The charm/bottom quark mass from heavy quarkonium at N${}^3$LO

Abstract

We determine the charm and bottom quark masses using the N${}^3$LO perturbative expression of the ground state (pseudoscalar) energy of the bottomonium, charmonium and $B_c$ systems: the ${\eta }_b$, ${\eta }_c$ and $B_c$ masses. We work in the renormalon subtracted scheme, which allows us to control the divergence of the perturbation series due to the pole mass renormalon. Our result for the $\overline{\mathrm{MS}}$ masses reads ${\overline{m}}_c({\overline{m}}_c)=1223(33)$ MeV and ${\overline{m}}_b({\overline{m}}_b)=4186(37)$ MeV. We also extract a value of ${\alpha }_s$ from a renormalon-free combination of the ${\eta }_b$, ${\eta }_c$ and $B_c$ masses: ${\alpha }_s(M_z)=0.1195(53)$. We explore the applicability of the weak coupling approximation to bottomonium $n=2$ states. Finally, we consider an alternative computational scheme that treats the static potential exactly and study its convergence properties.

arXiv comment29 pages, 31 figures; References added; Extra explanations; Conclusions unchanged; Accepted for publication at JHEP

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