Comparison of Improved and Unimproved Quenched Hadron Spectroscopy

We make a comparison between our quenched-hadron-spectroscopy results for the non-perturbatively-improved Wilson action and the corresponding unimproved case, at β = 6.2 on the same set of gauge configurations. Within our statistics, we find a sizeable improvement for the baryon spectrum and for the determination of the strange-quark mass . CERN-TH/98-110 April 1998 The computation cost of the extrapolation to the continuum limit of lattice QCD simulations can be significantly reduced by using improved actions, where the leading cutoff effects are cancelled by suitable counterterms. It has been shown that on-shell improvement of O(a) is achieved by adding to the usual Wilson action the clover term, with a coefficient that has been determined non-perturbatively by the ALPHA collaboration [1]. We have studied the influence of considering this non-perturbatively-improved Wilson action with respect to the usual, unimproved, action. A detailed analysis of our results for the improved case has appeared elsewhere [2], and here we concentrate on the comparison between the two cases (a preliminary study can be found in [3]). We refer to [1] for the description of the improvement programme. We consider a lattice of volume 24 × 48 and coupling β = 6.2. We choose the following values for the hopping parameter κ in the unimproved case: 0.1350, 0.1400, 0.1450, 0.1506, 0.1510, 0.1517, 0.1526 (for the improved case we used: 0.1240, 0.1275, 0.1310, 0.1340, 0.1345, 0.1350, 0.1352). We consider, for the improved as well as for the unimproved case, all nondegenerate flavor combinations from the different values of κ. Our simulations were carried out on the 512-processor computer of the APE100 series at the University of Rome “Tor Vergata”. Our statistics come from 104 quenched gauge configurations, generated by a hybrid over-relaxation algorithm, with each update corresponding to a heat-bath sweep followed by three over-relaxation sweeps. The configurations are separated by 1000 updates. The numerical inversion of the propagator for the improved case is described in [2]. For the unimproved case we have performed the inversion in a similar manner, but for the last part of our configurations we have implemented the SSOR algorithm [4], which corresponds roughly to a gain of a factor 4 in the inversion time. The analysis of the data for the improved case is described in [2]. For the unimproved case, we have followed the same procedure, namely hadron masses are obtained from single-mass fits to the large time behaviour of zero-momentum hadron correlators, and the errors are estimated through a single-elimination jack-knife procedure. We remark that we determine κc for both cases by using the so-called Ward identity mass mWI , considered in [2] (in the unimproved case we set the coefficient cA to zero). We thus obtain for the unimproved case the value κc = 0.153230(9) (from mWI = 0). (1) This may be compared with the value κc = 0.153291(15), obtained from M 2 PS = 0. For the fits to the dependence of hadron masses upon quark masses we use in the unimproved case the bare quark mass, defined as mq(κ) ≡ (1/κ − 1/κc)/2, while for the improved case we use an improved bare quark mass [1] defined by m̃q(κ) ≡ mq(κ) [1 + bm mq(κ)] . (2) (Note that m̃q is the renormalized mass with Zm = 1 .) The improvement coefficient bm has been determined non-perturbatively [5] to be bm = −0.62(3). For non-degenerateflavour cases, we use symmetric averages of the masses defined above.