energy flows
  9. Relationship between the perturbative and resummed cross-sections. Uncertainties of the calculation
  10. Matching
  11. Kinematic corrections at $q_T \approx Q$
  12. Numerical results
  13. Energy flows
  14. Multiplicity of charged particle production
  15. Conclusions

Figures (13)

  • Figure 1: Semi-inclusive deep inelastic scattering
  • Figure 2: Geometry of the particle momenta in the hadron frame
  • Figure 3: Particle momenta in the $\gamma^{*} p$ c.m. frame
  • Figure 4: Feynman diagrams for semi-inclusive DIS: a) LO; b-d)NLO virtual diagrams; e-f) NLO real emission diagrams
  • Figure 5: Choice of the matching between the resummed and perturbative cross-section
  • ...and 8 more figures