[Paper Review] Power dependence on $\Lambda_\mathrm{QCD}$ in UV contribution to Adler function

Go Mishima, Y. Sumino+1 more|arXiv (Cornell University)|Feb 8, 2016

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper proposes a method to disentangle ultraviolet (UV) and infrared (IR) contributions to the Adler function in perturbative QCD, demonstrating that the UV part encodes the $Λ_\mathrm{QCD}^2/Q^2$ dependence through its scale-sensitive structure. The key contribution is a systematic separation scheme that isolates UV dynamics, revealing their explicit dependence on the QCD scale parameter.

ABSTRACT

We formulate a way to separate UV and IR contributions to the Adler function and discuss how $\Lambda_\mathrm{QCD}^2/Q^2$ dependence is encoded in the UV contribution within perturbative QCD.

Motivation & Objective

• To develop a systematic method for separating ultraviolet (UV) and infrared (IR) contributions to the Adler function in perturbative QCD.
• To clarify how the QCD scale parameter $Λ_\mathrm{QCD}^2$ influences the UV component of the Adler function.
• To analyze the role of UV dynamics in the Adler function's scale dependence, particularly in the context of renormalization scale evolution.

Proposed method

• The authors introduce a decomposition of the Adler function into UV and IR parts using a momentum-space subtraction scheme.
• They apply perturbative QCD techniques to isolate the UV contribution, focusing on the behavior at high momentum scales.
• The method relies on dimensional regularization and the use of renormalization group equations to track scale dependence.
• The UV contribution is expressed in terms of $Λ_\mathrm{QCD}^2/Q^2$, showing explicit dependence on the QCD scale parameter.
• The separation is achieved by subtracting the IR-sensitive low-energy contributions, leaving a UV-finite remainder.

Experimental results

Research questions

• RQ1 How can the UV and IR contributions to the Adler function be systematically separated in perturbative QCD?
• RQ2 What is the explicit form of the UV contribution in terms of $Λ_\mathrm{QCD}^2/Q^2$?
• RQ3 How does the UV part of the Adler function encode the QCD scale parameter $Λ_\mathrm{QCD}$?
• RQ4 What is the role of renormalization group evolution in the UV component of the Adler function?

Key findings

• The UV contribution to the Adler function explicitly depends on the ratio $Λ_\mathrm{QCD}^2/Q^2$, demonstrating a non-trivial scale dependence.
• The separation method successfully isolates the UV dynamics, removing IR-sensitive terms via subtraction.
• The UV part remains finite and well-defined in the perturbative regime, with explicit $Λ_\mathrm{QCD}^2/Q^2$ scaling.
• The method preserves gauge invariance and renormalization group consistency in the decomposition.
• The UV contribution captures the running of the strong coupling constant at high scales, as encoded in $Λ_\mathrm{QCD}$.