[Paper Review] Two-loop next-to-leading $\mt$ corrections to the $ ho$ parameter

G. Degrassi, S. Fanchiotti+1 more|arXiv (Cornell University)|Mar 9, 1994

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper computes two-loop next-to-leading top quark mass corrections to the ρ parameter and the ratio of neutral-to-charged current amplitudes within the Standard Model using current algebra, demonstrating numerical significance of O(G²μmt²mZ²) terms comparable to leading O(G²μmt⁴) contributions for realistic top quark masses, with implications for higher-order resummation in precision electroweak theory.

ABSTRACT

The $O(G^2_\mu m_t^4)$ correction to the $ ho$ parameter is computed within the Standard Model using the current algebra formulation of radiative corrections. This approach is proved to be equivalent to the effective Lagrangian method proposed by Barbieri {\em et al.} Using the same framework, the $O(G^2_\mu m_t^2 m_z^2)$ correction to the ratio of neutral-to-charged current amplitudes is analysed in an $SU(2)$ model. The $O(G^2_\mu m_t^2 m_z^2)$ contribution is shown to be numerically comparable to the leading $O(G^2_\mu m_t^4)$ term for realistic values of the top mass. The resummation of higher-order effects is discussed.

Motivation & Objective

• To compute two-loop electroweak corrections to the ρ parameter involving the top quark mass at next-to-leading order in the top quark mass expansion.
• To analyze the O(G²μmt²mZ²) correction to the ratio of neutral-to-charged current amplitudes in an SU(2) gauge model.
• To assess the numerical relevance of subleading corrections relative to the leading O(G²μmt⁴) contribution for realistic top quark masses.
• To explore the resummation of higher-order corrections in the context of precision electroweak theory.

Proposed method

• Uses the current algebra formulation of radiative corrections to compute two-loop corrections to the ρ parameter in the Standard Model.
• Establishes equivalence between the current algebra approach and the effective Lagrangian method of Barbieri et al. for the same computation.
• Applies the same framework to compute corrections in an SU(2) model for the ratio of neutral-to-charged current amplitudes.
• Evaluates the numerical magnitude of O(G²μmt²mZ²) contributions relative to the leading O(G²μmt⁴) term.
• Discusses the resummation of higher-order corrections using the derived results.

Experimental results

Research questions

• RQ1 How significant are O(G²μmt²mZ²) corrections compared to the leading O(G²μmt⁴) term in the ρ parameter for realistic top quark masses?
• RQ2 Is the current algebra formulation equivalent to the effective Lagrangian method of Barbieri et al. for two-loop electroweak corrections?
• RQ3 What is the numerical impact of next-to-leading order top quark mass corrections on the ratio of neutral-to-charged current amplitudes?
• RQ4 Can higher-order corrections be meaningfully resummed in the context of precision electroweak theory?

Key findings

• The O(G²μmt²mZ²) correction to the ρ parameter is numerically comparable to the leading O(G²μmt⁴) term for realistic values of the top quark mass.
• The current algebra formulation is proven to be equivalent to the effective Lagrangian method proposed by Barbieri et al. for the same two-loop computation.
• The O(G²μmt²mZ²) contribution to the ratio of neutral-to-charged current amplitudes is found to be of comparable magnitude to the leading term in the SU(2) model.
• Higher-order corrections, particularly those involving mt²mZ², cannot be neglected in precision electroweak calculations when the top quark mass is large.