Determination of the bottom quark mass from the $Υ(1S)$ system

Abstract

We approximately compute the normalization constant of the first infrared renormalon of the pole mass (and the singlet static potential). Estimates of higher order terms in the perturbative relation between the pole mass and the $\MS$ mass (and in the relation between the singlet static potential and $α_s$) are given. We define a matching scheme (the renormalon subtracted scheme) between QCD and any effective field theory with heavy quarks where, besides the usual perturbative matching, the first renormalon in the Borel plane of the pole mass is subtracted. A determination of the bottom $\MS$ quark mass from the $Υ(1S)$ system is performed with this new scheme and the errors studied. Our result reads $m_{b,\MS}(m_{b,\MS})=4 210^{+90}_{-90}({\rm theory})^{-25}_{+25}(α_s)$ MeV. Using the mass difference between the $B$ and $D$ meson, we also obtain a value for the charm quark mass: $m_{c,\MS}(m_{c,\MS})=1 210^{+70}_{-70}({\rm theory})^{+65}_{-65}(m_{b,\MS})^{-45}_{+45}(λ_1)$ MeV. We finally discuss upon eventual improvements of these determinations.