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Jet Shapes in Hadron Collisions: Higher Orders, Resummation and Hadronization

Michael H. Seymour

TL;DR

The paper analyzes jet shapes in hadron collisions and demonstrates that current cone-based jet definitions are infrared unsafe at higher orders, hindering quantitative jet studies. It assesses higher-order perturbative corrections, all-orders resummation of large logs, and power-suppressed hadronization effects, showing these contributions can substantially modify jet-shape predictions. It argues for infrared-safe jet definitions, championing the $k$-perp algorithm (and improvements to cone schemes) to enable reliable theory–experiment comparisons, and develops a framework combining perturbative and non-perturbative effects, including Sudakov resummation and Dokshitzer–Webber power corrections. The results provide predictions for the jet shape and the radial moment, highlighting sizable corrections and offering guidance for future NLO calculations and experimental analyses, with a focus on universality of non-perturbative parameters and the importance of clear, public jet definitions.

Abstract

The jet shape is a simple measure of how widely a jet's energy is spread. At present jet shape distributions have only been calculated to leading order in perturbative QCD. In this paper we consider how much these predictions should be affected by higher order perturbative corrections, by resummation of enhanced corrections to all orders, and by (power-suppressed) non-perturbative corrections. We also show that current cone-type jet definitions are not infrared safe for final states with more than three partons. Unless this situation is rectified by using improved definitions, hadron collider experiments will never be able to study the internal properties of jets with the quantitative accuracy already achieved in $e^+e^-$ annihilation.

Jet Shapes in Hadron Collisions: Higher Orders, Resummation and Hadronization

TL;DR

The paper analyzes jet shapes in hadron collisions and demonstrates that current cone-based jet definitions are infrared unsafe at higher orders, hindering quantitative jet studies. It assesses higher-order perturbative corrections, all-orders resummation of large logs, and power-suppressed hadronization effects, showing these contributions can substantially modify jet-shape predictions. It argues for infrared-safe jet definitions, championing the -perp algorithm (and improvements to cone schemes) to enable reliable theory–experiment comparisons, and develops a framework combining perturbative and non-perturbative effects, including Sudakov resummation and Dokshitzer–Webber power corrections. The results provide predictions for the jet shape and the radial moment, highlighting sizable corrections and offering guidance for future NLO calculations and experimental analyses, with a focus on universality of non-perturbative parameters and the importance of clear, public jet definitions.

Abstract

The jet shape is a simple measure of how widely a jet's energy is spread. At present jet shape distributions have only been calculated to leading order in perturbative QCD. In this paper we consider how much these predictions should be affected by higher order perturbative corrections, by resummation of enhanced corrections to all orders, and by (power-suppressed) non-perturbative corrections. We also show that current cone-type jet definitions are not infrared safe for final states with more than three partons. Unless this situation is rectified by using improved definitions, hadron collider experiments will never be able to study the internal properties of jets with the quantitative accuracy already achieved in annihilation.

Paper Structure

This paper contains 20 sections, 50 equations, 19 figures.

Table of Contents

  1. Introduction
  2. Jet definitions, safeness and jet cross sections
  3. Jet definitions
  4. The ${k_\perp}$ algorithm
  5. The DØ algorithm
  6. The CDF algorithm
  7. Infrared and collinear safeness
  8. Jet cross sections
  9. All-orders cross section
  10. The $R_{\mathrm{sep}}$ 'solution'
  11. A solution
  12. A better solution
  13. The jet shape
  14. Leading order calculation
  15. Higher orders
  16. ...and 5 more sections

Figures (19)

  • Figure 1: The radius dependence of the inclusive jet cross section in the DØ jet algorithm with $E_0=1$ GeV in fixed-order (solid) and all-orders (dotted) calculations. The error bars come from Monte Carlo statistics.
  • Figure 2: The seed cell threshold dependence of the inclusive jet cross section in the DØ jet algorithm with $R=0.7$ in fixed-order (solid) and all-orders (dotted) calculations.
  • Figure 3: Illustration of the problem region for the iterative cone algorithm. In (a), there are two hard partons, with overlapping cones. In (b) there is an additional soft parton in the overlap region.
  • Figure 4: The radius dependence with $E_0=1$ GeV (left) and seed cell threshold dependence with $R=0.7$ (right) of the inclusive jet cross section in the improved iterative cone algorithm, in which midpoints of pairs of jets are used as additional seeds for the jet-finding, in fixed-order (solid) and all-orders (dotted) calculations.
  • Figure 5: The 'radius' dependence of the inclusive jet cross section in the ${k_\perp}$ jet algorithm in fixed-order (solid) and all-orders (dotted) calculations.
  • ...and 14 more figures