Quenched Wilson hadron spectroscopy on a 323 × 48 lattice at β = 6.3

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<ul><li><p>I ~ LIlIqil I f~Y ~'i N r, h"k"! [~,,,'li "t </p><p>PROCEEDINGS SUPPLEMENTS </p><p>Nuclear Physics B (Proc. Suppl.) 34 (1994) 338-340 North-Holland </p><p>Quenched Wilson hadron spectroscopy on a 323x48 lattice at /3 - 6.3 </p><p>QCD_TARO Collaboration </p><p>K. Akemi a, Ph. de Forcrand b, M. Fujisaki ~, T. Hashimoto , S. Hioki d O. Miyamura ~, A. Nakamura e, M. Okuda ~, I.O. Stamatescu f, Y. Tago ~ and T. Takaishi ~ </p><p>aComputational Science Research Laboratory, Fujitsu Limited, Mihama-ku, Chiba 261, Japan </p><p>bIPS,ETH-Zilrich, CH-8092 Ziirich, Switzerland </p><p>eDepartment of Applied Physics, Fukui University, Fukui 910, Japan </p><p>dDepartment of Physics, Hiroshima University, Higashi-Hiroshima 724, Japan </p><p>eFaculty of Education, Yamagata University, Yamagata 990, Japan </p><p>fFESt Heidelberg and Institut ffir Theoretische Physik, Universit/it Heidelberg, D-6900 Heidelberg, Germany </p><p>We briefly summarize our results of quenched Wilson hadron spectroscopy at/3 ---- 6.3 on a 323 48 lattice. The spectrum of pseudo scalar and vector mesons, (1/2) + and (3/2) + baryons composed of up, down, strange and charm quarks are presented. A decrease of mass splitting between (1/2) + and (3/2) + baryons is observed when heavy quark masses increase, as in the case of the mass difference between pseudo scalar and vector mesons. </p><p>1. INTRODUCTION </p><p>The results of hadron spectroscopy on a 323 x 48 lattice at/3 -- 6.3 are reported using the standard Wilson action in the quenched approximation. Our main result is the spectrum of hadrons com- posed of different flavors of quarks. Spectroscopy of these hadrons is theoretically important [1,2] as their scaling property in the heavy quark limit has a relation to many interesting properties of ma- trix elements. The properties of such hadrons are well described by the heavy quark effective the- ory, and flavor independent sum rules of hadron masses are obtained [3]. Some of them are not yet tested experimentally and results of lattice calcu- lations can be compared against them. The hop- ping parameters we choose correspond to mass re- gion between the strange quark and charm quark. The spectrum of hadrons composed of up, down, strange and charm quarks are presented. The calculation is performed on a massively parallel </p><p>computer AP1000 supported by Fujitsu. </p><p>2. GENERAL FEATURES OF THE SIM- ULAT ION </p><p>We measured propagators of hadrons composed of several combinations of 5 different Wilson hop- ping parameters ~, 0.150, 0.148, 0.143, 0.140 and 0.130. The numbers of measured configurations are typically 50, with small differences for the var- ious combinations of hopping parameters. The data are fitted by cosh and exponential type func- tions for mesons and baryons respectively. The fitting regions are 11-19 and 29-37 for mesons and 11-19 for baryons. A well-defined plateau of effective mass is observed in these regions for both cases. We made a single pole fit for the data. The configurations are separated by 250 sweeps using the overrelaxation and heatbath algorithm after 2000 sweeps of thermalization. The ratio of overrelaxation to heatbath is 9:1. Propagators </p><p>0920-5632/94/$07.00 1994 - Elsevier Science B.V. All rights reserved. SSDI 0920-5632(94)00278-4 </p></li><li><p>QCD-TARO Collaboration~Quenched Wilson hadron spectroscopy on a 323 x48 lattice at ~3 = 6.3 339 </p><p>Table 1 Strange and charmed meson spectrum in GeV. </p><p>K D Ds 7/c Lattice 0.566(50) 1922(50) 2.051(52) 3064(43) Experim. (0494) (1869) (1.969) (2.981) </p><p>K* D* D; J / Lattice 0.838(47) input 1992(45) 2.117(48) input Experim. (0891) (1019) (2.010) (2.110) (3.097) </p><p>Table 2 Pseudo scalar and vector mass difference in MeV. </p><p>K* -K D* -D D* -D, Lattice 272(47) 70(45) 66(43) Experim. (398) (141) (142) </p><p>J /C- 7o 33(21) (116) </p><p>1.6 </p><p>1.4 </p><p>1.2 </p><p>1 Mps </p><p>0.8 </p><p>323 x 48 pseudo scalar ] ~=6.3 .... </p><p>0 6V ~ " , / / </p><p>0.4 K </p><p>0"~[6:6 