Pade-Improvement of CP-odd Higgs Decay Rate into Two Gluons

TL;DR

This paper estimates four-loop corrections to the decay rate of a CP-odd Higgs boson into two gluons using Pade-approximant methods, showing the corrections are relatively small compared to the leading order.

Contribution

It introduces an asymptotic Pade-approximant approach to estimate higher-order loop coefficients in Higgs decay calculations, extending known 3-loop results.

Findings

Four-loop correction estimated to be 4.3% of the leading term.

Pade-approximant estimates are within 12% of actual coefficients.

Most coefficients are derived from 3-loop results using renormalization group methods.

Abstract

We present an asymptotic Pade-approximant estimate for the four-loop coefficients within the linear combination of correlators entering the recently calculated decay rate of a CP-odd Higgs boson, with an assumed mass $m_A = 100 GeV$, into two gluons. All but one of these coefficients are shown to be determined for arbitrary $m_A$ from the known 3-loop-order rate by renormalization group methods. Asymptotic Pade-approximant estimates for these coefficients are all seen to be within 12% of their correct values. The four-loop term in the decay rate for $m_A = 100 GeV$ is estimated to be only 4.3% of its leading one-loop contribution.