On the effects of heavy sea quarks at low energies

TL;DR

This paper develops a factorisation formula describing how light hadron masses depend on heavy quark masses, showing that heavy sea quark effects are minimal near the charm mass, with results supported by both perturbative and non-perturbative calculations.

Contribution

It introduces a factorisation approach for heavy quark effects on light hadron properties, validated through non-perturbative and perturbative methods, and provides numerical evidence for small sea quark effects near the charm mass.

Findings

Perturbation theory predictions match non-perturbative results.

Ratios of hadronic scales are largely independent of heavy quark mass.

Sea quark effects around the charm mass are very small.

Abstract

We present a factorisation formula for the dependence of light hadron masses and low energy hadronic scales on the mass $M$ of a heavy quark: apart from an overall factor $Q$, ratios such as $r_0(M)/r_0(0)$ are computable in perturbation theory at large $M$. The mass-independent factor $Q$ is obtained from the theory in the limit $M\to0$ and the decoupled theory with the heavy quark removed. The perturbation theory part is stable concerning different loop orders and our non-perturbative results match on quantitatively to the perturbative prediction. Upon taking ratios of different hadronic scales at the same mass, the perturbative function drops out and the ratios are given by the decoupled theory up to $M^{-2}$ corrections. Our present numerical results are obtained in a model calculation where there are no light quarks and a heavy doublet of quarks is decoupled. They are limited to masses a factor two below the charm. This is not large enough to see the $M^{-2}$ scaling predicted by the theory, but it is sufficient to verify - in the continuum limit - that the sea quark effects of quarks with masses around the charm mass are very small.