ERRORS IN LATTICE EXTRACTIONS OF ALPHA(S) DUE TO USE OF UNPHYSICAL PION MASSES

We investigate the errors due to the use of unphysical values of light quark masses in lattice extractions of alpha(s). A functional form fo r the pion mass dependence of the quarkonium mass splittings (Delta m) is given as an expansion in m(pi)/(4 pi f(pi)) and m(pi)r(B), where r (B) is the quarkonium Bohr radius. We find that, to lowest order, Delt a m similar or equal to A + Bm(pi)(2), where the scale of B is given b y f(pi)(2)r(B)(3). To order m(pi)(4) there are four unknown coefficien ts, however, utilizing multipole and operator product expansions, symm etry arguments eliminate one of the four unknowns. Using the central v alues for the lattice spacings which were extracted using two differen t, unphysical values for the pion mass, we find that the errors introd uced by extrapolating to the physical regime are comparable to the err ors quoted due to other sources. Extrapolation to physical values of t he pion mass increases the value of alpha(s)(M(Z)), bringing its value closer to the high energy extractions.