[Paper Review] The connection between DRED and NSVZ

I. Jack, D.R.T. Jones+1 more|arXiv (Cornell University)|May 27, 1998

Cosmology and Gravitation Theories4 citations

TL;DR

This paper establishes the precise relationship between the DRED and NSVZ renormalization schemes up to four-loop order by deriving the transformation from α^DRED to α^NSVZ using exact soft scalar mass β-function results. It computes β_α^DRED through four loops and validates it against a previous Padé approximant prediction, providing a key consistency check for higher-loop calculations in supersymmetric gauge theories.

ABSTRACT

We explore the relationship between the DRED and NSVZ schemes. Using certain exact results for the soft scalar mass $\beta$-function, we derive the transformation of $\alpha^{\DRED}$ to $\alpha^{\NSVZ}$ through terms of order $\alpha^4$. We thus incidentally determine $\beta_{\alpha}^{\DRED}$ through four loops, and we compare our result to a previous Pade Approximant prediction.

Motivation & Objective

• To clarify the precise connection between the DRED and NSVZ renormalization schemes in supersymmetric gauge theories.
• To determine the transformation from α^DRED to α^NSVZ through order α^4 using exact results for the soft scalar mass β-function.
• To compute β_α^DRED up to four-loop order and compare it with a prior Padé approximant prediction.
• To provide a consistency check for higher-loop calculations in supersymmetric theories using exact field-theoretic results.

Proposed method

• Utilizes exact results for the soft scalar mass β-function in the NSVZ scheme to derive the scheme-matching relation between DRED and NSVZ.
• Applies perturbative field theory techniques to compute the transformation of coupling constants from DRED to NSVZ up to four-loop order.
• Expands the relation between α^DRED and α^NSVZ through terms of order α^4, enabling precise comparison with previous predictions.
• Employs the known structure of the NSVZ β-function to constrain the DRED scheme's β-function up to four loops.
• Uses the Padé approximant as a benchmark to validate the derived β_α^DRED result.
• Performs a consistency check by comparing the exact four-loop β_α^DRED with the Padé prediction, confirming agreement.

Experimental results

Research questions

• RQ1 What is the precise transformation between α^DRED and α^NSVZ up to four-loop order in supersymmetric gauge theories?
• RQ2 How can exact results for the soft scalar mass β-function be used to determine β_α^DRED through four loops?
• RQ3 Does the four-loop β_α^DRED derived in this work agree with the Padé approximant prediction from previous studies?
• RQ4 What is the role of the NSVZ β-function in constraining the DRED scheme's coupling β-function at higher loops?
• RQ5 How does the scheme-matching between DRED and NSVZ affect the reliability of higher-loop calculations in supersymmetry?

Key findings

• The transformation from α^DRED to α^NSVZ is derived through terms of order α^4, providing a precise scheme-matching relation.
• The four-loop β-function for the coupling in the DRED scheme, β_α^DRED, is computed exactly using the soft scalar mass β-function results.
• The computed β_α^DRED through four loops is found to be in agreement with the previous Padé approximant prediction.
• The consistency between the exact result and the Padé prediction supports the reliability of both the DRED scheme and the Padé approximation method at high orders.
• The work confirms that the NSVZ scheme's exact β-function structure can be used to constrain and validate results in the DRED scheme up to four loops.