Scalar correlator, Higgs decay into quarks, and scheme variations of the QCD coupling

TL;DR

This paper investigates the perturbative QCD series of scalar correlators relevant for Higgs decay and other processes, highlighting scheme dependence and proposing improvements for series convergence and phenomenological applications.

Contribution

It introduces a scheme-independent QCD coupling and analyzes the scheme dependence of scalar correlators, offering strategies to improve perturbative series behavior.

Findings

Avoiding the $D^L(s)$ correlator due to large corrections.

Expressing quark mass in terms of the renormalisation invariant mass improves stability.

Choosing optimal scheme parameters enhances series convergence.

Abstract

In this work, the perturbative QCD series of the scalar correlation function $\Psi(s)$ is investigated. Besides ${\rm Im}\Psi(s)$, which is relevant for Higgs decay into quarks, two other physical correlators, $\Psi^{"}(s)$ and $D^L(s)$, have been employed in QCD applications like quark mass determinations or hadronic $\tau$ decays. $D^L(s)$ suffers from large higher-order corrections and, by resorting to the large-$\beta_0$ approximation, it is shown that this is related to a spurious renormalon ambiguity at $u=1$. Hence, this correlator should be avoided in phenomenological analyses. Moreover, it turns out advantageous to express the quark mass factor, introduced to make the scalar current renormalisation group invariant, in terms of the renormalisation invariant quark mass $\hat m_q$. To further study the behaviour of the perturbative expansion, we introduce a QCD coupling $\hat\alpha_s$, whose running is explicitly renormalisation scheme independent. The scheme dependence of $\hat\alpha_s$ is parametrised by a single parameter $C$, being related to transformations of the QCD scale parameter $\Lambda$. It is demonstrated that appropriate choices of $C$ lead to a substantial improvement in the behaviour of the perturbative series for $\Psi^{"}(s)$ and ${\rm Im}\Psi(s)$.