[Paper Review] Suppressed power-corrections for moments of event-shape variables in e+e- annihilation

Einan Gardi|arXiv (Cornell University)|Mar 17, 2000

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper investigates power corrections in higher moments of event-shape variables in e+e− annihilation, showing that for ⟨(1−T)²⟩, soft gluon emission leads to suppressed 1/Q³ corrections, while 1/Q² ambiguities dominate and are not tied to specific phase-space regions, suggesting they are not genuine non-perturbative effects.

ABSTRACT

Power-corrections that fall as 1/Q, where Q is the center-of-mass energy, play a significant role in the phenomenology of the average values of event-shape variables like the thrust T. These power-corrections can be analyzed in perturbative QCD using renormalon resummation in the single dressed gluon approximation. They originate in a particular part of phase-space where a soft gluon is emitted at a large angle. It is shown that for higher moments of 1 - thrust a single gluon emission leads to much suppressed power-corrections. In particular, the corrections to <(1-T)^2> from soft gluon emission fall as 1/Q^3. Other ambiguities of perturbation theory which scale as 1/Q^2 become dominant. However, finding that these ambiguities are not associated to any particular part of phase-space, we suggest that they do not signal any genuine non-perturbative effects.

Motivation & Objective

• To understand the origin and magnitude of power corrections in higher moments of event-shape variables like thrust in e+e− annihilation.
• To analyze how soft gluon emission at large angles contributes to power corrections in moments of 1−T.
• To determine whether 1/Q² ambiguities in perturbation theory correspond to genuine non-perturbative effects.
• To assess the role of renormalon resummation in the single dressed gluon approximation for modeling these corrections.

Proposed method

• Using perturbative QCD with renormalon resummation in the single dressed gluon approximation to model power corrections.
• Focusing on phase-space regions where soft gluons are emitted at large angles, which dominate the power corrections.
• Computing higher moments of 1−T, particularly ⟨(1−T)²⟩, to evaluate the scaling of corrections with center-of-mass energy Q.
• Identifying the origin of 1/Q² ambiguities in perturbation theory and assessing their phase-space dependence.
• Comparing the scaling of corrections from soft gluon emission (1/Q³) with other perturbative ambiguities (1/Q²).
• Concluding that 1/Q² ambiguities are not linked to any specific phase-space region, implying they are not indicative of non-perturbative physics.

Experimental results

Research questions

• RQ1 How do power corrections scale with center-of-mass energy Q in higher moments of 1−T, such as ⟨(1−T)²⟩?
• RQ2 What is the contribution of soft gluon emission at large angles to power corrections in event-shape moments?
• RQ3 Why are 1/Q² ambiguities in perturbation theory dominant for ⟨(1−T)²⟩, and what is their physical origin?
• RQ4 Are the 1/Q² ambiguities associated with specific regions of phase-space, indicating non-perturbative effects?
• RQ5 Can renormalon resummation in the single dressed gluon approximation accurately describe the scaling of these corrections?

Key findings

• Power corrections to ⟨(1−T)²⟩ from soft gluon emission scale as 1/Q³, indicating significant suppression compared to the standard 1/Q behavior.
• The 1/Q² ambiguities in perturbation theory become dominant for ⟨(1−T)²⟩, overshadowing the 1/Q³ corrections.
• These 1/Q² ambiguities are not associated with any particular region of phase-space, suggesting they are not signals of genuine non-perturbative effects.
• The suppression of 1/Q³ corrections arises due to the angular dependence of soft gluon emission in the single dressed gluon approximation.
• The absence of phase-space localization for 1/Q² ambiguities implies they are artifacts of the perturbative expansion rather than physical non-perturbative contributions.
• The results support the use of renormalon resummation in the single dressed gluon framework for modeling power corrections in event-shape moments.