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

We approximately compute the normalization constant of the first infrared r enormalon 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 a lpha (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 Bore l plane of the pole mass is subtracted. A determination of the bottom MS qu ark mass from the Y (1S) system is performed with this new scheme and the e rrors studied. Our result reads m(b,(MS) over bar)(m(b,(MS) over bar)) = 4 210(-90)(+90)(theory)(+25)(-25) (alpha (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) over bar)(m(c,(MS) over bar)) = 1 210(-70)(+70)(theory)(-65)(+65) (m(b,(MS) over bar))(+45)(-45)(lambda (1)) MeV. We finally discuss upon eve ntual improvements of these determinations.