Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Shape functions and power corrections to the event shapes

G. P. Korchemsky

TL;DR

Korchemsky develops a framework to describe hadronization corrections to event-shape distributions in e+e- annihilation by resumming leading power corrections into a universal, Q-independent shape function. The thrust distribution is expressed as a convolution of a perturbative Sudakov spectrum with this shape function, with factorization implemented via a scale μ and a renormalon-inspired analysis. The paper shows that at large t the spectrum is shifted by ⟨ε⟩/Q while for t ~ Λ_QCD/Q the full shape function governs the end-point region. A simple two-parameter ansatz for the shape function describes thrust data over a wide range of Q, supporting the universality of soft-gluon energy flow in nonperturbative corrections.

Abstract

We show that the leading power corrections to the event shape distributions can be resummed into nonperturbative shape functions that do not depend on the center-of-mass energy and measure the energy flow in the final state. In the case of the thrust variable, the distribution is given by the convolution of the perturbative spectrum with the shape function. Choosing the simplest ansatz for the shape function we find that our predictions for the thrust distribution provide a good description of the data throughout a wide range of energies.

Shape functions and power corrections to the event shapes

TL;DR

Korchemsky develops a framework to describe hadronization corrections to event-shape distributions in e+e- annihilation by resumming leading power corrections into a universal, Q-independent shape function. The thrust distribution is expressed as a convolution of a perturbative Sudakov spectrum with this shape function, with factorization implemented via a scale μ and a renormalon-inspired analysis. The paper shows that at large t the spectrum is shifted by ⟨ε⟩/Q while for t ~ Λ_QCD/Q the full shape function governs the end-point region. A simple two-parameter ansatz for the shape function describes thrust data over a wide range of Q, supporting the universality of soft-gluon energy flow in nonperturbative corrections.

Abstract

We show that the leading power corrections to the event shape distributions can be resummed into nonperturbative shape functions that do not depend on the center-of-mass energy and measure the energy flow in the final state. In the case of the thrust variable, the distribution is given by the convolution of the perturbative spectrum with the shape function. Choosing the simplest ansatz for the shape function we find that our predictions for the thrust distribution provide a good description of the data throughout a wide range of energies.

Paper Structure

This paper contains 5 sections, 27 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Analysis of soft gluon effects
  3. Factorization of the thrust distribution
  4. Nonperturbative ansatz for the shape function
  5. Conclusions

Figures (4)

  • Figure 1: The prediction (\ref{['thrust']}) for the thrust distribution at $Q=35\,{\rm GeV}$. The dotted and dashed lines describe the first and the second term in the r.h.s. of (\ref{['thrust']}), respectively, and the solid line is the sum of both. The dot-dashed line denotes the perturbative Sudakov spectrum $\frac{d\sigma_{{_{\rm PT}}}(t;\mu=0)}{dt}$ in the NLL approximation.
  • Figure 2: The nonperturbative ansatz for shape function.
  • Figure 3: The comparison of the data with the QCD prediction for the thrust distribution (\ref{['thrust']}) at $Q=91.2\,{\rm GeV}$
  • Figure 4: The comparison of the data with the QCD prediction for the thrust distribution at different energies (from bottom to top): $Q/{\rm GeV}=14\,,22\,,35\,,44\,,55\,,91\,,133\,,161.$data