[Paper Review] The Problem of Asymptotic Freedom

Adrian Patrascioiu, Erhard Seiler|ArXiv.org|Sep 9, 1996

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TL;DR

This paper challenges the standard perturbative prediction of asymptotic freedom in QCD, arguing instead that nonperturbative lattice QCD suggests an ultraviolet fixed point at αs ≈ 0.1, contradicting perturbation theory's ambiguous asymptotic expansion. The authors present lattice data as evidence for this alternative running behavior, proposing a revised understanding of QCD's high-energy behavior.

ABSTRACT

There is a growing body of evidence that the running of $α_s$ predicted by perturbation (PT) theory is not correctly describing the accelerator experiments at the highest energies. A natural explanation is provided by the authors' 1992 proposal that in fact the true running predicted by the nonperturbatively defined lattice QCD is different, leading to an ultraviolet fixed point near $α_s=.1$. It is explained how this can be understood from the fact that the conventional perturbative method is ambiguous and does not provide the correct asymptotic expansion. It is pointed out that there is a large amount of lattice data that are supporting this scenario rather than the conventional one.

Motivation & Objective

• To challenge the conventional perturbative prediction of asymptotic freedom in QCD.
• To argue that perturbation theory is ambiguous and fails to yield the correct asymptotic expansion for αs.
• To propose that nonperturbatively defined lattice QCD predicts a different running of αs, with an ultraviolet fixed point near αs = 0.1.
• To present lattice data as evidence favoring this nonperturbative scenario over the standard perturbative one.
• To reconcile accelerator data at high energies with a revised understanding of QCD's high-energy behavior.

Proposed method

• Analyzes the ambiguity in conventional perturbation theory for QCD's running coupling αs.
• Proposes that nonperturbative lattice QCD provides a more reliable definition of the running coupling.
• Uses lattice data to support the existence of a UV fixed point at αs ≈ 0.1.
• Contrasts the perturbative prediction with the nonperturbative lattice result, emphasizing the failure of perturbation theory to capture the correct asymptotic behavior.
• Relies on existing lattice simulations and phenomenological data from high-energy experiments to validate the proposed scenario.
• Applies the framework of nonperturbative quantum field theory to re-evaluate the behavior of αs in the ultraviolet regime.

Experimental results

Research questions

• RQ1 Does perturbation theory correctly describe the running of αs at high energies, as predicted by standard QCD?
• RQ2 What is the true nature of the ultraviolet behavior of QCD's coupling constant, as revealed by nonperturbative methods?
• RQ3 Can lattice QCD data support a UV fixed point in αs near 0.1, contradicting the standard asymptotic freedom prediction?
• RQ4 Why does the conventional perturbative approach fail to yield the correct asymptotic expansion for αs?
• RQ5 How do accelerator data at high energies align with the nonperturbative lattice QCD prediction of a fixed point in αs?

Key findings

• The paper argues that perturbation theory is ambiguous and does not provide the correct asymptotic expansion for αs.
• Nonperturbatively defined lattice QCD predicts a UV fixed point at αs ≈ 0.1, differing from the standard perturbative prediction.
• There is growing evidence from lattice data supporting this alternative scenario over the conventional one.
• The discrepancy between perturbative predictions and experimental data at the highest energies is explained by the failure of perturbation theory to capture the true nonperturbative behavior.
• The authors conclude that the standard asymptotic freedom scenario may not correctly describe QCD at high energies, based on lattice evidence.
• The paper presents a compelling case that the true running of αs is better described by a nonperturbative fixed point than by perturbative evolution.