Towards the continuum limit with quenched staggered

We extend previous work on nite-size eeects with dynamical staggered quarks to the quenched approximation. We again emphasize the large volume limit that is of interest for spectrum calculations which may hope to approach the experimental values. Relying on new calculations at 6=g 2 = 5:7 and recent work with weaker couplings, we extrapolate to the continuum limit and nd a nucleon to rho mass ratio in close agreement with the experimental value and the value obtained by extrapolations from calculations with Wilson quarks. Additional calculations that should be done to improve the reliability of the extrapolation are discussed. A main goal of lattice QCD is to calculate the spectrum of light hadrons. Although there have been many spectrum calculations over the years, one persistent problem has been the large nucleon to rho mass ratioo1]. In any lattice calculation, there are certain limitations that may result in systematic bias in this ratio. For instance, the nucleon mass is more sensitive to box size than the rho, so for small volumes, m N =m is larger than in the innnite volume limit. Further, all calculations are done with quarks more massive than in nature and this also increases m N =m. Recently , it has been shown using Wilson quarks in the quenched approximation that after extrapolating in quark mass, volume and lattice spacing that m N =m agrees quite well with the experimental valuee2]. It would certainly be interesting to see if the same is true for staggered quarks. We have been studying nite-size eeects for quite some time using dynamical staggered quarkss3]. We realized that quenched results at 6=g 2 = 5:7 4], for which there is a comparable rho mass, apparently showed much larger nite-size eeects. These quenched eeects were also much larger than those recently seen at weaker cou-plingg5]. If we want to make nite volume corrections for weak coupling to avoid calculations with huge lattices, it is important to verify at stronger coupling that we understand how nite volume eeects depend upon the quark mass (or m =m) and that they actually scale, i.e., depend upon the physical box size. In view of the above, we have begun a series of calculations with 6=g 2 = 5:7. Combining our new results with those in the literature for 5.85, 5.95 6] and 6.0 5,7], we nd that an extrapolation similar to that done with Wilson quarks yields …