6:8 7 7:2 7:4 7:6 7:8 </p><p>1/hi </p><p>Figure 1. Pseudo scalar meson mass spec- trum. The solid lines correspond to t2 = critical, strange and charm, from bottom to top. </p><p>are measured for various channels. In this re- port, the results of pseudo scalar, vector mesons, (1/2) + and (3/2) + baryons are presented. </p><p>We use standard local operators as point sources. The fundamental quantities, critical hopping parameter (t%~) and lattice spacing ( a ), are determined from the largest two hopping parameters. The squared pion mass is fitted lin- early and we obtain tcc, = 0.15159(52). The lat- tice spacing is a -1 = 2.99(28) GeV, determined from p meson mass taking the chiral limit of the linear fit of vector meson masses. It is consistent with the value (3.0 GeV) determined from our </p><p>M B </p><p>2.2 2 </p><p>1.8 1.6 1.4 1.2 </p><p>1 0.8 0.6 0.4 0.2 </p><p>0 </p><p>323 48 </p><p>~=6.3 </p><p>t 1 </p><p>t </p><p>t t </p><p>1)+ </p><p>6.6 6.8 7 7.2 7.4 7.6 7.8 </p><p>1/a 1 </p><p>Figure 2. (1/2) + baryon mass spectrum. </p><p>MCRG study [4] </p><p>3. HADRON SPECTRUM </p><p>Typical examples of our data are shown in Fig. 1, 2 and 3. Fig. 1 shows the mass spectrum of pseudo scalar mesons Fig. 2 and 3 correspond to (1/2) + and (3/2) + baryons having two same kind of quarks i.e. t2 =- t3. All masses are in lattice units. We use the following mass formula to fit the data [5], </p><p>rn 2 = aT b (ml -4- m2 -4- rn3) A- c(rn~ -4- rn~ -4- rn3 2) + d(m,m~ + "~'~3 + m3ml), (1) </p></li><li><p>340 QCD-TARO Collaboration~Quenched Wilson hadron spectroscopy on a 323 x48 lattice at/3 = 63 </p><p>Table 3 (1/2) + and (3/2) + Baryon mass spectrum in GeV. </p><p>N Z E ~"c Lattice 0.94(12) 1.19(12) 1.40(11) 2.47(13) Experim. (0.938) (1.183) (1.318) (2.453) </p><p>Lattice 1.16(13) 1.37(11) 1.55(12) 2.54(14) 1.67(13) Experim. (1.232) (1.385) (1.534) (1.672) </p><p>MB </p><p>2.2 </p><p>2 </p><p>1.8 </p><p>1.6 </p><p>1.4 1.2 </p><p>I 0.8 </p><p>0.6 0.4 </p><p>0 .2 </p><p>0 </p><p>323 48 </p><p>#=6.3 </p><p>I </p><p>" I I t " </p><p>(1)+ </p><p>6.6 6.8 7 7.2 7.4 7.6 7.8 8 </p><p>i/~i </p><p>Figure 3. (3/2) + baryon mass spectrum. </p><p>for baryons, where m/'s are naive lattice quark masses. For mesons we just put m3 = 0. </p><p>The results of the fit to this formula are shown by the dashed lines in the figures. They cor- respond to a2 ( = t3 ) = 0.150, 0.148, 0.143, 0.140 and 0.130 from bottom to top. It can be seen that the data are well described by this for- mula. Any inputs of two hadron masses which contain strange or charm quark determine the whole spectrum of strange and charmed hadrons by the use of the fitted formula. We use and J / mesons as inputs and obtain i,~,~,~g, = 0.14969(28) and ach=,,~ = 0.13455(84). They cor- respond to m,:,a,~ge = 138(20) MeV and mchar~,, = 1.438(76) GeV in the MS scheme [6]. Present best fits of hadron masses are summarized in Ta- ble 1 and 3. The values of nucleon and delta are obtained taking the chiral limit in the fitting for- mula (1). Our results are consistent with experi- mental values within error bars. But it is difficult </p><p>to see precise structures of the spectrum such as pseudo scalar and vector mass differences directly from Table 1 because of error bars. To improve errors on such mass differences, we take the ra- tio of the two propagators and fit it with a sin- gle exponential function. The results are much smaller than experimental values as shown in Ta- ble 2, as has been reported by other groups [1,2]. Our values are smaller than the values in ref.[2] for hadrons containing heavier quarks. The dif- ference becomes smaller when heavy quark mass becomes larger. We can see the same tendency between (1/2) + and (3/2) + baryons. </p><p>ACKNOWLEDGEMENTS </p><p>We are indebted to M. Ikesaka, Y. Inada, K. In- oue, M. Ishii, T. Saito, T. Shimizu and H. Shi- raishi at the Fujitsu parallel computing research facilities for their valuable comments on parallel computing. </p><p>REFERENCES </p><p>1. M. Bochicchio et al., Nucl. Phys. B372 (1992) 403. </p><p>2. A. Abada et al., Nucl. 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