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

Abstract

In this work, the perturbative QCD series of the scalar correlation function $\Psi (s)$ is investigated. Besides $\mathrm{Im}\Psi (s)$, 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 $\mathrm{Im}\Psi (s)$.

29 pages, 4 figures; minor modifications, version to be published in JHEP

References in corpus (7)

• Big-Bang Nucleosynthesis
• Five-Loop Running of the QCD coupling constant
• alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory
• Scalar K pi form factor and light quark masses
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• Determination of the QCD Coupling from ALEPH $\tau$ Decay Data
• Scheme variations of the QCD coupling and hadronic $\tau$ decays

Cited by in corpus (10)

• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• QCD Running Couplings and Effective Charges
• Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants
• A novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the $C$-scheme coupling
• Renormalons beyond the Borel plane
• Higher-order QCD corrections to $H\to b\bar{b}$ from rational approximants
• Higher-order behaviour of two-point current correlators
• Scheme variations of the QCD coupling
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Trans-series from condensates in the non-linear sigma model