Effects of Heavy Sea Quarks at Low Energies

We present a factorization 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 mass-independent factor Q, ratios such as r$_0$(M)/r$_0$(0) are computable in perturbation theory at large M. The perturbation theory part is stable concerning different loop orders. Our nonperturbative Monte Carlo results obtained in a model calculation, where a doublet of heavy quarks is decoupled, match 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. We verify—in the continuum limit—that the sea quark effects of quarks with masses around the charm mass are very small in such ratios