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

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PROCEEDINGS SUPPLEMENTS

Nuclear Physics B (Proc. Suppl.) 34 (1994) 338-340 North-Holland

Quenched Wilson hadron spectroscopy on a 323x48 lat t ice a t / 3 - 6.3

QCD_TARO Collaborat ion

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 ~

aComputa t iona l Science Research Laboratory, Fujitsu Limited, Mihama-ku, Chiba 261, Japan

bIPS,ETH-Zilrich, CH-8092 Ziirich, Switzerland

eDepar tment of Applied Physics, Fukui University, Fukui 910, Japan

dDepar tment of Physics, Hiroshima University, Higashi-Hiroshima 724, Japan

eFaculty of Education, Yamaga ta University, Yamaga ta 990, Japan

fFESt Heidelberg and Inst i tut ffir Theoretische Physik, Universit/it Heidelberg, D-6900 Heidelberg, Germany

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.

1. I N T R O D U C T I O N

The results of hadron spectroscopy on a 323 x 48 lattice a t /3 -- 6.3 are reported using the s tandard Wilson action in the quenched approximation. Our main result is the spectrum of hadrons composed of different flavors of quarks. Spectroscopy of these hadrons is theoretically impor tan t [1,2] as their scaling proper ty 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 experimental ly and results of lattice calcu- lations can be compared against them. The hopping parameters we choose correspond to mass re- gion between the strange quark and charm quark. The spect rum of hadrons composed of up, down, strange and charm quarks are presented. The calculation is performed on a massively parallel

computer AP1000 supported by Fujitsu.

2. G E N E R A L F E A T U R E S OF T H E SIM- U L A T I O N

We measured propagators of hadrons composed of several combinations of 5 different Wilson hopping 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 various combinations of hopping parameters . The da ta 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 algori thm after 2000 sweeps of thermalization. The ratio of overrelaxation to hea tba th is 9:1. Propagators

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Q C D - T A R O Collaboration~Quenched Wilson hadron spectroscopy on a 323 x48 lattice at ~3 = 6.3 339

Table 1 Strange and charmed meson spectrum in GeV.

K D Ds 7/c Lattice 0.566(50) 1•922(50) 2.051(52) 3•064(43) Experim. (0•494) (1•869) (1.969) (2.981)

K* ¢ D* D; J / ¢ Lattice 0.838(47) input 1•992(45) 2.117(48) input Experim. (0•891) (1•019) (2.010) (2.110) (3.097)

Table 2 Pseudo scalar and vector mass difference in MeV.

K * - K D * - D D * - D , Lattice 272(47) 70(45) 66(43) Experim. (398) (141) (142)

J / C - 7o 33(21) (116)

1.6

1.4

1.2

1 M p s

0.8

323 x 48 pseudo scalar ]

~=6.3 ....

0 6V ~ " , / /

0.4 K

0"~[6:6 6:8 7 7:2 7:4 7:6 7:8

1/hi

Figure 1. Pseudo scalar meson mass spectrum. The solid lines correspond to t¢2 = critical, strange and charm, from bot tom to top.

are measured for various channels. In this re- port, the results of pseudo scalar, vector mesons, (1/2) + and (3/2) + baryons are presented.

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 lattice 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

M B

2.2 2

1.8 1.6 1.4 1.2

1 0.8 0.6 0.4 0.2

0

323 × 48

~=6.3

t 1

t

t t

1)+

6.6 6.8 7 7.2 7.4 7.6 7.8

1/a 1

Figure 2. (1/2) + baryon mass spectrum.

MCRG study [4]•

3. H A D R O N S P E C T R U M

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. t¢2 =- t¢3. All masses are in lattice units. We use the following mass formula to fit the data [5],

r n 2 = a T b ( m l -4- m 2 -4- rn3) A- c(rn~ -4- rn~ -4- rn3 2) + d(m,m~ + "~'~3 + m3ml), (1)

340 QCD-TARO Collaboration~Quenched Wilson hadron spectroscopy on a 323 x48 lattice at/3 = 63

Table 3 (1/2) + and (3/2) + Baryon mass spectrum in GeV.

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)

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)

MB

2.2

2

1.8

1.6

1.4

1.2

I

0.8

0.6

0.4

0.2

0

323 × 48

#=6 .3

I

" I I

t "

(1)+

6.6 6.8 7 7.2 7.4 7.6 7.8 8

i/~i

Figure 3. (3/2) + baryon mass spectrum.

for baryons, where m/'s are naive lattice quark masses. For mesons we just put m3 = 0.

The results of the fit to this formula are shown by the dashed lines in the figures. They correspond to a2 ( = t¢3 ) = 0.150, 0.148, 0.143, 0.140 and 0.130 from bot tom to top. It can be seen that the data are well described by this formula. 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 correspond 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 formula (1). Our results are consistent with experimental values within error bars. But it is difficult

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 ratio of the two propagators and fit it with a single 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 difference becomes smaller when heavy quark mass becomes larger. We can see the same tendency between (1/2) + and (3/2) + baryons.

A C K N O W L E D G E M E N T S

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.

R E F E R E N C E S

1. M. Bochicchio et al., Nucl. Phys. B372 (1992) 403.

2. A. Abada et al., Nucl. Phys. B376 (1992) 172. 3. N. Isgur and M.B. Wise, Phys. Lett. B232

(1989) 113; B237 (1989) 527; T. Ito, T. Morii and M. Tanimoto, Z. Phys. C59 (1993) 57.

4. The QCD_TARO Collaboration, Phys. Rev. Lett. 71 (1993) 3063.

5. M. Guagnelli et al., Nucl. Phys. B378 (1992) 616.

6. H.W. Hamber and C.M. Wu, Phys. Lett. B133 (1983) 351.