On the effects of heavy sea quarks at low energies

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 $M\to 0$ 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.

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• FLAG Review 2024
• Gradient flow and scale setting on MILC HISQ ensembles
• ${\Lambda }_{c}N$ interaction from lattice QCD and its application to ${\Lambda }_c$ hypernuclei
• Neutron electric dipole moment using $N_f=2+1+1$ twisted mass fermions
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• Power corrections from decoupling of the charm quark
• Non-perturbative renormalization by decoupling
• How perturbative are heavy sea quarks?
• Lattice determinations of the strong coupling
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Background field method in the gradient flow
• How much do charm sea quarks affect the charmonium spectrum?
• Determination of the charm quark mass in lattice QCD with $2+1$ flavours on fine lattices
• Scale setting for $N_f=3+1$ QCD
• Charmonium and exotics from lattice QCD
• Precision Determination of ${\alpha }_s$ from Lattice QCD
• Charm sea effects on charmonium decay constants and heavy meson masses
• Determination of the Strong Coupling Constant by the ALPHA Collaboration
• Decoupling of charm beyond leading order
• Charm quark effects on the strong coupling extracted from the static force
• The determination of potential scales in 2+1 flavor QCD
• Determination of c_sw in N_f=3+1 Lattice QCD with massive Wilson fermions